D20.3 Hess’s Law

The standard enthalpy change for a particular reaction is the difference between the standard enthalpy of the products and the standard enthalpy of the reactants. That difference is same regardless of whether the reaction is carried out directly or in two or more steps. This fact allows us to calculate the enthalpy change for a chemical reaction from other experimentally determined enthalpy changes. This type of calculation usually involves Hess’s law: if a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps.

For example, we can think of the following reaction occurring in a single step:

C(s) + O2(g) ⟶ CO2(g)          ΔrH° = -394 kJ/mol

or in a two-step process, one in which carbon is partially oxidized to CO and a second in which CO is oxidized further to the overall product CO2:

step 1: C(s) + ½O2(g) ⟶ CO(g) ΔrH° = -111 kJ/mol
step 2: CO(g) + ½O2(g) ⟶ CO2(g) ΔrH° = -283 kJ/mol

According to Hess’s law, the ΔrH° of the one-step reaction equals the sum of the ΔrH° of the two steps in the two-step reaction:

step 1: C(s) + ½O2(g) ⟶ CO(g) ΔrH° = -111 kJ/mol
step 2: CO(g) + ½O2(g) ⟶ CO2(g) ΔrH° = -283 kJ/mol
Sum: C(s) + O2(g) + CO(g) ⟶ CO(g) + CO2(g) ΔrH° = -394 kJ/mol

Note that, because it appears on both sides of the equation arrow, CO(g) is cancelled. To think about this pictorially, consider this figure.

A diagram is shown. A long arrow faces upward on the left with the phrase “H increasing.” A horizontal line at the bottom of the diagram is shown with the formula “C O subscript 2 (g)” below it. A horizontal line at the top of the diagram has the formulas “C (s) + O subscript 2 (g)” above it. The top and bottom lines are connected by a downward facing arrow with the value “Δ H = –394 k J” written beside it. Below and to the right of the top horizontal line is a second horizontal line with the equations “C O (g) + one half O subscript 2 (g)” above it. This line and the bottom line are connected by a downward facing arrow with the value “Δ H = –283 k J” written beside it. The same line and the top line are connected by a downward facing arrow with the value “Δ H = –111 k J” written beside it. There are three brackets to the right of the diagram. The first bracket runs from the top horizontal line to the second horizontal line. It is labeled, “Enthalpy of reactants.” The second bracket runs from the second horizontal line to the bottom horizontal line. It is labeled, “Enthalpy of products.” Both of these brackets are included in the third bracket which runs from the top to the bottom of the diagram. It is labeled, “Enthalpy change of exothermic reaction in 1 or 2 steps.
Figure: Enthalpy Diagram. Enthalpy values based on one mole of reaction: C(s) + O2(g) ⟶ CO2(g). The reaction can be thought of as occurring in one step or two steps. The ΔrH° of the two steps sum to the ΔrH° of the overall reaction, as described by Hess’s law. For an exothermic process, the products are at lower enthalpy than the reactants.
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Chem 109 Fall 2022 Copyright © by Jia Zhou and John Moore is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.