Reaction Quotient (Q) - Chemistry

1. Fundamental Concepts

Definition: The Reaction Quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction mixture at a given time.
Expression: For a general reaction $$ aA + bB \rightarrow cC + dD $$, the Reaction Quotient is given by: $$Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$
Comparison with Equilibrium Constant (K): Q is compared to K to determine the direction in which a reaction will proceed to reach equilibrium. - If $$ Q < K $$, the reaction will proceed forward. - If $$ Q > K $$, the reaction will proceed backward. - If $$ Q = K $$, the system is at equilibrium.

2. Key Concepts

Calculation of Q: $$Q = \frac{[\text{products}]}{[\text{reactants}]}$$

Units: The units of Q depend on the stoichiometry of the reaction and the units of concentration or partial pressure used.

Application: Used to predict the direction of a reaction and to understand the state of a reaction mixture.

3. Examples

Example 1 (Basic)

Problem: For the reaction $$ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) $$, the concentrations are $$ [N_2] = 0.5 \, M $$, $$ [H_2] = 1.5 \, M $$, and $$ [NH_3] = 0.2 \, M $$. Calculate Q.

Step-by-Step Solution:

Write the expression for Q: $$Q = \frac{[NH_3]^2}{[N_2][H_2]^3}$$
Substitute the given concentrations: $$Q = \frac{(0.2)^2}{(0.5)(1.5)^3}$$
Calculate the value: $$Q = \frac{0.04}{(0.5)(3.375)} = \frac{0.04}{1.6875} \approx 0.0237$$

Validation: Substitute the values back into the expression to confirm the calculation.

Example 2 (Intermediate)

Problem: For the reaction $$ 2SO_2(g) + O_2(g) \rightarrow 2SO_3(g) $$, the partial pressures are $$ P_{SO_2} = 0.8 \, atm $$, $$ P_{O_2} = 0.4 \, atm $$, and $$ P_{SO_3} = 0.6 \, atm $$. Calculate Q.

Step-by-Step Solution:

Write the expression for Q using partial pressures: $$Q = \frac{P_{SO_3}^2}{P_{SO_2}^2 P_{O_2}}$$
Substitute the given partial pressures: $$Q = \frac{(0.6)^2}{(0.8)^2 (0.4)}$$
Calculate the value: $$Q = \frac{0.36}{(0.64)(0.4)} = \frac{0.36}{0.256} \approx 1.406$$

Validation: Substitute the values back into the expression to confirm the calculation.

4. Problem-Solving Techniques

Identify the Reaction: Write the balanced chemical equation and identify the reactants and products.
Write the Expression for Q: Use the stoichiometric coefficients from the balanced equation to write the expression for Q.
Substitute Values: Substitute the given concentrations or partial pressures into the expression for Q.
Calculate Q: Perform the necessary calculations to find the value of Q.
Compare with K: Compare the calculated Q with the known equilibrium constant (K) to determine the direction of the reaction.