Enthalpy and Hess's Law: Quick Revision

A brief note on Enthalpy and Hess's Law. Read it before a test. Try each question at the end before you open its answer.

Enthalpy

• $H = U + pV$, a state function. At constant pressure, the heat taken in is $\Delta H$.
• $\Delta H = \Delta U + \Delta n_g R T$. Count gases only. $R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}$.
• Exothermic: $\Delta H < 0$. Endothermic: $\Delta H > 0$.
• $q = C\Delta T = m c \Delta T$. For an ideal gas, $C_p - C_v = R$.
• Bomb calorimeter: constant volume, gives $\Delta U$. Coffee-cup calorimeter: constant pressure, gives $\Delta H$.

Standard enthalpies

• Standard state: the pure substance at 1 bar, at the stated temperature.
• Reverse an equation: change the sign of $\Delta H$. Multiply it: multiply $\Delta H$.
• $\Delta_{sub}H = \Delta_{fus}H + \Delta_{vap}H$.
• $\Delta_f H^\ominus$: one mole of a compound from its elements. Elements in their standard states have zero.
• $\Delta_r H^\ominus = \sum a_i \Delta_f H^\ominus(\text{products}) - \sum b_i \Delta_f H^\ominus(\text{reactants})$.
• Combustion is always negative, atomisation always positive. $\Delta_{sol}H = \Delta_{lattice}H + \Delta_{hyd}H$.

Hess's law and bond enthalpies

• The enthalpy change is the same by any route. Add equations like algebra.
• For gases, $\Delta_r H \approx \sum(\text{bonds broken}) - \sum(\text{bonds formed})$.
• Mean bond enthalpies are averages, so the answer is an estimate.

A worked example

Find $\Delta_f H^\ominus$ of CO from two combustions: carbon gives $-393.5\ \text{kJ mol}^{-1}$, and CO gives $-283.0\ \text{kJ mol}^{-1}$.

1. Target. $\text{C} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO}$.
2. Steps. Burn the carbon, then reverse the burning of CO: $-393.5$ and $+283.0$.
3. Add. $\Delta_f H^\ominus = -393.5 + 283.0 = -110.5\ \text{kJ mol}^{-1}$.

Practice with new numbers

A program to try

The program writes each equation as a dictionary and adds them with their enthalpy changes.

Mistakes to avoid

• Liquids in $\Delta n_g$. Count gases only.
• Joules with kilojoules. $RT$ comes out in joules.
• Reactants minus products. Formation enthalpies go products minus reactants.
• Formed minus broken. Bond enthalpies go broken minus formed.
• A reversed equation with the old sign. Change the sign.

Check yourself

1. What is $\Delta_f H^\ominus$ of graphite?

2. Which calorimeter measures $\Delta H$ directly?

3. For $\text{CaCO}_3\text{(s)} \rightarrow \text{CaO(s)} + \text{CO}_2\text{(g)}$, is $\Delta H$ larger or smaller than $\Delta U$?

4. Why is breaking a bond always endothermic?

5. If $\text{X} \rightarrow \text{Y}$ has $\Delta H = +30\ \text{kJ}$ and $\text{Y} \rightarrow \text{Z}$ has $\Delta H = -50\ \text{kJ}$, what is $\Delta H$ for $\text{X} \rightarrow \text{Z}$?