Enthalpy, Heats of Reaction, and Hess's Law

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Introduction to Heats of Reaction

The study of thermodynamics in chemistry involves understanding how energy, particularly heat, is transferred during chemical reactions. One of the central concepts is the enthalpy change (ΔH), which quantifies the heat absorbed or released at constant pressure.

• Goal: To predict ΔH for any reaction, even if it cannot be performed directly in the laboratory.

• Heat of Reaction (ΔHrxn): The enthalpy change for the isothermal (constant temperature) reaction at constant pressure.

• General Equation: For a reaction: \[ \Delta H_{rxn} = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants}) \]

• Example: For the reaction: \[ \mathrm{Fe_2O_3(s, T, p) + 3H_2(g, T, p) \rightarrow 2Fe(s, T, p) + 3H_2O(l, T, p)} \] \[ \Delta H_{rxn}(T, p) = 2\Delta H_f(\mathrm{Fe}, T, p) + 3\Delta H_f(\mathrm{H_2O}, T, p) - \Delta H_f(\mathrm{Fe_2O_3}, T, p) - 3\Delta H_f(\mathrm{H_2}, T, p) \]

Reference States and Standard Enthalpy of Formation

Because enthalpy is not measured on an absolute scale, only differences in enthalpy can be determined. To standardize measurements, chemists define a reference state for each element.

• Reference State: The most stable form of an element at 1 bar pressure and 298.15 K (25°C).

• Standard Enthalpy of Formation (ΔHf⦵): The enthalpy change when 1 mole of a compound is formed from its constituent elements in their standard states.

• Notation: \[ \Delta H_f^\circ(298.15\,\text{K}, 1\,\text{bar}) = 0 \] for any element in its most stable form.

• Example: \[ \Delta H_f^\circ(\mathrm{H_2}(g, 1\,\text{bar}), 298.15\,\text{K}) = 0 \] \[ \Delta H_f^\circ(\mathrm{Br_2}(l, 1\,\text{bar}), 298.15\,\text{K}) = 0 \]

Calculating Enthalpy Changes for Reactions

To determine the enthalpy change for a reaction, follow these steps:

1. Decompose reactants into their constituent elements in standard states.

2. Form products from these elements.

3. Apply Hess's Law: Because enthalpy is a state function, the total enthalpy change is independent of the path taken. Thus, enthalpy changes for individual steps can be added.

Example: Formation of HBr from H2 and Br2 at 298.15 K and 1 bar:

• Reaction: \[ \frac{1}{2} \mathrm{H_2}(g, 1\,\text{bar}) + \frac{1}{2} \mathrm{Br_2}(l, 1\,\text{bar}) \rightarrow \mathrm{HBr}(g, 1\,\text{bar}) \]

• Enthalpy change: \[ \Delta H_{rxn} = \Delta H_f^\circ(\mathrm{HBr}) - \frac{1}{2}\Delta H_f^\circ(\mathrm{H_2}) - \frac{1}{2}\Delta H_f^\circ(\mathrm{Br_2}) \] Since ΔHf⦵ for elements in their standard states is zero, this simplifies to ΔHrxn = ΔHf⦵(HBr).

Hess's Law and Path Independence

Hess's 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 is because enthalpy is a state function.

• Application: Allows calculation of ΔH for reactions that cannot be performed directly by combining known enthalpy changes for related reactions.

• Example: Combustion of methane:

  • CH4(g, 1 bar) + 2O2(g, 1 bar) → CO2(g, 1 bar) + 2H2O(l, 1 bar)

  • Breakdown into steps:

    1. Decompose CH4 and O2 into elements (C, H2, O2).

    2. Form CO2 and H2O from elements.

  • Sum the enthalpy changes for each step to find the overall ΔHrxn.

General Formula for Enthalpy of Reaction

The enthalpy change for a reaction at constant pressure is given by:

• \[ \Delta H_{rxn} = \sum_{\text{products}} \nu_i \Delta H_f^\circ(i) - \sum_{\text{reactants}} \nu_j \Delta H_f^\circ(j) \] where ν is the stoichiometric coefficient.

Exothermic and Endothermic Reactions

The sign of ΔH indicates the direction of heat flow:

• Exothermic Reaction: ΔH < 0. Heat flows from the reaction to the surroundings.

• Endothermic Reaction: ΔH > 0. Heat flows into the reaction from the surroundings.

Temperature Dependence of Enthalpy

The enthalpy change of a reaction can depend on temperature. The relationship is given by the heat capacity at constant pressure (Cp):

• \[ \left( \frac{\partial H}{\partial T} \right)_p = C_p \]

• For a reaction: \[ \Delta C_p = \sum_{\text{products}} \nu_i C_{p,i} - \sum_{\text{reactants}} \nu_j C_{p,j} \]

• To find ΔH at a new temperature T: \[ \Delta H(T_2) = \Delta H(T_1) + \int_{T_1}^{T_2} \Delta C_p \, dT \] This is especially simple if ΔCp is temperature-independent.

Summary Table: Key Terms

• Enthalpy (H): A thermodynamic quantity equivalent to the total heat content of a system at constant pressure.

• Standard Enthalpy of Formation (ΔHf⦵): The enthalpy change for the formation of 1 mole of a compound from its elements in their standard states.

• Hess's Law: The enthalpy change for a reaction is the sum of the enthalpy changes for any set of reactions into which the overall reaction can be divided.

• Exothermic: Reaction releases heat (ΔH < 0).

• Endothermic: Reaction absorbs heat (ΔH > 0).

Additional info: The notes above expand on the original slides by providing full definitions, context for standard states, and explicit examples of Hess's Law and enthalpy calculations, as would be found in a modern General Chemistry textbook.