## The Reaction Quotient Q

The status of a reversible reaction is conveniently assessed by evaluating its **reaction quotient ( Q)**. For a reversible reaction described by

$$mA+nB+⇌xC+yD$$

the reaction quotient is derived directly from the stoichiometry of the balanced equation as

$$Q_c = \frac{[C]^x [D]^y}{[A]^m[B]^n}$$where the subscript c denotes the use of molar concentrations in the expression. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures:

$$Q_p= \frac{P_C^xP_D^y}{P_A^mP_B^n}$$

Note that the reaction quotient equations above are a simplification of more rigorous expressions that use *relative* values for concentrations and pressures rather than *absolute* values. These relative concentration and pressure values are dimensionless (they have no units); consequently, so are the reaction quotients. For purposes of this introductory text, it will suffice to use the simplified equations and to disregard units when computing *Q*. In most cases, this will introduce only modest errors in calculations involving reaction quotients.

### Writing Reaction Quotient Expressions

Write the concentration-based reaction quotient expression for each of the following reactions:

(a)$\qquad 3\, O_2\:(g)\rightleftharpoons 2\, O_3\: (g)$

(b)$\qquad N_2\: ( g) + 3\, H_2\: ( g) \rightleftharpoons 2\, NH_3\: ( g)$

(c)$\qquad 4\, NH_3\: (g) + 7\, O_2\: (g) \rightleftharpoons 4\, NO_2\: (g) + 6\, H_2O\: (g)$

Solution

(a)$\qquad Q_c=\frac{[O_3]^2}{[O_2]^3}$

(b)$\qquad Q_c=\frac{[NH_3]^2}{[N_2][H_2]^3}$

(c)$\qquad Q_c=\frac{[NO_2]^4[H_2O]^6}{[NH_3]^4[O_2]^7}$

### Check Your Learning

Write the concentration-based reaction quotient expression for each of the following reactions:

(a)$\qquad 2\, SO_2\: (g) + O_2\: (g) \rightleftharpoons 2\, SO_3\: (g)$

(b)$\qquad C_4H_8\: (g) \rightleftharpoons 2\, C_2H_4\: (g)$

(c)$\qquad 2\, C_4H_{10}\: (g) + 13\, O_2\: (g) \rightleftharpoons 8\, CO_2\: (g) + 10\, H_2O\: (g)$

**Answer:**

(a)$\qquad Q_c=\frac{[SO_3]^2}{[SO_2]^2[O_2]}$

(b)$\qquad Q_c=\frac{[C_2H_4]^2}{[C_4H_8]}$

(c)$\qquad Q_c=\frac{[CO_2]^8[H_2O]^{10}}{[C_4H_{10}]^2[O_2]^{13}}$