KEY2CHEM

Magnitude of Equilibrium Constant (\(K\)

The mass action expression for the chemical reaction \(\require{mhchem}\ce{aA + bB <=> cC + dD}\) at equilibrium is \(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\) when based on molar concentrations. The magnitude of \( K\) provides insight into whether the reaction contains mostly products (large magnitude of \(K\), since products are in the numerator) or mostly reactants (small magnitude of \(K\), since reactants are in the denominator) when the reaction reaches equilibrium.


Example 1.

 

A reaction has an equilibrium constant of \(1.0 \times 10^{-12}\). What is true about the reaction mixture at equilibrium?

 

A. It contains equal concentrations of reactants and products.

B. It contains mostly reactants.

C. It contains mostly products.

 

 

 

Solution

 

B. It contains mostly reactants.

 

The general expression for equilibrium constant is \(K = \frac{\text{products}}{\text{reactants}}\)

A small value of \(K\) (\(1.0 \times 10^{-12} = \frac{\text{products}}{\text{reactants}}\)) means there is a small concentration of products and large concentration of reactants at equilibrium.


Example 2.

For the reaction \(\require{mhchem}\ce{N2(g) + O2(g) <=> 2 NO(g)} \;\;\;\; K = 1.0 \times 10^{-34}\), which species is present is the smallest concentration at equilibrium?

 

A. \(\require{mhchem}\ce{N2}\)

B. \(\require{mhchem}\ce{O2}\)

C. \(\require{mhchem}\ce{NO}\)

 

 

 

Solution

C. \(\require{mhchem}\ce{NO}\)

The value of \(K\) is very small, meaning the reactants are favored at equilibrium (the reaction reaches equilibrium with very little products formed and mostly reactants remaining).


Example 3.

 

A reaction that reaches equilibrium with mostly products formed has a _______ value of equilibrium constant \(K\).

 

A. small

B. large

C. intermediate

 

 

 

 

Solution

 

B. large

A large magnitude of K means equilibrium is reached with mostly products formed. A reaction of this type is said to “favor the products” since mostly products are present at equilibrium.