2. (a) Given the following equations and H0rxn at 250C
H3BO3(aq) �¨ HBO2(aq) + H2O(l) ∆H0rxn = -0.02kJ
H2B4 O7(s) + H2O(l) �¨ 4HBO2(aq) ∆H0rxn = -11.3kJ
H2B4O7(s) �¨ 2B2O3(s) + H2O(l) ∆H0rxn = +17.5kJ
(i) Calculate ∆H0rxn for the reaction 2H3BO3(aq) �¨ 2B2O3(s) + H2O(l)
(ii) How does your calculation above illustrate Hess�fs law of heat summation?
See your previous post. All of these are done the same way more or less.
To calculate ∆H0rxn for the reaction 2H3BO3(aq) �¨ 2B2O3(s) + H2O(l), we can use Hess's law of heat summation. Hess's law states that the enthalpy change (∆H) for a reaction is independent of the pathway taken and depends only on the initial and final states.
(i) To calculate ∆H0rxn, we can use the given equations and their enthalpy changes to manipulate and combine them to obtain the desired reaction.
1. Multiply the first equation by 2 to match the stoichiometric coefficients of H3BO3:
2H3BO3(aq) �¨ 2HBO2(aq) + 2H2O(l) (multiply by 2)
∆H1 = -0.02 kJ/mol
2. Reverse the second equation to match the desired reaction:
4HBO2(aq) �¨ H2B4O7(s) + H2O(l) (reverse)
∆H2 = 11.3 kJ/mol
3. Multiply the third equation by 2 to match the stoichiometric coefficients of B2O3:
H2B4O7(s) �¨ 2B2O3(s) + 2H2O(l) (multiply by 2)
∆H3 = -17.5 kJ/mol
Now, we can add these equations together and cancel out the common species to obtain the desired reaction:
2H3BO3(aq) + 4HBO2(aq) �¨ 2HBO2(aq) + 2B2O3(s) + 2H2O(l)
We can also add the enthalpy change values:
∆H0rxn = (# of times equation 1 is used * ∆H1) + (# of times equation 2 is used * ∆H2) + (# of times equation 3 is used * ∆H3)
Using the above equation and substituting the values we obtained:
∆H0rxn = (2 * -0.02 kJ) + (1 * 11.3 kJ) + (2 * -17.5 kJ)
∆H0rxn = -0.04 kJ + 11.3 kJ - 35 kJ
∆H0rxn = -23.74 kJ
(ii) The calculation above illustrates Hess's law of heat summation because instead of measuring the enthalpy change directly for the desired reaction, we were able to use the enthalpy changes of other known reactions to calculate it indirectly. This shows that the enthalpy change of any reaction is determined only by the initial and final states, and the pathway taken does not affect the result.