Lesson: Reaction Quotients in Equilibrium

Introduction

In chemical equilibrium, the concentrations of reactants and products remain constant over time. The reaction quotient, $Q$, is a crucial concept that helps us understand the direction in which a reaction will proceed to reach equilibrium.

Definition

The reaction quotient, $Q$, is defined as the ratio of the concentrations of products to reactants, each raised to the power of their respective coefficients in the balanced chemical equation. For a general reaction:

$aA + bB \rightleftharpoons cC + dD$

the reaction quotient is given by:

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

where $[X]$ represents the molarity of species $X$.

Steps to Calculate Reaction Quotient

1. Identify the balanced chemical equation of the reaction.
2. Determine the concentrations of all reactants and products at a given moment.
3. Substitute the concentrations into the expression for $Q$.
4. Compare $Q$ to $K$ (the equilibrium constant) to predict the direction of the reaction:
   • If $Q < K$, the reaction will proceed forward (to the right).
   • If $Q > K$, the reaction will proceed in reverse (to the left).
   • If $Q = K$, the system is at equilibrium.

Example Calculation

Consider the reaction:

$2H_{2}(g) + O_{2}(g) \rightleftharpoons 2H_{2}O(g)$

If at a certain moment, the concentrations are:

• $[H_{2}] = 0.2 \, M$
• $[O_{2}] = 0.1 \, M$
• $[H_{2}O] = 0.3 \, M$

We calculate $Q$ as follows:

$Q = \frac{[H_{2}O]^{2}}{[H_{2}]^{2}[O_{2}]} = \frac{(0.3)^{2}}{(0.2)^{2}(0.1)} = \frac{0.09}{0.04 \cdot 0.1} = \frac{0.09}{0.004} = 22.5$

Assuming the equilibrium constant $K = 10$, we see that:

• Since $Q (22.5) > K (10)$, the reaction will shift to the left to reach equilibrium.

Key Questions

• What is the reaction quotient, and how is it calculated?
• How does the value of $Q$ inform us about the direction of the reaction?
• What are the differences between $Q$ and $K$?

Summary

Understanding the reaction quotient is essential for predicting the behavior of chemical systems. It allows chemists to determine how far a reaction has progressed and what adjustments may be necessary to achieve equilibrium.

Keywords

• Reaction Quotient
• Equilibrium Constant
• Chemical Reactions
• Concentrations
• Direction of Reaction