Question

Determine the relationship between the ideal gas equilibrium constants $K_1$ and $K_2$ for the following two alternative ways of expressing the ammonia synthesis reaction: 1\. $\frac{1}{2}{\mathrm{N}}_2+\frac{3}{2}{\mathrm{H}}_2\rightleftarrows {\mathrm{NH}}_3$ 2\. ${\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftarrows 2{\mathrm{NH}}_3$

Short answer

The equilibrium constants for the reactions are related by the equation:

Step-by-step solution

- Write down the expressions for the equilibrium constants

For the first reaction: }

- Derive the relationship between the two constants

Take the square of the first equilibrium constant to the power equal to the ratio of coefficients from the two reactions. This gives you

- Apply the obtained relationship

You will get the unique formula from the previous step. Now, solve the following equation for simplified terms to find the relationship between the two equilibrium constants.

Key concepts

Ideal Gas Law

The ideal gas law is a fundamental principle in chemistry and physics that relates the pressure, volume, temperature, and number of moles of a gas. The equation is expressed as

Ammonia Synthesis

Ammonia synthesis, also known as the Haber-Bosch process, is an industrial method used to produce ammonia by combining nitrogen and hydrogen gases. The balanced chemical equation for this process is:

Chemical Equilibrium

Chemical equilibrium describes a state in a chemical reaction where the concentrations of reactants and products remain constant over time. This occurs when the forward and reverse reactions happen at the same rate.