Predicting Extent & Direction of Reaction
Using the Equilibrium Constant ($K_c$) and Reaction Quotient ($Q_c$) to understand chemical processes.
Two fundamental questions in chemistry are: "How far will this reaction go?" and "Which way is the reaction moving right now?" We answer these using two quantitative tools: the **Equilibrium Constant ($K_c$)** and the **Reaction Quotient ($Q_c$)**.
1. Predicting the Extent of Reaction
The magnitude of the equilibrium constant $K_c$ tells us about the relative concentrations of reactants and products once equilibrium is reached. It indicates how "complete" a reaction is.
Case 1: $K_c > 10^3$ (Very Large)
The reaction proceeds nearly to completion. At equilibrium, products dominate, and reactants are negligible.
Example: $H_2 + Cl_2 \rightarrow 2HCl \quad (K_c \approx 4 \times 10^{31})$
Case 2: $K_c < 10^{-3}$ (Very Small)
The reaction hardly proceeds. At equilibrium, reactants dominate, and product formation is negligible.
Example: $N_2 + O_2 \rightarrow 2NO \quad (K_c \approx 4.8 \times 10^{-31})$
Case 3: $10^{-3} < K_c < 10^3$ (Intermediate)
Considerable concentrations of both reactants and products are present at equilibrium.
Example: $H_2 + I_2 \rightleftharpoons 2HI \quad (K_c \approx 57 \text{ at } 700K)$
2. Predicting the Direction of Reaction
If a reaction mixture is not yet at equilibrium, we calculate the **Reaction Quotient ($Q_c$)**. It has the same formula as $K_c$ but uses concentrations at that specific instant of time.
Comparing $Q_c$ and $K_c$:
| Condition | Interpretation | Direction |
|---|---|---|
| $Q_c < K_c$ | Ratio of products is too low. | Forward Direction $\rightarrow$ |
| $Q_c > K_c$ | Ratio of products is too high. | Backward Direction $\leftarrow$ |
| $Q_c = K_c$ | Ratio matches equilibrium. | Equilibrium Reached |
3. Thermodynamic Perspective (Gibbs Energy)
The direction can also be predicted using Gibbs Free Energy change ($\Delta G$):
- $\Delta G < 0$: Reaction is spontaneous in the forward direction.
- $\Delta G > 0$: Reaction is non-spontaneous forward (spontaneous in reverse).
- $\Delta G = 0$: Reaction is at equilibrium.
At equilibrium, $\Delta G = 0$ and $Q_c = K_c$, leading to: $\Delta G^\circ = -RT \ln K_c$.
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