Thermochemistry: Enthalpy, Calorimetry, and Stoichiometry in Chemical Reactions

Thermochemistry: The Heat Evolved in Chemical Reactions

Enthalpy and Energy Changes at Constant Pressure

Thermochemistry studies the energy changes, especially heat, that accompany chemical reactions. When reactions occur at constant pressure, the heat exchanged is called enthalpy (ΔH).

• Enthalpy (ΔH): The total energy change (heat and work) during a reaction at constant pressure.

• At constant pressure, the enthalpy change equals the heat exchanged: $\Delta H = q_p$

• ΔE: Measures all energy (heat and work) exchanged with surroundings.

• For reactions with no PV work (e.g., solution reactions), ΔH and ΔE are nearly identical.

Example: Burning fuel in open air (constant pressure) releases heat; ΔH quantifies this heat.

Comparing ΔH and ΔE

ΔH and ΔE differ when reactions involve gases and volume changes. The difference is given by:

• $\Delta H = \Delta E + P\Delta V$

• For reactions where gases are produced or consumed, $P\Delta V$ can be significant.

Reaction	ΔH (kJ)	ΔE (kJ)
C3H8 + 5 O2 → 3 CO2 + 4 H2O	-2044	-2010
2 H2 + O2 → 2 H2O	-571.6	-569.4
CH4 + 2 O2 → CO2 + 2 H2O	-890.4	-882.0
2 CO + O2 → 2 CO2	-566.0	-553.3

Additional info: The table compares ΔH and ΔE for several combustion reactions, showing that ΔH is typically slightly more negative due to the work done by expanding gases.

Endothermic vs. Exothermic Reactions

Identifying Reaction Types by ΔH

Reactions can absorb or release heat:

• Endothermic: Absorbs heat; ΔH is positive.

• Exothermic: Releases heat; ΔH is negative.

Examples:

• Evaporation of sweat (endothermic, ΔH > 0)

• Freezing water (exothermic, ΔH < 0)

• Burning wood (exothermic, ΔH < 0)

Stoichiometry Involving ΔH: Thermochemical Equations

Relating Heat to Amounts of Reactants and Products

Thermochemical equations show the enthalpy change for a reaction and relate it to the stoichiometric amounts of reactants and products.

• The magnitude of ΔH reflects the amounts of substances reacting.

• Example equation: $\mathrm{C_3H_8} + 5\mathrm{O_2} \rightarrow 3\mathrm{CO_2} + 4\mathrm{H_2O} \quad \Delta H = -2044\ \mathrm{kJ}$

• This means 1 mol of C3H8 releases 2044 kJ of heat when combusted.

Sample Calculation: Stoichiometry with ΔH

To calculate the heat evolved or absorbed in a reaction:

• Convert mass of reactant to moles.

• Use the thermochemical equation to find heat per mole.

• Multiply moles by ΔH to get total heat.

Example: Burning 13.2 kg of propane (C3H8):

• Calculate moles: $\frac{13,200\ \mathrm{g}}{44.09\ \mathrm{g/mol}} = 299\ \mathrm{mol}$

• Total heat: $299\ \mathrm{mol} \times -2044\ \mathrm{kJ/mol} = -6.11 \times 10^5\ \mathrm{kJ}$

Calorimetry: Measuring ΔHrxn Experimentally

Coffee-Cup Calorimeter (Constant Pressure)

A coffee-cup calorimeter is used to measure the heat evolved or absorbed in reactions at constant pressure.

• Reactants are mixed in a solution inside an insulated cup.

• The temperature change (ΔT) is measured.

• Heat gained by solution: $q_{\text{solution}} = m_{\text{solution}} \times C_{\text{solution}} \times \Delta T$

• Assume $q_{\text{rxn}} = -q_{\text{solution}}$

• For reactions at constant pressure: $\Delta H_{\text{rxn}} = q_{\text{rxn}}$

Example: Mixing Mg metal with HCl and measuring temperature rise to calculate ΔHrxn.

Constant-Volume Calorimetry (Bomb Calorimeter)

For reactions at constant volume, a bomb calorimeter is used. The heat measured is ΔE, not ΔH.

• Heat change: $q_{\text{cal}} = C_{\text{cal}} \times \Delta T$

• For constant volume: $\Delta E_{\text{rxn}} = q_{\text{rxn}}$

Relationships Involving ΔHrxn

Quantitative Relationships and Hess's Law

Three key relationships allow calculation of ΔHrxn:

• If a reaction is multiplied by a factor, ΔHrxn is multiplied by the same factor.

• If a reaction is reversed, ΔHrxn changes sign.

• If a reaction is the sum of several steps, ΔHrxn is the sum of the ΔH values for each step (Hess's Law).

Example:

• Given: $A + 2B \rightarrow C \quad \Delta H_1$ $C + 2D \rightarrow E \quad \Delta H_2$ Overall: $A + 2B + 2D \rightarrow E$ $\Delta H_{\text{overall}} = \Delta H_1 + \Delta H_2$

Additional info: These relationships allow determination of ΔHrxn for reactions that are difficult to measure directly.