Set up a Hess’s law cycle, and use the following information to calculate ΔH∘f for aqueous nitric acid, HNO3(aq). You will need to use fractional coefficients for some equations.
3NO2(g)+H2O(l)→2HNO3(aq)+NO(g) ΔH∘ = -137.3 kJ
2NO(g)+O2(g)→2NO2(g) ΔH∘ = -116.2 kJ
4NH3(g)+5O2(g)→4NO(g)+6H2O(l) ΔH∘ = -1165.2 kJ
NH3(g) ΔH∘f = -46.1 kJ
H2O(l) ΔH∘f = -285.8 kJ
To set up a Hess's law cycle, we need to manipulate the given reactions algebraically such that the target reaction, which is the formation of aqueous nitric acid (HNO3(aq)), can be obtained. The general procedure is as follows:
1. Manipulate the given reactions by multiplying or reversing them to match the target reaction:
a) Reverse the first equation and multiply it by 2 to obtain 2 HNO3(aq) + 2 NO(g) + H2O(l) -> 4 NO2(g).
b) Multiply the second equation by 2 to obtain 4 NO(g) + 2 O2(g) -> 4 NO2(g).
c) Multiply the third equation by 2 to obtain 8 NO(g) + 12 H2O(l) -> 8 HNO3(aq) + 10 H2O(l).
2. After manipulating the equations, you should add them up to cancel out the intermediate compounds and obtain the target reaction:
a) Add the first manipulated equation (multiplied by 2) to the second manipulated equation: 4 HNO3(aq) + 4 NO(g) + 2 O2(g) + 2 H2O(l) -> 8 NO2(g).
b) Add the third manipulated equation (multiplied by 5) to the result of step 2a: 40 HNO3(aq) + 40 NO(g) + 60 H2O(l) + 2 O2(g) -> 8 HNO3(aq) + 8 NO2(g).
c) Simplify the equation by canceling out the common compounds: 40 HNO3(aq) + 40 NO(g) + 60 H2O(l) + 2 O2(g) -> 8 NO2(g).
Now we have the equation that represents the target reaction: 40 HNO3(aq) + 40 NO(g) + 60 H2O(l) + 2 O2(g) -> 8 NO2(g).
3. Calculate the enthalpy change (ΔH) for the target reaction by summing the enthalpy changes of the manipulated equations:
a) Multiply the first equation by -137.3 to obtain -274.6 kJ.
b) Multiply the second equation by -116.2 to obtain -232.4 kJ.
c) Multiply the third equation by -1165.2 to obtain -9321.6 kJ.
d) Sum up the enthalpy changes: -274.6 kJ + -232.4 kJ + -9321.6 kJ = -9828.6 kJ.
Thus, the enthalpy change (ΔH) for the formation of aqueous nitric acid is -9828.6 kJ.