Question

Suppose that stoichiometric amounts of nitrogen gas and hydrogen gas react in a calorimeter to produce 5.00 g of ammonia gas. The calorimeter temperature rises 0.42°C. The calorimeter and water have a combined heat capacity of 32.16 kJ/K. Calculate the heat of formation of ammonia, ΔH°f, in kJ/mol. The formation reaction for ammonia is: 0.5N2(g) + 1.5H2(g) → NH3(g).

Answer 1

What you're looking for is the amount of heat that would be released if you formed 1.00mol of NH3 inside the calorimeter. The 2nd Law of Thermodynamics lets us assume that all the heat generated by the reaction goes into the calorimeter, which makes the temperature rise.

You know the temperature change is 0.42C. You also know that the calorimeter will absorb 32.16kJ PER DEGREE that it changes temp. This lets you make a ratio of temp to energy absorbed.
\[0.42^0C * \frac{32.14kJ}{1^0C} = 13.499kJ\]

So 5.00g of ammonia formed releases 13.5kJ of energy. 5.00g of NH3 is less than 1 mol of NH3, so the ratio will be:
\[5.00g NH_3 * \frac{1 mol NH_3}{17g NH_3} = 0.294 mol NH_3\]

So 0.294 moles of NH3 released 13.5kJ of energy. If that is turned into a ratio of kJ/mol, then:
\[\frac{kJ}{mol} = \frac{13.5kJ}{0.294mol NH_3} = 45.9kJ/mol\]