Thermochemistry6.5: Determining Enthalpies of Reaction from Standard Enthalpies of Formation

Chapter 6 - Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions. A key focus is on enthalpy changes, which allow chemists to quantify the heat absorbed or released during reactions under constant pressure.

Enthalpy of a Reaction

Bond Dissociation Enthalpy and Reaction Enthalpy

The enthalpy of a reaction ($\Delta H$) is the heat change that occurs during a chemical reaction at constant pressure. It can be estimated using bond dissociation enthalpies, which are the energies required to break specific chemical bonds in one mole of a substance.

• Bond Dissociation Enthalpy: The energy required to break one mole of a particular bond in a gaseous molecule.

• Example: For the formation of HCl from H2 and Cl2:

  • Dissociation enthalpy of H2: 434 kJ mol-1

  • Dissociation enthalpy of Cl2: 242 kJ mol-1

  • Dissociation enthalpy of HCl: 431 kJ mol-1

• Calculation: The enthalpy of formation of HCl can be calculated by considering the energy required to break the bonds in H2 and Cl2 and the energy released when HCl is formed.

  • Reaction: $\frac{1}{2} \text{H}_2 (g) + \frac{1}{2} \text{Cl}_2 (g) \rightarrow \text{HCl} (g)$

  • Calculated $\Delta H$: -93 kJ mol-1

Relationships Involving $\Delta H$ – Hess' Law

Hess' Law and Reaction Enthalpy

Hess' Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This allows chemists to calculate enthalpy changes for complex reactions by combining known enthalpy changes of simpler reactions.

• General Strategy:

  1. Write the thermochemical equations for the reactions involved.

  2. Multiply, reverse, or rearrange equations as needed so that when added, the unwanted species cancel out and the desired reaction remains.

  3. Add the $\Delta H$ values for each step to obtain the overall $\Delta H$.

• Example:

  • Given reactions:

    • CH4(g) + 2O2(g) → CO2(g) + 2H2O(g), $\Delta H = -890.7$ kJ mol-1

    • CH4(g) → C(graphite) + 2H2(g), $\Delta H = +74.8$ kJ mol-1

    • C(graphite) + O2(g) → CO2(g), $\Delta H = -393.5$ kJ mol-1

    • 2H2(g) + O2(g) → 2H2O(g), $\Delta H = -484.0$ kJ mol-1

  • By combining these reactions, the overall enthalpy change for the combustion of methane can be determined.

Standard Heat of Reaction $\Delta H^\circ$

Definition and Standard States

The standard heat of reaction ($\Delta H^\circ$) is the enthalpy change measured when all reactants and products are in their standard states. Standard states are defined as follows:

• Gas: 1 bar (105 Pa) pressure

• Aqueous solution: 1 mol L-1 concentration

• Pure substance: Most stable form at 1 bar and the temperature of interest

When reporting $\Delta H^\circ$, the temperature should also be specified.

Standard Heat of Formation $\Delta H_f^\circ$

Definition and Examples

The standard heat of formation ($\Delta H_f^\circ$) of a compound is the enthalpy change when one mole of the compound is formed from its elements in their standard states.

• General Reaction: Elements in standard states → 1 mole of compound

• Examples:

  • C(graphite) + 2H2(g) → CH4(g), $\Delta H_f^\circ = -74.9$ kJ mol-1

  • Na(s) + 1/2 Cl2(g) → NaCl(s), $\Delta H_f^\circ = -411.1$ kJ mol-1

  • 2C(graphite) + 3H2(g) + 1/2 O2(g) → C2H5OH(l), $\Delta H_f^\circ = -277.6$ kJ mol-1

• Key Point: The $\Delta H_f^\circ$ of any element in its standard state is defined as zero.

Table: Standard Heats of Formation

The following table summarizes standard heats of formation for selected substances:

Substance	Formula	$\Delta H_f^\circ$ (kJ mol-1)
Carbon (graphite)	C(graphite)	0
Hydrogen (gas)	H2(g)	0
Water (liquid)	H2O(l)	-285.8
Carbon dioxide (gas)	CO2(g)	-393.5
Methane (gas)	CH4(g)	-74.9
Sodium chloride (solid)	NaCl(s)	-411.1
Ethanol (liquid)	CH3CH2OH(l)	-277.6
Additional info: Table values inferred from context and standard reference tables.

Using $\Delta H_f^\circ$ to Calculate Reaction Enthalpy

Calculating $\Delta H^\circ$ from Heats of Formation

The enthalpy change for any reaction can be calculated using standard heats of formation:

• Formula:

  • $\Delta H^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$

• Example: For the combustion of methane:

  • CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

  • $\Delta H^\circ = [\Delta H_f^\circ(\text{CO}_2) + 2\Delta H_f^\circ(\text{H}_2\text{O})] - [\Delta H_f^\circ(\text{CH}_4) + 2\Delta H_f^\circ(\text{O}_2)]$

  • Using values: $\Delta H^\circ = [-393.5 + 2(-285.8)] - [-74.9 + 2(0)] = -890.1$ kJ mol-1

Key Concepts Summary

• Enthalpy of reaction ($\Delta H$): Heat change at constant pressure.

• Bond dissociation enthalpy: Used to estimate reaction enthalpy.

• Hess' Law: Allows calculation of $\Delta H$ for complex reactions by combining known reactions.

• Standard states: Reference conditions for thermodynamic measurements.

• Standard heat of formation ($\Delta H_f^\circ$): Enthalpy change for forming 1 mole of a compound from its elements in standard states.

• Calculating $\Delta H^\circ$: Use heats of formation for products and reactants.

Additional info:

• Some values and table entries have been inferred from standard chemistry references and context.

• Examples and equations have been expanded for clarity and completeness.