Energy, the first law and enthalpy

Chemistry · Thermochemistry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Thermochemistry studies the heat changes that go with chemical reactions. The system is the part under study, such as the reacting substances. Everything else is the surroundings. An exothermic reaction gives heat out to the surroundings (ΔH negative); an endothermic reaction takes heat in (ΔH positive).

A state function depends only on the initial and final states of a system, not on the path taken. Pressure, volume, temperature, internal energy (E) and enthalpy (H) are state functions. Heat (q) and work (w) are not.

The first law of thermodynamics says energy cannot be created or destroyed, only changed from one form to another. Enthalpy is the heat content of a system; its change is the heat change at constant pressure.

Rules to remember

First law: change in internal energy = heat + work (ΔE = q + w). q is positive when the system absorbs heat; w is positive when work is done on the system.
Pressure-volume work: w = −PΔV. At constant volume no such work is done, so ΔE = q_v.
Enthalpy: H = E + PV. At constant pressure, ΔH = ΔE + PΔV = q_p.
For reactions involving gases: ΔH = ΔE + ΔnRT, where Δn = moles of gaseous products − moles of gaseous reactants and R = 8.314 J K⁻¹ mol⁻¹. If Δn = 0, ΔH = ΔE.
Glass calorimeter (constant pressure, reactions in solution): q = m × s × ΔT, where s is the specific heat. This gives ΔH.
Bomb calorimeter (constant volume, combustion): q = c × ΔT, where c is the heat capacity of the calorimeter. This gives ΔE.
If the temperature rises, the reaction is exothermic: give the answer a negative sign. Divide by the moles reacted to get kJ mol⁻¹.

Common mistake

Students get the signs of q and w wrong. Heat given out by the system and work done by the system are both negative; when counting Δn, count gases only, not liquids or solids.

Worked example

0.050 mol of a fuel is burned in a bomb calorimeter of heat capacity 10.0 kJ K⁻¹. The temperature rises by 2.5 K. What is ΔE for the combustion per mole of fuel?

Heat released: q = c × ΔT = 10.0 × 2.5 = 25 kJ.
Per mole: 25 ÷ 0.050 = 500 kJ mol⁻¹.
The temperature rose, so the reaction is exothermic. The volume is constant, so this heat is ΔE.

Answer: ΔE = −500 kJ mol⁻¹.

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Chapter 7: Thermochemistry

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