# Equilibrium Constant

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### Concepts

For the hypothetical chemical reaction:

$aA + bB \rightleftharpoons cC + dD$

the equilibrium constant is defined as:

$K_C = \dfrac{[C]^c[D]^d}{[A]^a[B]^b}$

The notation [A] signifies the molar concentration of species A. An alternative expression for the equilibrium constant involves partial pressures:

$K_P = \dfrac{P_C^c P_D^d}{P_A^aP_B^b}$

Note that the expression for the equilibrium constant includes only solutes and gases; pure solids and liquids do not appear in the expression. For example, the equilibrium expression for the reaction

$CaH_2 (s) + 2H_2O (g) \rightleftharpoons Ca(OH)_2 (s) + 2H_2 (g)$

is the following:

$K_C = \dfrac{[H_2]^2}{[H_2O]^2}$

Observe that the gas-phase species H2O and H2 appear in the expression but the solids CaH2 and Ca(OH)2 do not appear.

The equilibrium constant is most readily determined by allowing a reaction to reach equilibrium, measuring the concentrations of the various solution-phase or gas-phase reactants and products, and substituting these values into the Law of Mass Action.

## Experiment

Objective: Determine the equilibrium constant for a chemical reaction.

### Part 1.

In this part of the experiment, the following reaction is studied:

$NaHCO_3 (s) \rightleftharpoons NaOH (s) + CO_2 (g)$

The steps in the experiment are those that would be performed in practice in the laboratory:

1. A 1 gram portion of sodium hydrogen carbonate powder is placed in the glass bulb
2. The bulb is evacuated (that is, all gases are removed from the flask)
3. The bulb is heated to 800 K and the reaction is allowed to reach equilibrium

At room temperature, the reaction does not proceed at a measurable rate. At 800 K, however, the rate of reaction is relatively fast and equilibrium is quickly achieved.

A manometer is attached to the bulb to measure the partial pressure of carbon dioxide in the bulb. Assume the sodium hydrogen carbonate occupies a negligible fraction of the volume of the 500 mL bulb. Also assume that the connections to the manometer have a negligible volume. (The stopcock to the bulb is always open, because the bulb is always open to the manometer so that the pressure may be continually monitored. Both air and carbon dioxide are colorless gases.)

Use the experimental data to calculate KP and KC for this reaction. In this part of the experiment, the value KP and KC are provided for verification. Dr. David Blauch (Davidson College)

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