**Reaction Quotient (\(Q\))**

The reaction quotient (\(Q\)) is formulated as a ratio of product to reactant for a particular point in a reversible reaction. Specifically, the format of reaction quotient based on molar concentrations for a reaction

\(\require{mhchem}\ce{aA + bB <=> cC + dD}\)

\(Q = \frac{[A]^a[B]^b}{[C]^c[D]^d}\)

When more products are present, the magnitude of \(Q\) is larger. Modification of the chemical equation results in a change in the value of \(Q\), since its format is derived for a particular chemical equation.

**Example 1.**

What is the reaction quotient expression for the equation \(\require{mhchem}\ce{cC + dD <=> aA + bB}\)?

A. \(Q = \frac{[A]^a[B]^b}{[C]^c[D]^d}\)

B. \(Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\)

C. \(Q = \frac{[C][D]}{[A][B]}\)

*Solution*

B. \(Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\)

The general format of \(Q\) is products divided by reactants, with each component raised to its respective coefficient. Notice that reversing the reaction (from \(\require{mhchem}\ce{aA + bB <=> cC + dD}\) to \(\require{mhchem}\ce{cC + dD <=> aA + bB}\)) results in a reaction quotient which is the reciprocal of the original value.

**Example 2.**

What is the missing value of \(K\)?

\(\require{mhchem}\ce{N2 + O2 <=> 2 NO}\;\;\;\;\;\;\;\;\;\;K_1 = 3.2 \times 10^ {-24}\)

\(\require{mhchem}\ce{2NO + O2 <=> 2NO2}\;\;\;\;\;K_2 = 1.6 \times 10^ {9}\)

\(\require{mhchem}\ce{N2 + 2O2 <=> 2NO2}\;\;\;\;\;\;\;K_{missing} = ?\)

A. \(5.1 \times 10 ^{-15}\)

B. \(1.6 \times 10^{9}\)

C. \(1.6 \times 10^{-15}\)

*Solution*

A. \(5.1 \times 10 ^{-15}\)

Adding chemical equations together requires multiplication of their equilibrium constants. The format of the equilibrium constant is the same as the reaction quotient.

\(K_{missing} = K_1 \times K_2 = (3.2 \times 10^ {-24}) \times (1.6 \times 10^ {9}) = 5.1 \times 10 ^{-15}\)

**Example 3.**

A reaction has a reaction quotient of \(25\). What is the value of the reaction quotient of the reverse reaction under the same conditions?

A. \(25\)

B. \(2.5\)

C. \( 0.04\)

*Solution*

C. \(0.04\)

The reverse reaction has a reaction quotient that is the reciprocal of the original reaction quotient.

\(Q = \frac{1}{25} = 0.04\)