DPST1031 Chap.10 Heat, Enthalpy and Hess's Law
Heat, Enthalpy and Hess's Law
Thermochemistry measures the energy that chemical change exchanges with its surroundings. This chapter defines system, surroundings and the open, closed and isolated cases, applies the first law as ΔU = q + w with the system's sign convention, and turns calorimeter temperature changes into heat using specific, molar and calorimeter heat capacities.
It distinguishes internal energy from enthalpy, links them through the moles of gas in a reaction, and lists the named standard enthalpy changes. Hess's law, formation enthalpies, bond enthalpies and the Born-Haber cycle then let you calculate enthalpy changes that cannot be measured directly, which the Mastery questions on this topic rely on.
What this chapter covers
- 01
System, surroundings and universe
- 02
The first law and the sign of q and w
- 03
Heat capacity and calorimetry
- 04
Constant-volume and constant-pressure heat
- 05
Enthalpy versus internal energy
- 06
Standard enthalpy changes and standard states
- 07
Hess's law and enthalpy cycles
- 08
Formation enthalpies, bond enthalpies and Born-Haber
Worked example · free
Enthalpy of forming carbon monoxide by Hess's law
- +1Keep C(s) + O₂(g) → CO₂(g), ΔH° = −393.5 kJ.
- +1Reverse CO(g) + ½O₂(g) → CO₂(g): CO₂(g) → CO(g) + ½O₂(g), ΔH° = +283.0 kJ.
- +1Add the two equations: CO₂ and ½O₂ cancel, leaving C(s) + ½O₂(g) → CO(g).
- +1ΔH° = −393.5 + 283.0 = −110.5 kJ.
Key terms
- State function
- A property, such as U or H, whose change depends only on the initial and final states.
- Internal energy
- The total kinetic and potential energy of the particles in a system.
- Heat capacity
- The heat needed to raise the temperature of an object or sample by one kelvin.
- Enthalpy
- The state function H whose change equals the heat exchanged at constant pressure.
- Exothermic reaction
- A reaction that releases heat to the surroundings, with a negative ΔH.
- Hess's law
- The rule that a reaction's enthalpy change is the same for every route between the same states.
- Lattice enthalpy
- The enthalpy change when one mole of an ionic solid forms from its gaseous ions.
Heat, Enthalpy and Hess's Law FAQ
What sign convention does the course use for work?
Signs are taken from the system's point of view. Heat absorbed by the system and work done on the system are positive; heat released and work done by the system are negative. With that convention the first law is written ΔU = q + w.
When are ΔU and ΔH different?
They differ by the expansion or compression work of gases, ΔH = ΔU + Δn(gas)RT. If a reaction does not change the number of moles of gas, the two are almost equal. A bomb calorimeter measures ΔU, while a constant-pressure calorimeter measures ΔH.
Why is the formation enthalpy of an element zero?
Formation enthalpy is defined as the change when a compound forms from its elements in their standard states. An element already in its standard state needs no change to form itself, so its value is zero by definition. A different form, such as diamond rather than graphite, is not zero.
Why use a Born-Haber cycle?
The lattice enthalpy of an ionic solid cannot be measured directly. The Born-Haber cycle links it, through Hess's law, to quantities that can be measured: sublimation, bond, ionisation and electron affinity energies and the enthalpy of formation, so the unknown can be calculated.
What is the difference between heat and temperature?
Temperature measures the average kinetic energy of the particles and is read with a thermometer. Heat is energy transferred because of a temperature difference. The same heat raises the temperature of a small sample more than a large one, which is why calorimetry needs a heat capacity to connect the two.
Exam move
Learn the sign convention by working three first-law problems in which heat and work have different signs. Next practise calorimetry in both forms, a bomb calorimeter with a heat capacity and a solution with mcΔT, and always state whether the result is ΔU or ΔH. Then work Hess's law problems in three styles: combining given equations, using formation enthalpy tables, and building a Born-Haber cycle.
For each, write the target equation first and sketch the cycle or level diagram before calculating. Finish by converting between ΔU and ΔH for reactions with and without a change in gas moles.
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