8.5 Ways to Recognize Chemical Equilibrium

The establishment of equilibrium in a chemical reaction can be confirmed by monitoring the concentrations of reactants and products over time. When these concentrations no longer change, the system has reached equilibrium. This can be achieved through both physical and chemical methods.

The state of equilibrium can be identified by observing that the macroscopic properties of the system become constant. Two main approaches are used for this purpose.

a) Physical Method (Spectrometric Method)

This method relies on measuring a physical property of the reaction mixture that changes as the reaction progresses. A key advantage is that the measurement can often be done without disturbing the system.

Principle: A physical property such as color, pressure, density, or refractive index that is proportional to the concentration of a reactant or product is monitored over time. Equilibrium is reached when this property becomes constant.

Example: Spectrometry

This method is suitable when at least one substance in the reaction absorbs light in the ultraviolet (UV), visible, or infrared (IR) spectrum. The amount of light absorbed (absorbance) is directly proportional to the concentration of the absorbing species.

Consider the reversible decomposition of dinitrogen tetroxide:

${\mathrm{N}}_2{\mathrm{O}}_{4(\mathrm{g})}\rightleftharpoons 2\mathrm{N}{\mathrm{O}}_{2(\mathrm{g})}$

• ${\mathrm{N}}_2{\mathrm{O}}_4$ is a colorless gas, while $\mathrm{N}{\mathrm{O}}_2$ is a reddish-brown gas.
• As the reaction proceeds, the concentration of $\mathrm{N}{\mathrm{O}}_2$ increases, and the mixture becomes more intensely reddish-brown. A spectrometer can measure the absorbance of light by the $\mathrm{N}{\mathrm{O}}_2$ gas.
• The reaction is at equilibrium when the spectrometer reading for absorbance remains constant over time, indicating that the concentration of $\mathrm{N}{\mathrm{O}}_2$ is no longer changing.

b) Chemical Method

In this approach, a small sample of the reaction mixture is periodically withdrawn and its chemical composition is analyzed, typically through titration. This determines the concentration of a specific reactant or product.

Principle: The concentration of a reactant or product is determined at regular intervals using a suitable chemical reaction. Equilibrium is confirmed when repeated measurements show that the concentration has become constant.

Example: Esterification

Consider the formation of ethyl acetate from acetic acid and ethanol, a reversible reaction catalyzed by a small amount of mineral acid.

$\mathrm{C}{\mathrm{H}}_3\mathrm{COO}{\mathrm{H}}_{(\mathrm{l})}+{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{O}{\mathrm{H}}_{(\mathrm{l})}\rightleftharpoons \mathrm{C}{\mathrm{H}}_3\mathrm{COO}{\mathrm{C}}_2{\mathrm{H}}_{5(\mathrm{l})}+{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{l})}$

To track the progress of the reaction, we can measure the concentration of the unreacted acetic acid.

1. A small, known volume of the reaction mixture is withdrawn at regular time intervals.
2. Quenching: The reaction in the sample is stopped (quenched) by sudden cooling or dilution to ensure the concentration represents the state at the exact moment of withdrawal.
3. Each sample is immediately titrated against a standard solution of a strong base, such as Sodium Hydroxide ($\mathrm{NaOH}$), using an indicator like phenolphthalein.

Initially, the concentration of acetic acid will decrease as it is consumed. The reaction has reached equilibrium when the volume of $\mathrm{NaOH}$ required to neutralize the acetic acid in successive samples becomes constant. This signifies that the concentration of acetic acid is no longer changing.