Chemistry Form 4 Notes : THERMOCHEMISTRY

THERMOCHEMISTRY

1.Introduction to Energy changes

Energy is the capacity to do work. There are many/various forms of energy like heat, electric, mechanical, and/ or chemical energy.There are two types of energy:

 (i)Kinetic Energy(KE) the energy in motion.

 (ii)Potential Energy(PE); the stored/internal energy.

Energy like matter , is neither created nor destroyed but can be transformed /changed from one form to the other/ is interconvertible. This is the principle of conservation of energy. e.g. Electrical energy into heat through a filament in bulb.

Chemical and physical processes take place with absorption or evolution/production of energy mainly in form of heat

The study of energy changes that accompany physical/chemical reaction/changes is called Thermochemistry. Physical/chemical reaction/changes that involve energy changes are called thermochemical reactions. The SI unit of energy is the Joule(J).Kilo Joules(kJ)and megaJoules(MJ) are also used. The Joule(J) is defined as the:

(i) quantity of energy transferred when a force of one newton acts through a distance of one metre.

(ii) quantity of energy transferred when one coulomb of electric charge is passed through a potential difference of one volt.

All thermochemical reactions should be carried out at standard conditions of:

 (i) 298K /25^oC temperature

 (ii)101300Pa/101300N/m² /760mmHg/1 atmosphere pressure.

 2.Exothermic and endothermic processes/reactions

Some reactions / processes take place with evolution/production of energy. They are said to be exothermic while others take place with absorption of energy. They are said to be endothermic.

Practically exothermic reactions / processes cause a rise in temperature (by a rise in thermometer reading/mercury or alcohol level rise)

Practically endothermic reactions / processes cause a fall in temperature (by a fall in thermometer reading/mercury or alcohol level decrease)

To demonstrate/illustrate exothermic and endothermic processes/reactions

1. Dissolving Potassium nitrate(V)/ammonium chloride crystals

   Procedure:
   

Measure 20cm3 of water in a beaker. Determine and record its temperature T₁.Put about 1.0g of Potassium nitrate(V) crystals into the beaker. Stir the mixture carefully and note the highest temperature rise /fall T₂.Repeat the whole procedure by using ammonium chloride in place of Potassium nitrate (V) crystals.

Sample results

Note:

(i)Initial(T₁) temperature of dissolution of both potassium nitrate(V) crystals and ammonium chloride crystals is higher than the final temperature(T₂)

(ii) Change in temperature(T₂ –T₁) is not a mathematical “-4.0″ or
“-3.0″.

(iii)Dissolution of both potassium nitrate(V) and ammonium chloride crystals is
an endothermic process because
initial(T₁) temperature
is higher than the final temperature(T₂) thus causes a fall/drop in temperature.

1. Dissolving concentrated sulphuric(VI) acid/sodium hydroxide crystals

   Procedure:
   

Measure 20cm3 of water in a beaker. Determine and record its temperature T₁.Carefully put about 1.0g/four pellets of sodium hydroxide crystals into the beaker. Stir the mixture carefully and note the highest temperature rise /fall T₂.Repeat the whole procedure by using 2cm3 of concentrated sulphuric(VI) acid in place of sodium hydroxide crystals.

CAUTION:

(i)Sodium hydroxide crystals are caustic and cause painful blisters on contact with skin.

(ii) Concentrated sulphuric (VI) acid is corrosive and cause painful wounds on contact with skin.

Sample results

Note:

(i)Initial (T₁) temperature of dissolution of both concentrated sulphuric (VI) acid and sodium hydroxide pellets is lower than the final temperature (T₂).

(ii)Dissolution of both Sodium hydroxide pellets and concentrated sulphuric (VI) acid is
an exothermic process because
final (T₂) temperature
is higher than the initial temperature (T₁) thus causes a rise in temperature.

The above reactions show heat loss to and heat gain from the surrounding as illustrated by a rise and fall in temperature/thermometer readings.

Dissolving both potassium nitrate(V) and ammonium chloride crystals causes heat gain
from the surrounding that causes fall in thermometer reading.

Dissolving both Sodium hydroxide pellets and concentrated sulphuric (VI) acid causes heat loss to the surrounding that causes rise in thermometer reading.

At the same temperature and pressure ,heat absorbed and released is called enthalpy/ heat content denoted H.

Energy change is measured from the heat content/enthalpy of the final and initial products. It is denoted ∆H(delta H).i.e.

 Enthalpy/energy/ change in heat content ∆H = H_final – H_initial

For chemical reactions:

 ∆H = H_products – H_reactants

For exothermic reactions, the heat contents of the reactants is more than/higher than the heat contents of products, therefore the ∆H is negative (-∆H)

For endothermic reactions, the heat contents of the reactants is less than/lower than the heat contents of products, therefore the ∆H is negative (+∆H)

Graphically, in a sketch energy level diagram:

(i)For endothermic reactions the heat content of the reactants should be relatively/slightly lower than the heat content of the products

(ii)For exothermic reactions the heat content of the reactants should be relatively/slightly higher than the heat content of the products

Sketch energy level diagrams for endothermic dissolution

  Energy

  (kJ)   H₂  KNO₃(aq)

+∆H = H₂ – H₁

H₁  KNO₃(s)

Reaction path/coordinate/progress

  Energy

  (kJ)   H₂  NH₄Cl
(aq)

+∆H = H₂ – H₁

H₁  NH₄Cl (s)

  Reaction path/coordinate/progress

Sketch energy level diagrams for exothermic dissolution

  H₂   NaOH
(s)

Energy(kJ)

-∆H = H₂ – H₁

H₁  NaOH (aq)

Reaction path/coordinate/progress

H₂   H₂SO₄ (l)

Energy

    (kJ)

-∆H = H₂ – H₁

H₁  H₂SO₄ (aq)

Reaction path/coordinate/progress

3.Energy changes in physical processes

Melting/freezing/fusion/solidification and boiling/vaporization/evaporation are the two physical processes. Melting /freezing point of pure substances is fixed /constant. The boiling point of pure substance depend on external atmospheric pressure.

Melting/fusion is the physical change of a solid to liquid. Freezing is the physical change of a liquid to solid.

Melting/freezing/fusion/solidification are therefore two opposite but same reversible physical processes. i.e

A (s) ========A(l)

Boiling/vaporization/evaporation is the physical change of a liquid to gas/vapour. Condensation/liquidification is the physical change of gas/vapour to liquid. Boiling/vaporization/evaporation and condensation/liquidification are therefore two opposite but same reversible physical processes. i.e

B (l) ========B(g)

Practically

(i) Melting/liquidification/fusion involves heating a solid to weaken the strong bonds holding the solid particles together. Solids are made up of very strong bonds holding the particles very close to each other (Kinetic Theory of matter).On heating these particles gain energy/heat from the surrounding heat source to form a liquid with weaker bonds holding the particles close together but with some degree of freedom. Melting/freezing/fusion is an endothermic (+∆H)process that require/absorb energy from the surrounding.

(ii)Freezing/fusion/solidification involves cooling a a liquid to reform /rejoin the very strong bonds to hold the particles very close to each other as solid and thus lose their degree of freedom (Kinetic Theory of matter). Freezing /fusion / solidification is an exothermic (–∆H)process that require particles holding the liquid together to lose energy to the surrounding.

(iii)Boiling/vaporization/evaporation involves heating a liquid to completely break/free the bonds holding the liquid particles together. Gaseous particles have high degree of freedom (Kinetic Theory of matter). Boiling /vaporization / evaporation is an endothermic (+∆H) process that require/absorb energy from the surrounding.

(iv)Condensation/liquidification is reverse process of boiling /vaporization / evaporation.It involves gaseous particles losing energy to the surrounding to form a liquid.It is an exothermic(+∆H) process.

The quantity of energy required to change one mole of a solid to liquid or to form one mole of a solid from liquid at constant temperature is called molar enthalpy/latent heat of fusion. e.g.

H₂O(s) -> H₂O(l)   ∆H = +6.0kJ mole^-1 (endothermic process)

H₂O(l) -> H₂O(s)   ∆H = -6.0kJ mole^-1 (exothermic process)

The quantity of energy required to change one mole of a liquid to gas/vapour or to form one mole of a liquid from gas/vapour at constant temperature is called molar enthalpy/latent heat of vapourization. e.g.

H₂O(l) -> H₂O(g)   ∆H = +44.0kJ mole^-1 (endothermic process)

H₂O(g) -> H₂O(l)   ∆H = -44.0kJ mole^-1 (exothermic process)

The following experiments illustrate/demonstrate practical determination of melting and boiling

1. To determine the boiling point of water
   

Procedure:

Measure 20cm3 of tap water into a 50cm3 glass beaker. Determine and record its temperature.Heat the water on a strong Bunsen burner flame and record its temperature after every thirty seconds for four minutes.

Sample results

Questions

1.Plot a graph of temperature against time(y-axis)

Sketch graph of temperature against time

boiling point

96 ^oC

Temperature(⁰C)

25^oC  

 time(seconds)

2.From the graph show and determine the boiling point of water

Note:

 Water boils at 100^oC at sea level/one atmosphere pressure/101300Pa but boils at below 100^oC at higher altitudes. The sample results above are from Kiriari Girls High School-Embu County on the slopes of Mt Kenya in Kenya. Water here boils at 96^oC.

3.Calculate the molar heat of vaporization of water.(H= 1.0,O= 16.O)

Working:

Mass of water = density x volume => (20 x 1) /1000 = 0.02kg

Quantity of heat produced

= mass of water x specific heat capacity of water x temperature change

=>0.02kg x 4.2 x ( 96 – 25 ) = 5.964kJ  

Heat of vaporization of one mole H₂O = Quantity of heat

Molar mass of H₂O

=>5.964kJ = 0.3313 kJ mole ^-1

18

To determine the melting point of candle wax

Procedure

Weigh exactly 5.0 g of candle wax into a boiling tube. Heat it on a strongly Bunsen burner flame until it completely melts. Insert a thermometer and remove the boiling tube from the flame. Stir continuously. Determine and record the temperature after every 30seconds for four minutes.

Sample results

Questions

1.Plot a graph of temperature against time(y-axis)

Sketch graph of temperature against time

93 ^oC

Temperature(⁰C) melting point

69^oC

time(seconds)

2.From the graph show and determine the melting point of the candle wax

4.Energy changes in chemical processes

Thermochemical reactions measured at standard conditions of 298K(25^oC) and 101300Pa/101300Nm²/ 1 atmospheres/760mmHg/76cmHg produce standard enthalpies denoted ∆Hᶿ.

Thermochemical reactions are named from the type of reaction producing the energy change. Below are some thermochemical reactions:

1. Standard enthalpy/heat of reaction ∆Hᶿ_r
2. Standard enthalpy/heat of combustion ∆Hᶿ_c
3. Standard enthalpy/heat of displacement ∆Hᶿ_d
4. Standard enthalpy/heat of neutralization ∆Hᶿ_n
5. Standard enthalpy/heat of solution/dissolution ∆Hᶿ_s
6. Standard enthalpy/heat of formation ∆Hᶿ_f

(a)Standard enthalpy/heat of reaction ∆Hᶿ_r

The molar standard enthalpy/heat of reaction may be defined as the energy/heat change when one mole of products is formed at standard conditions

A chemical reaction involves the reactants forming products. For the reaction to take place the bonds holding the reactants must be broken so that new bonds of the products are formed. i.e.

A–B + C-D -> A-C + B-D

 Old Bonds broken A-B and C-D on reactants

 New Bonds formed A-C and B-D on products

The energy required to break one mole of a (covalent) bond is called bond dissociation energy. The SI unit of bond dissociation energy is kJmole^-1

The higher the bond dissociation energy the stronger the (covalent)bond

Bond dissociation energies of some (covalent)bonds

The molar enthalpy of reaction can be calculated from the bond dissociation energy by:

 (i)adding the total bond dissociation energy of the reactants(endothermic process/+∆H) and total bond dissociation energy of the products(exothermic process/-∆H).

 (ii)subtracting total bond dissociation energy of the reactants
from the total bond dissociation energy of the products(exothermic process/-∆H less/minus endothermic process/+∆H).

Practice examples/Calculating ∆H_r

1.Calculate ∆H_r from the following reaction:

1. H₂(g)   + Cl₂(g)   ->  2HCl(g)
   

   Working

   Old bonds broken (endothermic process/+∆H )

   = (H-H + Cl-Cl) => (+431 + (+ 239)) = + 670kJ
   

   New bonds broken (exothermic process/-∆H )

   = (2(H-Cl ) => (- 428 x 2)) = -856kJ

 ∆H_r =(
+ 670kJ + -856kJ) = 186 kJ = -93kJ mole^-1

2

The above reaction has negative -∆H enthalpy change and is therefore practically exothermic.

The thermochemical reaction is thus:

½ H₂(g)   + ½ Cl₂(g)   ->  HCl(g) ∆H_r = -93kJ

1. CH₄(g)   + Cl₂(g)   ->  CH₃Cl + HCl(g)
   

   Working

   Old bonds broken (endothermic process/+∆H )

   = (4(C-H) + Cl-Cl)

   => ((4 x +413) + (+ 239)) = + 1891kJ
   

   New bonds broken (exothermic process/-∆H )

   = (3(C-H + H-Cl + C-Cl)

   => (( 3 x – 413) + 428 + 346) = –2013 kJ

∆H_r =( + 1891kJ + -2013 kJ) = -122 kJ mole^-1

The above reaction has negative -∆H enthalpy change and is therefore practically exothermic.

The thermochemical reaction is thus:

CH₄(g)   + Cl₂(g)   ->  CH₃Cl(g) + HCl(g) ∆H = -122 kJ

1. CH₂CH₂(g)   + Cl₂(g)   ->  CH₃Cl CH₃Cl (g)
   

   Working

   Old bonds broken (endothermic process/+∆H )

   = (4(C-H) + Cl-Cl + C=C)

   => ((4 x +413) + (+ 239) +(612)) = + 2503kJ
   

   New bonds broken (exothermic process/-∆H )

   = (4(C-H + C-C + 2(C-Cl) )

   => (( 3 x – 413) + -436 +2 x 346 = –2367 kJ

∆H_r =( + 2503kJ + -2367 kJ) = +136 kJ mole^-1

The above reaction has negative +∆H enthalpy change and is therefore practically endothermic.

The thermochemical reaction is thus:

CH₂CH₂(g)   + Cl₂(g)   ->  CH₃Cl CH₃Cl (g) ∆H = +136 kJ

Note that:

 (i)a reaction is exothermic if the bond dissociation energy of reactants is more than bond dissociation energy of products.

 (ii)a reaction is endothermic if the bond dissociation energy of reactants is less than bond dissociation energy of products.

(b)Standard enthalpy/heat of combustion ∆Hᶿ_c

The molar standard enthalpy/heat of combustion(∆Hᶿ_c) is defined as the energy/heat change when one mole of a substance is burnt in oxygen/excess air at standard conditions.

Burning is the reaction of a substance with oxygen/air. It is an exothermic process producing a lot of energy in form of heat.

A substance that undergoes burning is called a fuel. A fuel is defined as the combustible substance which burns in air to give heat energy for domestic or industrial use. A fuel may be solid (e.g coal, wood, charcoal) liquid (e.g petrol, paraffin, ethanol, kerosene) or gas (e.g liquefied petroleum gas/LPG, Water gas-CO₂/H₂, biogas-methane, Natural gas-mixture of hydrocarbons)

To determine the molar standard enthalpy/heat of combustion(∆Hᶿ_c) of ethanol

Procedure

Put 20cm3 of distilled water into a 50cm3 beaker. Clamp the beaker. Determine the temperature of the water T₁.Weigh an empty burner(empty tin with wick).

Record its mass M₁.Put some ethanol into the burner. Weigh again the burner with the ethanol and record its mass M₂. Ignite the burner and place it below the clamped 50cm3 beaker. Heat the water in the beaker for about one minute. Put off the burner. Record the highest temperature rise of the water, T₂. Weigh the burner again and record its mass M₃

Sample results:

Sample calculations:

1.Calculate:

(a) ∆T the change in temperature

 ∆T = T₂ – T₁ => (35.0^oC – 25.0^oC) = 10.0^oC

 (b) the mass of ethanol used in burning

mass of ethanol used = M₂ – M₁ => 29.1g – 28.7g = 0.4g

(c) the number of moles of ethanol used in burning

 moles of ethanol = mass used   => 0.4 = 0.0087 /8.7 x 10^-3
moles  

molar mass of ethanol 46

2. Given that the specific heat capacity of water is 4.2 kJ^-1kg^-1K^-1,determine the heat produced during the burning.

Heat produced ∆H = mass of water(m) x specific heat capacity (c)x ∆T

=> 20 x 4.2 x 10 = 840 Joules = 0.84 kJ

1000

3.Calculate the molar heat of combustion of ethanol

Molar heat of combustion ∆H_c = Heat produced ∆H

Number of moles of fuel

=> 0.84 kJ = 96.5517 kJmole^-1

0.0087 /8.7 x 10^-3 moles

4.List two sources of error in the above experiment.

(i)Heat loss to the surrounding lowers the practical value of the molar heat of combustion of ethanol.

A draught shield tries to minimize the loss by protecting wind from wobbling the flame.

(ii) Heat gain by reaction vessels/beaker lowers ∆T and hence ∆H_c

5.Calculate the heating value of the fuel.

Heating value = molar heat of combustion => 96.5517 kJmole^-1 = 2.0989 kJg^-1

  Molar mass of fuel   46 g

Heating value is the enrgy produced when a unit mass/gram of a fuel is completely burnt

6.Explain other factors used to determine the choice of fuel for domestic and industrial use.

 (i) availability and affordability-some fuels are more available cheaply in rural than in urban areas at a lower cost.

 (ii)cost of storage and transmission-a fuel should be easy to transport and store safely. e.g LPG is very convenient to store and use. Charcoal and wood are bulky.

 (iii)environmental effects –Most fuels after burning produce carbon(IV) oxide gas as a byproduct. Carbon(IV) oxide gas is green house gas that causes global warming. Some other fuel produce acidic gases like sulphur(IV) oxide ,and nitrogen(IV) oxide. These gases cause acid rain. Internal combustion engines exhaust produce lead vapour from leaded petrol and diesel. Lead is carcinogenic.

(iv)ignition point-The temperature at which a fuel must be heated before it burns in air is the ignition point. Fuels like petrol have very low ignition point, making it highly flammable. Charcoal and wood have very high ignition point.

7.Explain the methods used to reduce pollution from common fuels.

(i)Planting trees-Plants absorb excess carbon(IV)oxide for photosynthesis and release oxygen gas to the atmosphere.

(ii)using catalytic converters in internal combustion engines that convert harmful/toxic/poisonous gases like carbon(II)oxide and nitrogen(IV)oxide to harmless non-poisonous carbon(IV)oxide, water and nitrogen gas by using platinum-rhodium catalyst along the engine exhaust pipes.

Further practice calculations

1.Calculate the heating value of methanol CH₃OH given that 0.87g of the fuel burn in air to raise the temperature of 500g of water from 20^oC to 27^oC.(C-12.0,H=1.0 O=16.0).

Moles of methanol used = Mass of methanol used => 0.87 g = 0.02718 moles

 Molar mass of methanol 32

Heat produced ∆H = mass of water(m) x specific heat capacity (c)x ∆T

=> 500 x 4.2 x 7 = 14700 Joules = 14.7 kJ

1000

Molar heat of combustion ∆H_c = Heat produced ∆H

Number of moles of fuel

=> 14.7 kJ = 540.8389 kJmole^-1

0.02718 moles

Heating value = molar heat of combustion => 540.8389 kJmole^-1 = 16.9012 kJg^-1

  Molar mass of fuel   32 g

2. 1.0 g of carbon burn in excess air to raise the temperature of 400g of water by 18^oC.Determine the molar heat of combustion and hence the heating value of carbon(C-12.0,).

Moles of carbon used = Mass of carbon used => 1.0 g = 0.0833 moles

 Molar mass of carbon 12

Heat produced ∆H = mass of water(m) x specific heat capacity (c)x ∆T

=> 400 x 4.2 x 18 = 30240 Joules = 30.24 kJ

1000

Molar heat of combustion ∆H_c = Heat produced ∆H

Number of moles of fuel

=> 30.24 kJ = 363.0252 kJmole^-1

0.0833 moles

Heating value = molar heat of combustion => 363.0252 kJmole^-1= 30.2521 kJg^-1

  Molar mass of fuel   12 g

(c)Standard enthalpy/heat of displacement ∆Hᶿ_d

The molar standard enthalpy/heat of displacement ∆Hᶿ_d is defined as the energy/heat change when one mole of a substance is displaced from its solution.

A displacement reaction takes place when a more reactive element/with less electrode potential Eᶿ /
negative Eᶿ /higher in the reactivity/electrochemical series remove/displace another with less reactive element/with higher electrode potential Eᶿ /
positive Eᶿ /lower in the reactivity/electrochemical series from its solution.e.g.

(i)Zn(s) + CuSO₄(aq) -> Cu(s) + ZnSO₄(aq)

Ionically: Zn(s) + Cu²⁺(aq) -> Cu(s) + Zn²⁺ (aq)

(ii)Fe(s) + CuSO₄(aq) -> Cu(s) + FeSO₄(aq)

Ionically: Fe(s) + Cu²⁺(aq) -> Cu(s) + Fe²⁺ (aq)

(iii)Pb(s) + CuSO₄(aq) -> Cu(s) + PbSO₄(s)

This reaction stops after some time as insoluble PbSO₄(s) coat/cover unreacted lead.

(iv)Cl₂(g) + 2NaBr(aq) -> Br₂(aq) + 2NaCl(aq)

Ionically: Cl₂(g)+ 2Br^– (aq) -> Br₂(aq) + 2Cl^– (aq)

Practically, a displacement reaction takes place when a known amount /volume of a solution is added excess of a more reactive metal.

To determine the molar standard enthalpy/heat of displacement(∆Hᶿ_d) of copper

Procedure

Place 20cm3 of 0.2M copper(II)sulphate(VI)solution into a 50cm3 plastic beaker/calorimeter. Determine and record the temperature of the solution T₁.Put all the Zinc powder provided into the plastic beaker. Stir the mixture using the thermometer. Determine and record the highest temperature change to the nearest 0.5^oC- T₂ . Repeat the experiment to complete table 1 below

Table 1

Questions

1.(a) Calculate:

 (i)average ∆T

Average∆T = change in temperature in experiment I and II

=>5.0 + 6.0 = 5.5^oC

 2

  (ii)the number of moles of solution used

Moles used = molarity x volume of solution = 0.2 x 20 = 0.004 moles

1000 1000

 (iii)the enthalpy change ∆H for the reaction

Heat produced ∆H = mass of solution(m) x specific heat capacity (c)x ∆T

=> 20 x 4.2 x 5.5 = 462 Joules = 0.462 kJ

1000

 (iv)State two assumptions made in the above calculations.

Density of solution = density of water = 1gcm^-3

Specific heat capacity of solution=Specific heat capacity of solution=4.2 kJ^-1kg^-1K

This is because the solution is assumed to be infinite dilute.

2. Calculate the enthalpy change for one mole of displacement of Cu²⁺ (aq) ions.

Molar heat of displacement ∆H_d = Heat produced ∆H

Number of moles of fuel

=> 0.462 kJ = 115.5 kJmole^-1

0.004

3.Write an ionic equation for the reaction taking place.

 Zn(s) + Cu²⁺(aq) -> Cu(s) + Zn²⁺(aq)

4.State the observation made during the reaction.

Blue colour of copper(II)sulphate(VI) fades/becomes less blue/colourless.

Brown solid deposits are formed at the bottom of reaction vessel/ beaker.

5.Illustrate the above reaction using an energy level diagram.

Zn(s) + Cu²⁺(aq)

Energy ∆H = -115.5 kJmole^-1

  (kJ)

Cu(s) + Zn²⁺(aq)

 Reaction progress/path/coordinates

6. Iron is less reactive than Zinc. Explain the effect of using iron instead of Zinc on the standard molar heat of displacement ∆H_d of copper(II)sulphate (VI) solution.

No effect.
Cu²⁺ (aq) are displaced from their solution.The element used to displace it does not matter.The reaction however faster if a more reactive metal is used.

7.(a)If the standard molar heat of displacement ∆H_d of copper(II)sulphate (VI) solution is 209kJmole^-1 calculate the temperature change if 50cm3 of 0.2M solution was displaced by excess magnesium.

Moles used = molarity x volume of solution = 0.2 x 50 = 0.01 moles

1000 1000

Heat produced ∆H = Molar heat of displacement ∆H_d x Number of moles

 =>209kJmole^-1x 0.01 moles   =  2.09 kJ

∆T (change in temperature) = Heat produced ∆H   Molar heat of displacement ∆H_d x Number of moles

=>2.09 kJ =  9.9524Kelvin

  0.01 moles

(b)Draw an energy level diagram to show the above energy changes

Mg(s) + Cu²⁺(aq)

Energy ∆H = -209 kJmole^-1

  (kJ)

Cu(s) + Mg²⁺(aq)

 Reaction progress/path/coordinates

8. The enthalpy of displacement ∆H_d of copper(II)sulphate (VI) solution is 12k6kJmole^-1.Calculate the molarity of the solution given that 40cm3 of this solution produces 2.204kJ of energy during a displacement reaction with excess iron filings.

Number of moles = Heat produced ∆H   Molar heat of displacement ∆H_d

=>2.204 kJ =  0.0206moles

  126 moles

Molarity of the solution  = moles x 1000   Volume of solution used

 = 0.0206moles x 1000 = 0.5167 M

40

9. If the molar heat of displacement of Zinc(II)nitrate(V)by magnesium powder is 25.05kJmole^-1 ,calculate the volume of solution which must be added 0.5 moles solution if there was a 3.0K rise in temperature.

Heat produced ∆H = Molar heat of displacement ∆H_d x Number of moles

=>25.08kJmole^-1x 0.5 moles   = 1.254 kJ x 1000 =1254J

Mass of solution (m) =   Heat produced ∆H

 specific heat capacity (c)x ∆T

=>   1254J  =  99.5238 g

4.2 x 3

Volume = mass x density = 99.5238 g x 1 = 99.5238cm3

Note: The solution assumes to be too dilute /infinite dilute such that the density and specific heat capacity is assumed to be that of water.

Graphical determination of the molar enthalpy of displacement of copper

Procedure:

Place 20cm3 of 0.2M copper(II)sulphate (VI) solution into a calorimeter/50cm3 of plastic beaker wrapped in cotton wool/tissue paper.

Record its temperature at time T= 0.

Stir the solution with the thermometer carefully and continue recording the temperature after every 30 seconds .

Place all the (1.5g) Zinc powder provided.

Stir the solution with the thermometer carefully and continue recording the temperature after every 30 seconds for five minutes.

Determine the highest temperature change to the nearest 0.5^oC.

Sample results

Sketch graph of temperature against time

36.5

 Extrapolation

  Temperature   point ∆T

^oC

130 Time(seconds)

Questions

1. Show and determine the change in temperature ∆T
   

From a well constructed graph ∆T= T2 –T1 at 150 second by extrapolation

∆T = 36.5 – 25.0 = 11.5^oC

2.Calculate the number of moles of copper(II) sulphate(VI)used given the molar heat of displacement of Cu²⁺ (aq)ions is 125kJmole^-1

Heat produced ∆H = mass of solution(m) x specific heat capacity (c)x ∆T

=> 20 x 4.2 x 11.5 = 966 Joules = 0.966 kJ

1000

Number of moles = Heat produced ∆H   Molar heat of displacement ∆H_d

=>.966 kJ =  0.007728moles

  125 moles 7.728 x 10^-3moles

1. What was the concentration of copper(II)sulphate(VI) in moles per litre.
   

 Molarity = moles x 1000 => 7.728 x 10^-3moles x 1000 = 0.3864M

Volume used 20

4.The actual concentration of copper(II)sulphate(VI) solution was 0.4M.Explain the differences between the two.

 Practical value is lower than theoretical. Heat/energy loss to the surrounding and that absorbed by the reaction vessel decreases ∆T hence lowering the practical number of moles and molarity against the theoretical value

5.a)  In an experiment to determine the molar heat of reaction when magnesium displaces copper ,0.15g of magnesium powder were added to 25.0cm³ of 2.0M copper (II) chloride solution. The temperature of copper (II) chloride solution was 25^oC.While that of the mixture was 43^oC.

i)Other than increase in temperature, state and explain the observations which were made during the reaction.(3mks)

ii)Calculate the heat change during the reaction (specific heat capacity of the solution = 4.2jg^-1k^-1and the density of the solution = 1g/cm³(2mks)

iii)Determine the molar heat of displacement of copper by magnesium.(Mg=24.0).

iv)Write the ionic equation for the reaction.(1mk)

v)Sketch an energy level diagram for the reaction.(2mks)

(c)Standard enthalpy/heat of neutralization ∆Hᶿ_n

The molar standard enthalpy/heat of neutralization ∆Hᶿ_n is defined as the energy/heat change when one mole of a H⁺ (H₃O⁺)ions react completely with one mole of OH^– ions to form one mole of H₂O/water.

Neutralization is thus a reaction of an acid /H⁺ (H₃O⁺)ions with a base/alkali/ OH^– ions to form salt and water only.

Strong acids/bases/alkalis are completely dissociated to many free ions(H⁺ /H₃O⁺ and OH^– ions).

Weak acids/bases/alkalis are partially dissociated to few free ions(H⁺ (H₃O⁺ and OH^– ions) and exist more as molecules.

Neutralization is an exothermic(-∆H) process.The enrgy produced during neutralization depend on the amount of
free ions (H⁺ H₃O⁺ and OH^–)ions existing in the acid/base/alkali reactant:

 (i)for weak acid-base/alkali neutralization,some of the energy is used to dissociate /ionize the molecule into free H⁺ H₃O⁺ and OH^– ions therefore the overall energy evolved is comparatively lower/lesser/smaller than strong acid / base/ alkali neutralizations.

 (ii) (i)for strong acid/base/alkali neutralization, no energy is used to dissociate /ionize since molecule is wholly/fully dissociated/ionized into free H⁺ H₃O⁺ and OH^– ions.The overall energy evolved is comparatively higher/more than weak acid-base/ alkali neutralizations. For strong acid-base/alkali neutralization, the enthalpy of neutralization is constant at about 57.3kJmole^-1 irrespective of the acid-base used. This is because ionically:

OH^–(aq)+ H⁺(aq) -> H₂O(l) for any wholly dissociated acid/base/alkali

Practically ∆Hᶿ_n can be determined as in the examples below:

To determine the molar enthalpy of neutralization ∆H_n of Hydrochloric acid

Procedure

Place 50cm3 of 2M hydrochloric acid into a calorimeter/200cm3 plastic beaker wrapped in cotton wool/tissue paper. Record its temperature T₁.Using a clean measuring cylinder, measure another 50cm3 of 2M sodium hydroxide. Rinse the bulb of the thermometer in distilled water. Determine the temperature of the sodium hydroxide T₂.Average T₂ andT₁ to get the initial temperature of the mixture T₃.

Carefully add all the alkali into the calorimeter/200cm3 plastic beaker wrapped in cotton wool/tissue paper containing the acid. Stir vigorously the mixture with the thermometer.

Determine the highest temperature change to the nearest 0.5^oC T₄ as the final temperature of the mixture. Repeat the experiment to complete table 1.

 Table I . Sample results

(a)Calculate T₆ the average temperature change T₆ =  13.25 +13.75 = 13.5 ^oC 2

(b)Why should the apparatus be very clean?

Impurities present in the apparatus reacts with acid /base lowering the overall temperature change and hence  ∆Hᶿ_n.  

(c)Calculate the:

(i)number of moles of the acid used

 number of moles = molarity x volume => 2 x 50 = 0.1moles   1000 1000

(ii)enthalpy change ∆H of neutralization.

∆H = (m)mass of solution(acid+base) x (c)specific heat capacity of solution x ∆T(T₆) => (50 +50) x 4.2 x 13.5 = 5670Joules = 5.67kJ

 (iii) the molar heat of neutralization the acid.

∆H_n = Enthalpy change ∆H => 5.67kJ  = 56.7kJ mole^-1

  Number of moles 0.1moles

(c)Write the ionic equation for the reaction that takes place

 OH^–(aq)+ H⁺(aq) -> H₂O(l)

(d)The theoretical enthalpy change is 57.4kJ. Explain the difference with the results above.

 The theoretical value is higher

 Heat/energy loss to the surrounding/environment lowers ∆T/T₆ and thus ∆H_n

 Heat/energy is absorbed by the reaction vessel/calorimeter/plastic cup lowers ∆T and hence ∆H_n

(e)Compare the ∆H_n of the experiment above with similar experiment repeated with neutralization of a solution of:

 (i) potassium hydroxide with nitric(V) acid

The results would be the same/similar.

Both are neutralization reactions of strong acids and bases/alkalis that are fully /wholly dissociated into many free H⁺ / H₃O⁺ and OH^– ions.

(ii) ammonia with ethanoic acid

The results would be lower/∆H_n would be less.

Both are neutralization reactions of weak acids and bases/alkalis that are partially /partly dissociated into few free H⁺ / H₃O⁺ and OH^– ions. Some energy is used to ionize the molecule.

(f)Draw an energy level diagram to illustrate the energy changes

H₂ H⁺
(aq)+OH^–
(aq)

Energy

(kJ)

∆H = -56.7kJ

  H₁   H₂O (l)

Reaction path/coordinate/progress

Theoretical examples

1.The molar enthalpy of neutralization was experimentary shown to be 51.5kJ per mole of 0.5M hydrochloric acid and 0.5M sodium hydroxide. If the volume of sodium hydroxide was 20cm3, what was the volume of hydrochloric acid used if the reaction produced a 5.0^oC rise in temperature?

Working:

Moles of
sodium hydroxide = molarity x volume => 0.5 M x 20cm3 = 0.01 moles

   1000  1000

Enthalpy change
∆H = ∆H_n   =>
51.5 = 0.515kJ

Moles
sodium hydroxide 0.01 moles

Mass of base + acid = Enthalpy change
∆H in Joules

Specific heat capacity x ∆T

=> 0.515kJ x 1000 = 24.5238g

  4.2 x 5

Mass/volume of HCl = Total volume – volume of NaOH

=>24.5238 – 20.0 = 4.5238 cm3

1. ∆H_n of potassium hydroxide was practically determined to be 56.7kJmole^-1.Calculate the molarity of 50.0 cm3 potassium hydroxide used to neutralize 25.0cm3 of dilute sulphuric(VI) acid raising the temperature of the solution from 10.0^oC to 16.5^oC.
   

∆H = (m)mass of solution(acid+base) x (c)specific heat capacity of solution x ∆T

  => (50 +25) x 4.2 x 6.5 = 2047.5Joules

Moles
potassium hydroxide =Enthalpy change
∆H

∆H_n

2047.5Joules = 0.0361 moles

  56700Joules

Molarity of KOH = moles x 1000 => 0.0361 moles x 1000 = 0.722M

Volume used 50cm3

3.Determine the specific heat capacity of a solution of a solution mixture of 50.0cm3 of 2M potassium hydroxide neutralizing 50.0cm3 of 2M nitric(V) acid if a 13.25^oC rise in temperature is recorded.(1mole of potassium hydroxide produce 55.4kJ of energy)

Moles of
potassium hydroxide = molarity KOH x volume

1000

=> 2 M x 50cm3 = 0.1 moles

 1000

Enthalpy change
∆H   =  ∆H_n x Moles
potassium hydroxide   => 55.4kJ x 0.1 moles = 5.54kJ x 1000=5540Joules

Specific heat capacity = Enthalpy change
∆H in Joules

Mass of base + acid x ∆T

=> 5540   = 4.1811J^-1g^-1K^-1

  (50+50) x 13.25

Graphically ∆H_n can be determined as in the example below:

Procedure

Place 8 test tubes in a test tube rack .Put 5cm3 of 2M sodium hydroxide solution into each test tube.

Measure 25cm3 of 1M hydrochloric acid into 100cm3 plastic beaker.

Record its initial temperature at volume of base =0. Put one portion of the base into the beaker containing the acid.

Stir carefully with the thermometer and record the highest temperature change to the nearest 0.5^oC.

Repeat the procedure above with other portions of the base to complete table 1 below

Table 1:Sample results.

(a)Complete the table to determine the change in temperature.

(b)Plot a graph of volume of sodium hydroxide against temperature change.

6.7=T₂

∆T (^oC)

From the graph show and determine :

(i)the highest temperature change ∆T

∆T =T₂-T₁ => highest temperature-T₂ (from extrapolating a correctly plotted graph) less lowest temperature at volume of base=0 :T₁

=>∆T = 6.7 – 0.0 = 6.7⁰C

(ii)the volume of sodium hydroxide used for complete neutralization

From a correctly plotted graph – 16.75cm3

(c)Calculate the number of moles of the alkali used

 Moles NaOH = molarity x volume =>2M x 16.75cm3 = 0.0335 moles

 1000  1000

(d)Calculate ∆H for the reaction

 ∆H = mass of solution(acid+base) x c x ∆T

  =>(25.0 + 16.75)
x 4.2 x 6.7 = 1174.845 J = 1.174845kJ

1000

(e)Calculate the molar enthalpy of neutralization of the alkali.

∆H_n =   ∆H_n   = 1.174845kJ = 35.0701kJ

Number of moles 0.0335

(d)Standard enthalpy/heat of solution ∆Hᶿ_s

The standard enthalpy of solution ∆Hᶿ_sis defined as the energy change when one mole of a substance is dissolve in excess distilled water to form an infinite dilute solution. An infinite dilute solution is one which is too dilute to be diluted further.

Dissolving a solid involves two processes:

 (i) breaking the crystal of the solid into free ions(cations and anion).This process is the opposite of the formation of the crystal itself. The energy required to form one mole of a crystal structure from its gaseous ions is called Lattice energy/heat/enthalpy of lattice (∆H_l).
Lattice energy /heat/enthalpy of lattice (∆H_l) is an endothermic process (+∆Hl).

The table below shows some ∆H_l in kJ for the process MX(s) -> M⁺ (g) + X^– (g)

 (ii)surrounding the free ions by polar water molecules. This process is called hydration. The energy produced when one mole of ions are completely hydrated is called hydration energy/ heat/enthalpy of hydration(∆H_h).Hydration energy /enthalpy of hydration(∆H_h) is an exothermic process(∆H_h).

The table below shows some ∆H_h
in kJ for some ions;

The sum of the lattice energy +∆H_l
(endothermic) and hydration energy -∆H_h (exothermic) gives the heat of solution-∆H_s

∆H_s = ∆H_l +∆H_h

Note

Since ∆H_l is an endothermic process and ∆H_h is an exothermic process then ∆H_s is:

 (i)exothermic if ∆H_l is less than ∆H_h and hence a solid dissolve easily in water.

 (ii)endothermic if ∆H_l is more than ∆H_h and hence a solid does not dissolve easily in water.

(a)Dissolving sodium chloride crystal/s:

(i) NaCl –—breaking the crystal into free ions–-> Na ⁺(g)+ Cl^–(g) ∆H_l =+771 kJ

(ii) Hydrating the ions;

Na ⁺(g) + aq -> Na(aq) ∆Hh = – 406 kJ

  Cl^–(g) + aq -> Cl^–(aq) ∆Hh = – 364 kJ

∆H_s =∆H_h +∆H_s ->
(- 406 kJ + – 364 kJ) + +771 kJ = + 1.0 kJmole^-1

NaCl does not dissolve easily in water because overall ∆H_s
is endothermic

Solubility of NaCl therefore increases with increase in temperature.

Increase in temperature increases the energy to break the crystal lattice of NaCl to free
Na ⁺(g)+ Cl^–(g)

(b)Dissolving magnesium chloride crystal/s//
MgCl₂ (s) ->MgCl₂ (aq)

(i) MgCl₂ –-breaking the crystal into free ions-->Mg ²⁺(g)+ 2Cl^–(g) ∆H_l =+2493 kJ

(ii) Hydrating the ions;

Mg ²⁺(g) + aq -> Mg ²⁺(g) (aq) ∆Hh = – 1920 kJ

  2Cl^–(g) + aq -> 2Cl^–(aq) ∆Hh = (- 364 x 2) kJ

∆H_s =∆H_h +∆H_s -> (- 1920 kJ + (- 364 x 2 kJ)) + +2493 kJ = –155.0 kJmole^-1

MgCl₂ (s) dissolve easily in water because overall ∆H_s
is exothermic .

Solubility of MgCl₂ (s) therefore decreases with increase in temperature.

(c)Dissolving Calcium floride crystal/s//
CaF₂ (s) -> CaF₂ (aq)

(i) CaF₂ –>Ca ²⁺(g)+ 2F^–(g) ∆H_l =+760 kJ

(ii) Hydrating the ions;

Ca ²⁺(g) + aq -> Ca ²⁺(g) (aq) ∆Hh = – 1650 kJ

  2F^–(g) + aq -> 2F^–(aq) ∆Hh = (- 506 x 2) kJ

∆H_s =∆H_h +∆H_s -> (- 1650 kJ + (- 506 x 2 kJ)) + +760 kJ = –1902.0 kJmole^-1

CaF₂ (s) dissolve easily in water because overall ∆H_s
is exothermic .

Solubility of CaF₂ (s) therefore decreases with increase in temperature.

(d)Dissolving magnesium bromide crystal/s//
MgBr₂ (s) ->MgBr₂ (aq)

(i) MgCl₂ –-breaking the crystal into free ions-->Mg ²⁺(g)+ 2Br^–(g) ∆H_l =+2226 kJ

(ii) Hydrating the ions;

Mg ²⁺(g) + aq -> Mg ²⁺(g) (aq) ∆Hh = – 1920 kJ

  2Br^–(g) + aq -> 2Br^–(aq) ∆Hh = (- 335x 2) kJ

∆H_s =∆H_h +∆H_s -> (- 1920 kJ + (- 335 x 2 kJ)) + +2226 kJ = –364.0 kJmole^-1

MgBr₂ (s) dissolve easily in water because overall ∆H_s
is exothermic .

Solubility of MgBr₂(s) therefore decreases with increase in temperature.

Practically the heat of solution can be determined from dissolving known amount /mass/volume of solute in known mass /volume of water/solvent.

From the temperature of solvent before and after dissolving the change in temperature(∆T) during dissolution is determined.

To determine the ∆H_s ammonium nitrate

Place 100cm3 of distilled water into a plastic beaker/calorimeter. Determine its temperature and record it at time =0 in table I below.

Put all the 5.0g of ammonium nitrate (potassium nitrate/ammonium chloride can also be used)provided into the plastic beaker/calorimeter, stir using a thermometer and record the highest temperature change to the nearest 0.5^oCafter every ½ minute to complete table I.

Continue stirring the mixture throughout the experiment.

Sample results: Table I

(a)Plot a graph of temperature against time(x-axis)

22.0=T₁

temperature(^oC) ∆T  

(b)From the graph show and determine the highest temperature change ∆T

∆T =T₂-T₁ => lowest temperature-T₂ (from extrapolating a correctly plotted graph) less highest temperature at volume of base=0 :T₁

=>∆T =18.7 – 22.0 = 3.3⁰C

(c)Calculate the number of moles of ammonium nitrate(V) used

 Moles NH₄NO₃ = mass used => 5.0 = 0.0625 moles

 Molar mass   80

(d)Calculate ∆H for the reaction

 ∆H = mass of water x c x ∆T

->100 x 4.2 x 3.3 = +1386 J = +1.386kJ

  1000

(e)Calculate the molar enthalpy of dissolution of ammonium nitrate(V).

∆H_s =   ∆H
  = +1.386kJ = + 22.176kJ mole^-1

Number of moles 0.0625 moles

(f)What would happen if the distilled water was heated before the experiment was performed.

The ammonium nitrate(V)would take less time to dissolves. Increase in temperature reduces lattice energy causing endothermic dissolution to be faster

(g)Illustrate the process above in an energy level diagram

NH₄⁺ (g) + NO₃^–(g)

 +∆H NH₄⁺ (aq)+NO₃^–(aq) Energy(kJ) +∆H   ∆H = -22.176kJ   NH₄NO₃^–(s)  Reaction path /progress/coordinate

(h) 100cm3 of distilled water at 25^oC was added carefully 3cm3 concentrated sulphuric(VI)acid of density 1.84gcm^-3.The temperature of the mixture rose from 25⁰C to 38^oC.Calculate the molar heat of solution of sulphuric(VI)acid (S=32.0,H=1.0,0=16.0)

Working

 Molar mass of H₂SO₄ = 98g

 Mass of H₂SO₄= Density x volume => 1.84gcm^-3 x 3cm3 = 5.52 g

 Mass of H₂O = Density x volume => 1.00gcm^-3 x 100cm3 = 100 g

 Moles of H₂SO₄= mass => 5.52 g = 0.0563 moles

 Molar mass of H₂SO₄   98g

Enthalpy change ∆H= (mass of acid + water) x specific heat capacity of water x ∆T   => (100 +5.52 g) x 4.2 x 13^oC = 5761.392 J = 5.761392 kJ

1000

∆H_s of H₂SO₄= ∆H => 5.761392 kJ = -102.33378kJmoles^-1

Moles of H₂SO₄   0.0563 moles

(e)Standard enthalpy/heat of formation ∆Hᶿ_f

The molar enthalpy of formation ∆Hᶿ_f is defined as the energy change when one mole of a compound is formed from its elements at 298K(25^oC) and 101325Pa(one atmosphere)pressure. ∆Hᶿ_f is practically difficult to determine in a school laboratory.

It is determined normally determined by applying Hess^‘ law of constant heat summation.

Hess^‘ law of constant heat summation states that “the total enthalpy/heat/energy change of a reaction is the same regardless of the route taken from reactants to products at the same temperature and pressure”.

Hess^‘ law of constant heat summation is as a result of a series of experiments done by the German Scientist Henri Hess(1802-1850).

He found that the total energy change from the reactants to products was the same irrespective of the intermediate products between. i.e.

A(s) —∆H₁–>C(s) = A(s) —∆H₂–>B(s)–∆H₃–>C(s)

Applying Hess^‘ law of constant heat summation then:

A(s) ∆H₂ B(s)

  ∆H₁ ∆H₃

C(s)

The above is called an energy cycle diagram. It can be used to calculate any of the missing energy changes since:

  (i) ∆H₁ =∆H₂ + ∆H₃

(ii) ∆H₂ =∆H₁ + -∆H₃

(iii) ∆H₃ = – ∆H₁ + ∆H₂

Examples of applying Hess^‘ law of constant heat summation

1.Calculate the molar enthalpy of formation of methane (CH₄) given that ∆Hᶿ_c of carbon-graphite is -393.5kJmole^-1,Hydrogen is -285.7 kJmole^-1 and that of methane is 890 kJmole^-1

Working

Carbon-graphite ,hydrogen and oxygen can react to first form methane.

Methane will then burn in the oxygen present to form carbon(IV)oxide and water. Carbon-graphite can burn in the oxygen to form carbon(IV)oxide.

Hydrogen can burn in the oxygen to form water.

C(s)+ 2H₂ (g)+2O₂ (g) —∆H₁–> CH₄(g) +2O₂(g) —∆H₂–> CO₂(g)+2H₂O(l)

C(s)+ 2H₂ (g)+2O₂ (g) —∆H₃–> CO₂(g)+2H₂O(l)

Energy cycle diagram

 C(s) + 2H₂ (g) + 2O₂(g)   ∆H₁=∆Hᶿ_c =-890.4kJ   CH₄(g)+2O₂(g)

 ∆H₃=∆Hᶿ_c =-393.5kJ ∆H₃=∆Hᶿ_c =-285.7kJ x 2 ∆H₂= ∆Hᶿ_f= x

  CO₂(g) + 2H₂O(l)

Substituting:

∆H₃ = ∆H₁ + ∆H₂

-393.5 + (-285.7 x 2) = -890.4kJ + x

x = -74.5 kJ

 Heat of formation ∆Hᶿ_f CH₄ = -74.5 kJmole^-1

2. Calculate the molar enthalpy of formation of ethyne (C₂H₂) given : ∆Hᶿ_c of carbon-graphite = -394kJmole^-1,Hydrogen = -286 kJmole^-1 , (C₂H₂) = -1300 kJmole^-1

Working

Carbon-graphite ,hydrogen and oxygen can react to first form ethyne.

Ethyne will then burn in the oxygen present to form carbon(IV)oxide and water. Carbon-graphite can burn in the oxygen to form carbon(IV)oxide.

Hydrogen can burn in the oxygen to form water.

2C(s)+ H₂ (g)+2 ½ O₂ (g) —∆H₁–> C₂
H₂ (g) +2 ½ O₂(g) —∆H₂–> CO₂(g)+H₂O(l)

2C(s)+ H₂ (g)+ 2 ½ O₂ (g) —∆H₃–> 2CO₂(g)+H₂O(l)

Energy cycle diagram

2C(s) + H₂ (g) +2½O₂(g)   ∆H₁=∆Hᶿ_f =x   C₂
H₂+2½O₂(g)

∆H₃=∆Hᶿ_c =-394kJx 2 ∆H₃=∆Hᶿ_c =-286kJ ∆H₂= ∆Hᶿ_c= -1300kJ

  2CO₂(g) + H₂O(l)

Substituting:

∆H₃ = ∆H₁ + ∆H₂

( -394 x 2) + -286 = -1300kJ + x

x = +244 kJ

 Heat of formation ∆Hᶿ_f CH₄ = +244 kJmole^-1

3. Calculate the molar enthalpy of formation of carbon(II)oxide (CO) given : ∆Hᶿ_c of carbon-graphite = -393.5kJmole^-1, ∆Hᶿ_c of carbon(II)oxide (CO)= -283 kJmole^-1

Working

Carbon-graphite reacts with oxygen first to form
carbon (II)oxide (CO).

Carbon(II)oxide (CO) then burn in the excess oxygen to form carbon(IV)oxide. Carbon-graphite can burn in excess oxygen to form carbon (IV) oxide.

C(s)+ ½O₂ (g) —∆H₁–> CO (g) + ½ O₂(g) —∆H₂–> CO₂(g)

C(s)+ O₂ (g) —∆H₃–> CO₂(g)

Energy cycle diagram

C(s) + ½O₂(g)   ∆H₁=∆Hᶿ_f =x   CO+½O₂(g)

∆H₃=∆Hᶿ_c =-393.5kJ ∆H₂= ∆Hᶿ_c= -283kJ

  CO₂(g)

Substituting:

∆H₃ = ∆H₁ + ∆H₂

-393.5kJ = -283kJ + x

x = -110 kJ

 Heat of formation ∆Hᶿ_f CO = -110 kJmole^-1

4.Study the information below:

 H₂(g) + ½ O₂(g)
-> H₂O(l) ∆H₁=-286 kJmole^-1  

C(s) + O₂(g)
-> CO₂(g) ∆H₂=-393 kJmole^-1  

 2C(s) + H₂(g) + ½ O₂(g)
->C₂H₅OH(l) ∆H₃=-277 kJmole^-1  

Use the information to calculate the molar enthalpy of combustion ∆H₄ of ethanol

Energy cycle diagram

2C(s) + 3H₂ (g) +3½O₂(g)   ∆H₃=∆Hᶿ_f =-227kJ   C₂
H₅OH +3O₂(g)

∆H₂=∆Hᶿ_c =-394kJx 2 ∆H₁=∆Hᶿ_c =-286kJx 3 ∆H₄= ∆Hᶿ_c= x

  2CO₂(g) + 3H₂O(l)

Substituting:

∆H₁ + ∆H₂ = ∆H₃ +
∆H₄

( -394 x 2) + -286 x 3 = -277 + x

∆H₄ = -1369 kJ

 Heat of combustion ∆Hᶿ_c C₂H₅OH = -1369 kJmole^-1

5.Given the following information below:

 CuSO₄(s) + (aq)
-> CuSO₄(aq) ∆H=-66.1 kJmole^-1  

CuSO₄(s) + (aq)
+
5H₂O(l)-> CuSO₄ .5H₂O (aq) ∆H=-77.4 kJmole^-1  

Calculate ∆H
for the reaction;

CuSO₄(aq) +
5H₂O-> CuSO₄ .5H₂O (aq) ∆H=-77.4 kJmole^-1

Working

CuSO₄(s) + (aq)
+
5H₂O(l)-> CuSO₄(aq)+ 5H₂O(l)-> CuSO₄ .5H₂O (aq)

CuSO₄(s) + (aq)
+
5H₂O(l)-> CuSO₄ .5H₂O (aq)

Energy cycle diagram

CuSO₄(s) + (aq)
+
5H₂O(l) ∆H₁=+66.1kJ   CuSO₄(aq)+ 5H₂O(l)

∆H₃= =-77.4kJ ∆H₂= x

  CuSO₄ .5H₂O (aq)

Substituting:

∆H₃ = ∆H₂ +
∆H₁

( -77.4kJ = x + +66.1kJ

∆H₄ = -10.9 kJ

Heat of dissolution of CuSO₄ = -10.9kJmole^-1

Practically, Hess’ law can be applied practically as in the following examples

a)Practical example 1

Determination of the enthalpy of formation of CuSO₄.5H₂O

Experiment I

Weigh accurately 12.5 g of copper(II)sulphate(VI)pentahydrate. Measure 100cm3 of distilled water into a beaker. Determine its temperature T₁ .Put all the crystals of the copper(II)sulphate(VI)pentahydrate carefully into the beaker. Stir using a thermometer and determine the highest temperature change T₂ Repeat the procedure again to complete table 1.

Table 1:Sample results

Experiment II

Weigh accurately 8.0g of anhydrous copper(II)sulphate(VI). Measure 100cm3 of distilled water into a beaker. Determine its temperature T₁ .Put all the crystals of the copper(II)sulphate(VI)pentahydrate carefully into the beaker. Stir using a thermometer and determine the highest temperature change T₂ Repeat the procedure again to complete table II.

Table II :Sample results

Questions

(a)Calculate the average ∆T in

 (i)Table I

∆T= T₂ -T₁ => 3.0 +4.0 = 3.5 ^oC

2

 (ii)Table II

∆T= T₂ -T₁ => 1.0 +2.0 = 1.5 ^oC

2

(b)Calculate the number of moles of solid used in:

 (i)Experiment I

  Moles of CuSO₄.5H₂O =   Mass  => 12.5 = 0.05 moles

 Molar mass 250

 (ii)Experiment II

  Moles of CuSO₄ =   Mass =>   8.0 = 0.05 moles

Molar mass 160

(c)Calculate the enthalpy change for the reaction in:

 (i)Experiment I

Enthalpy change of CuSO₄.5H₂O= mass of Water(m) x c x ∆T

=>100cm3 x 4.2 x 3.5 ^oC = -1.47kJ

 1000

(ii)Experiment II

Enthalpy change of CuSO₄ = mass of water(m) x c x ∆T

=>100cm3 x 4.2 x 1.5 ^oC = -0.63kJ

 1000

(c)Calculate the molar enthalpy of solution CuSO₄ .5H₂O (s) form the results in (i)experiment I.

∆Hs = CuSO₄.5H₂O= ∆H   => -1.47kJ = 29.4kJ

  Number of Moles  0.05 moles

(ii)experiment II.

∆Hs = CuSO₄= ∆H   => -0.63kJ = 12.6kJ

  Number of Moles 0.05 moles

(d) Using an energy level diagram, calculate the molar enthalpy change for the reaction:

CuSO₄ .5H₂O (s) -> CuSO₄(s)
+
5H₂O(l)

Energy cycle diagram

CuSO₄(s) + (aq)
+
5H₂O(l) ∆H₁=x CuSO₄. 5H₂O (s)+ (aq)

∆H₃= =-29.4kJ ∆H₂= -12.6kJ

  CuSO₄ .5H₂O (aq)

∆H₃ = ∆H₁ +∆H₂

=>-29.4kJ = -12.6kJ + x

=>-29.4kJ – (+12.6kJ) = x

x = 16.8kJ

b)Practical example II

Determination of enthalpy of solution of ammonium chloride

Theoretical information.

Ammonium chloride dissolves in water to form ammonium chloride solution. Aqueous ammonia can react with excess dilute hydrochloric acid to form ammonium chloride solution. The heat change taking place can be calculated from the heat of reactions:

(i) NH₃(aq) + HCl(aq) -> NH₄Cl(s)

(ii) NH₄Cl(s) + (aq) -> NH₄Cl(aq)

(iii) NH₃(aq) + HCl(aq) -> NH₄Cl(aq)

Experiment procedure I

Measure 50cm3 of water into a 100cm3 beaker. Record its temperature T₁ as initial temperature to the nearest 0.5^oC in table I. Add exactly 5.0g of ammonium chloride crystals weighed carefully into the water. Stir and record the highest temperature change T₂ as the final temperature change. Repeat the above procedure to complete table I.

Sample results TableI

Experiment procedure II

Measure 25cm3 of 2M aqueous ammonia into a 100cm3 beaker. Record its temperature T₁ as initial temperature to the nearest 0.5^oC in table II. Measure 25cm3 of 2M hydrochloric acid solution. Add the acid into the beaker containing aqueous ammonia. Stir and record the highest temperature change T₂ as the final temperature change. Repeat the above procedure to complete table II.

Sample results:Table II

Sample Calculations:

(a)Calculate the average ∆T in

 (i)Table I

∆T= T₂ -T₁ => -3.0 +-2.0 = 2.5 ^oC

2

 (ii)Table II

∆T= T₂ -T₁ => 7.0 +7.0 = 7.0 ^oC

2

(b)Calculate the enthalpy change for the reaction in:

 (i)Experiment I

 Enthalpy change ∆H = mass of Water(m) x c x ∆T

=>50cm3 x 4.2 x 2.5 ^oC = +0.525kJ

1000

(ii)Experiment II

Enthalpy change of CuSO₄ = mass of water(m) x c x ∆T

=>25+25cm3 x 4.2 x 7 ^oC = +1.47kJ

  1000

(c)Write the equation for the reaction taking place in:

 (i)Experiment I

 NH₄Cl(s) + (aq) -> NH₄Cl(aq)

(ii)Experiment I

 NH₃(aq) + HCl(aq) -> NH₄Cl(aq)

(d)Calculate the enthalpy change ∆H for the reaction:

  NH₃(g) + HCl(g) -> NH₄Cl(s) given that:

(i) NH₃(g) + (aq) -> NH₃(aq) ∆H= -40.3kJ

(ii) (aq) + HCl(g) -> HCl(aq) ∆H= -16.45kJ

(e)Applying Hess’ Law of constant heat summation:

Energy level diagram

 N₂(g)  + 1½ H₂(g)  + ½ Cl₂  ∆H_f
 NH₄Cl(s) + aq

  +0.525kJ=∆H₄

(aq) (aq)

 – 40.3kJ=∆H₁
-16.43kJ=∆H₂

NH₃ (aq) + HCl(aq)  -1.47kJ=∆H₃   NH₄Cl(s)

∆H₁   +  ∆H₂   +   ∆H₃   =   ∆H₄   +  ∆H_f

  – 40.3kJ + -16.43kJ + -1.47kJ = +0.525kJ + ∆H_f

=>∆H_f = -58.865kJ.

Practice theoretical examples:

1. Using an energy level diagram calculate the ∆H_s of ammonium chloride crystals given that.

∆H_f of NH₃ (aq) = -80.54kJ mole^-1

∆H_f of HCl (aq) = -164.46kJ mole^-1

∆H_f of NH₄Cl (aq) = -261.7483kJ mole^-1

∆H_s of NH₄Cl (aq) = -16.8517kJ mole^-1

N₂(g) + 1½ H₂(g) + ½ Cl₂ ∆H_f=-261.7483kJ  NH₄Cl(s) + aq

 x=∆H_s

(aq) (aq)

– 80.54kJ=∆H₁
-164.46kJ=∆H₂

NH₃ (aq) + HCl(aq) 16.8517kJ=∆H₃   NH₄Cl(s)

∆H₁   +  ∆H₂   +   ∆H₃   =   ∆H₄   +  ∆H_f

  – 80.54kJ + -164.46kJ + -16.8517kJ = -261.7483kJ + ∆H_f

=>∆H_f = -33.6kJmole^-1.

Study the energy cycle diagram below and use it to:

(a)Identify the energy changes ∆H₁ ∆H₂ ∆H₃ ∆H₄ ∆H₅ ∆H₆

∆H₁ – enthalpy/heat of formation of sodium chloride (∆H_f)

∆H₂ -enthalpy/heat of atomization of sodium (∆H_at)

∆H₃ -enthalpy/heat of ionization/ionization energy of sodium (∆H _i)

∆H₄ -enthalpy/heat of atomization of chlorine (∆H_at)

∆H₅ -enthalpy/heat of electron affinity of chlorine (∆H_e)

∆H₆ enthalpy/heat of lattice/Lattice energy of sodium chloride(∆H _l)

(b) Calculate ∆H₁ given that ∆H₂ =+108kJ , ∆H₃=+500kJ, ∆H₄ =+121kJ ,∆H₅ =-364kJ and ∆H₆ =-766kJ

Working:

∆H₁ =∆H₂ +∆H₃ +∆H₄ +∆H₅ +∆H₆

Substituting:

∆H₁= +108kJ + +500kJ + +121kJ +-364kJ + -766kJ

∆H₁= -401kJmole^-1

(c) Given the that:

(i) Ionization energy of sodium = + 500kJmole^-1

(ii)∆H_at of sodium = + 110kJmole^-1

(iii) Electron affinity of chlorine = – 363kJmole^-1

(iv)∆H_at of chlorine = + 120kJmole^-1

(v) ∆H_f of sodium chloride = -411kJ , calculate the lattice energy of sodium chloride using an energy cycle diagram.

Working:

Applying Hess law then:

∆H_f =∆H_a +∆H_i +∆H_a +∆H_e +∆H_l

Substituting:

-411= +108kJ + +500kJ + +121kJ +-364kJ + x

-411 + -108kJ + -500kJ + -121kJ + +364kJ = x

x= -776kJmole^-1