Result
A) Reaction of Calcium with dilute hydrochloric acid:
The ionic reaction for the reaction is Ca(s)+2H+(aq) →Ca2+ (aq) +H2 (g)
Assuming that the solution in the plastic beaker has the same soecific heat as water, the heat of formation of CaCl2 (aq) was released in the reaction between the calcium and the acid.
Assume that the density of the solution is the same as that of water, i.e. 1 g cm-3
Mass of the hydrochloric acid = 100 cm3 × 1 g cm-3 = 100 g = 0.1 kg
Heat given out = 0.1× 4200 ×25
= 10.5 kJ
Number of moles of Ca = 1.00 ÷ 40.1 = 0.0249 mol
Heat evolved by one mole of calcium atoms = 10.5 ÷ 0.0249
= 421 kJ mol -1
The exact concentration of the hydrochloric acid is unimportant because the acid is in excess and the number of moles of acid do not need to find out accurately. Instead, the calcium metal is a limiting agent.
B) Reaction of calcium carbonate with hydrochloric acid:
The ionic equation for the reaction is CO32- (aq) +2H+(aq) →CO2 (g) + H2O (l)
Assuming that the solution in the plastic beaker has the same specific heat as water, the heat of formation of CO2 (g), H2O (l) and CaCl2 (aq) was evolved in the reaction between the hydrochloric acid and the amount if calcium carbonate used.
Assume that the density of the solution is the same as that of water, i.e. 1 g cm-3
Mass of the hydrochloric acid = 100 cm3 × 1 g cm-3 = 100 g = 0.1 kg
Heat given out = 0.1× 4200 ×1
= 420J
Number of moles of CaCO3 = 2.39 ÷ (40.1 +12 +16×3) = 0.0239 mol
Heat evolved by one mole of calcium atoms = 0.42 ÷ 0.0239
= 17.6 kJ mol -1
Discussion
In these two experiments, there are some errors. There was heat loss by the system to the thermometer and the vacuum flask, otherwise, the temperature will drop even lower. Besides, some powered calcium and its carbonate might be lost during experiment and the volume of hydrochloric acid might be measured inaccurately using the measuring cylinder. Also, the experiment was not carried out under standard conditions. The pressure and room temperature is not exactly equal to 1 atm (101 325 Nm-2) and 250C (298 K). Besides, the density of the solution is not absolutely the same as that of water, i.e. not 1 g cm-3
Therefore, the experimentally determined values were less than the theoretical values of the standard enthalpy change of the reactions as shown as follow.
For reaction A,
theoretical value of standard enthalpy change
= ΔHfO (CaCl2 (aq)) - 2×ΔHfO (HCl (aq))
= -795 – 2×(-92.3)
= - 610.4 kJ mol -1
and the experimentally determined value was- 421 kJ mol –1.
So, the experimentally determined value was less then the standard enthalpy change by
189.4 kJ mol –1
Percentage of error =
For reaction B,
theoretical value of standard enthalpy change
= ΔHfO (CO2 (g)) +ΔHfO (H2O (l)) +ΔHfO (CaCl2 (aq))
- ΔHfO (CaCO3 (aq)) - 2×ΔHfO (HCl (aq))
= -393.5 + (-285.8) + (-795) – (-1207) – 2×(-92.3)
= -82.7 kJ mol –1
and the experimentally determined value is –17.6 kJ mol -1
So, the experimentally determined value is less than the theoretical value by 65.1 kJ mol -1
Percentage of error =
ΔH
Ca(s)+C (graphite)+O2 (g) CaCO3(s).
ΔH1 + ΔHf (CO2 (g)) +2HCl (aq ) ΔH2 + 2HCl (aq)
ΔHf (H2O (l))
CaCl2 (aq)+ H2 (g) + CO2 (g) + O2 (g) CaCl2 (aq)+ H2O (l) + CO2 (g)
Besides of the experimentental results , we need to know ΔHfO (CO2 (g)) and ΔHfO (H2O (l)) ,in order to enable us to calculate the heat of formation of calcium carbonate.
ΔHfO (CO2 (g)) = -393.5 kJ mol -1
ΔHfO (H2O (l)) = -285.5 kJ mol -1
Heat of formation of calcium carbonate = ΔH1 + ΔHf (CO2 (g)) +ΔHf (H2O (l))- ΔH2
= -421+(-393.5)+(-285.5)- (-17.6)
= -1082.4 kJ mol -1
In order to achieve the answer, Hess’s law is used. Hess’s law states that the total enthalpy change of a reaction is independent of the route by which the reaction takes place. In other words, the standard enthalpy change of a reaction depends on the differences in standard enthalpy between the reactants and the products. It means that the enthalpy of the reaction system is conserved. As the absolute enthalpy of a substance isn’t possible to be determined and only the difference between reactants and products can be measured experimentally. This law helps us to define the standard enthalpy change of a reaction.
Conclusion
After carrying out the experiment, we found out that the heat of formation of calcium carbonate was -1082.4 kJ mol –1, by applying the Hess’s law, using the data in reaction of dilute hydrochloric acid with calcium and calcium carbonate, and the theoretical values of ΔHfO (CO2 (g)) and ΔHfO (H2O (l)).