Determination of the Enthalpy Change of a Reaction

Determine the enthalpy change of the thermal decomposition of calcium carbonate by an indirect method based on Hess' law.

Using the proposed method of obtaining results, these values were gathered:

Reaction 1: CaCO3(s) + 2HCl(aq) ?Cl2(aq) + CO2(g) + H2O(l)

Experiment Number

Mass of CaCO3 (g)

Temperature Change (?)

2.50

2

2

2.55

2 1/6

3

2.50

2 1/4

4

2.53

2 1/6

5

2.47

2

µ

2.51

2.12

Reaction 2: CaO(s) + 2HCl(aq) ?Cl2(aq) +H2O(l)

Experiment Number

Mass of CaO (g)

Temperature Change (oK)

.30

9 1/2

2

.36

0 1/3

3

.46

1

4

.35

0 1/6

5

.40

0 1/2

µ

.37

0.3

µ in both cases represents the mean of the data.

Using the equation for enthalpy change: ?H = mc?T

Where: m = Mass of liquid to which heat is transferred to (g)

c = Specific heat capacity of aqueous solution (taken as water = 4.18 J.g-1.K-1)

?T = Temperature change (oK)

We can thus determine the enthalpy changes of reaction 1 and reaction 2 using the mean (µ) of the data obtained.

Reaction 1: ?H = 50 x 4.18 x -2.12

?H = -443.08

This value is for 2.51g of calcium carbonate, not 100.1g which is its molecular weight.

Therefore: ?H = -443.08 x (100.1 / 2.51) = -17670.2 J.mol-1.

?H = -17.67 kJ.mol-1.

Reaction 2: ?H = 50 x 4.18 x -10.3

?H = -2152.7

This value is for 1.37g of calcium oxide, not 56.1g which is its relative molecular mass.

Therefore: ?H = -2152.7 x (56.1 / 1.37) = -88150.7 J.mol-1.

?H = -88.15 kJ.mol-1.

Hess' law states that: 1"The total enthalpy change for a chemical reaction is independent of the route by which the reaction takes place, provided initial and final conditions are the same."

This means that therefore the enthalpy change of a reaction can be measured by the calculation of 2 other reactions which relate directly to the reactants used in the first reaction and provided the same reaction conditions are used, the results will not be affected.

We have the problem set by the experiment: to determine the enthalpy change of the thermal decomposition of calcium carbonate. This is difficult because we cannot accurately measure how much thermal energy is taken from the surroundings and provided via thermal energy from a Bunsen flame into the reactants, due to its endothermic nature. Therefore using the enthalpy changes obtained in reaction 1 and reaction 2 we can set up a Hess cycle:

Thus using Hess' law we can calculate the enthalpy change of reaction 3.

Reaction 3: ?H = Reaction 1 - Reaction 2

?H = -17.67 - (-88.15) = +70.48 kJ.mol-1.

Comparing the value +70.48 kJ.mol-1 to the theoretical value of this enthalpy change (101kPa, 298K): +177.8 kJ.mol-1, there is a huge difference.

Percentage error is calculated by:

00 x Theoretical Value - Actual Value

Theoretical Value

Percentage error = (177.8 - 70.48) / 177.8 = 60.4%

Considering the scatter diagrams, they show the expected positive correlation. This is, the more reagents added, the more products there are. The amount of products formed is directly proportional to the temperature change since this is the amount of energy transferred as a result of the breaking and forming of intra-molecular bonds.

The scatter diagrams at first glance look as if they follow different gradients, however considering the scales upon which the results in either diagram is measured, it shows they both increase at the same rate represented by a positive linear relationship.

This can described in the form y = mx, m being the gradient of the rate of temperature increase in respect to mass of reagents present.

Standard deviation will give us an indication as to the accuracy of the results.

Variance (?2)

Standard Deviation (?)

Reaction 1

7.6 x 10-4

2.76 x 10-2

Reaction 2

2.88 x 10-3

5.37 x 10-2

However these very small standard deviations show us that all results are very closely distributed and inaccuracy in this experiment could have been slightly contributed from this source, but to no great degree.

Determine the enthalpy change of the thermal decomposition of calcium carbonate by an indirect method based on Hess' law.

Using the proposed method of obtaining results, these values were gathered:

Reaction 1: CaCO3(s) + 2HCl(aq) ?Cl2(aq) + CO2(g) + H2O(l)

Experiment Number

Mass of CaCO3 (g)

Temperature Change (?)

2.50

2

2

2.55

2 1/6

3

2.50

2 1/4

4

2.53

2 1/6

5

2.47

2

µ

2.51

2.12

Reaction 2: CaO(s) + 2HCl(aq) ?Cl2(aq) +H2O(l)

Experiment Number

Mass of CaO (g)

Temperature Change (oK)

.30

9 1/2

2

.36

0 1/3

3

.46

1

4

.35

0 1/6

5

.40

0 1/2

µ

.37

0.3

µ in both cases represents the mean of the data.

Using the equation for enthalpy change: ?H = mc?T

Where: m = Mass of liquid to which heat is transferred to (g)

c = Specific heat capacity of aqueous solution (taken as water = 4.18 J.g-1.K-1)

?T = Temperature change (oK)

We can thus determine the enthalpy changes of reaction 1 and reaction 2 using the mean (µ) of the data obtained.

Reaction 1: ?H = 50 x 4.18 x -2.12

?H = -443.08

This value is for 2.51g of calcium carbonate, not 100.1g which is its molecular weight.

Therefore: ?H = -443.08 x (100.1 / 2.51) = -17670.2 J.mol-1.

?H = -17.67 kJ.mol-1.

Reaction 2: ?H = 50 x 4.18 x -10.3

?H = -2152.7

This value is for 1.37g of calcium oxide, not 56.1g which is its relative molecular mass.

Therefore: ?H = -2152.7 x (56.1 / 1.37) = -88150.7 J.mol-1.

?H = -88.15 kJ.mol-1.

Hess' law states that: 1"The total enthalpy change for a chemical reaction is independent of the route by which the reaction takes place, provided initial and final conditions are the same."

This means that therefore the enthalpy change of a reaction can be measured by the calculation of 2 other reactions which relate directly to the reactants used in the first reaction and provided the same reaction conditions are used, the results will not be affected.

We have the problem set by the experiment: to determine the enthalpy change of the thermal decomposition of calcium carbonate. This is difficult because we cannot accurately measure how much thermal energy is taken from the surroundings and provided via thermal energy from a Bunsen flame into the reactants, due to its endothermic nature. Therefore using the enthalpy changes obtained in reaction 1 and reaction 2 we can set up a Hess cycle:

Thus using Hess' law we can calculate the enthalpy change of reaction 3.

Reaction 3: ?H = Reaction 1 - Reaction 2

?H = -17.67 - (-88.15) = +70.48 kJ.mol-1.

Comparing the value +70.48 kJ.mol-1 to the theoretical value of this enthalpy change (101kPa, 298K): +177.8 kJ.mol-1, there is a huge difference.

Percentage error is calculated by:

00 x Theoretical Value - Actual Value

Theoretical Value

Percentage error = (177.8 - 70.48) / 177.8 = 60.4%

Considering the scatter diagrams, they show the expected positive correlation. This is, the more reagents added, the more products there are. The amount of products formed is directly proportional to the temperature change since this is the amount of energy transferred as a result of the breaking and forming of intra-molecular bonds.

The scatter diagrams at first glance look as if they follow different gradients, however considering the scales upon which the results in either diagram is measured, it shows they both increase at the same rate represented by a positive linear relationship.

This can described in the form y = mx, m being the gradient of the rate of temperature increase in respect to mass of reagents present.

Standard deviation will give us an indication as to the accuracy of the results.

Variance (?2)

Standard Deviation (?)

Reaction 1

7.6 x 10-4

2.76 x 10-2

Reaction 2

2.88 x 10-3

5.37 x 10-2

However these very small standard deviations show us that all results are very closely distributed and inaccuracy in this experiment could have been slightly contributed from this source, but to no great degree.