Reaction quotient vs equilibrium constant — predicting reaction direction

Question

What is the difference between the reaction quotient ( $Q$ ) and the equilibrium constant ( $K$ )? How do you use the comparison of $Q$ and $K$ to predict the direction a reaction will shift? Solve a numerical example.

(JEE Main + NEET + CBSE Board — concept + application)

Solution — Step by Step

For a general reaction: $aA + bB \rightleftharpoons cC + dD$

K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \quad \text{(at equilibrium)}

Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} \quad \text{(at any point in time)}

$K$ is calculated using equilibrium concentrations — it is a constant at a given temperature.

$Q$ is calculated using current concentrations — it changes as the reaction proceeds.

Comparison	What It Means	Reaction Shifts
$Q < K$	Too few products relative to equilibrium	Forward (→) to produce more products
$Q = K$	System is at equilibrium	No shift
$Q > K$	Too many products relative to equilibrium	Backward (←) to produce more reactants

Think of it as: the reaction always moves toward making $Q$ equal to $K$ .

For the reaction: $\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$ , $K_c = 0.50$ at a certain temperature.

At a particular moment: $[\text{N}_2] = 0.1$ M, $[\text{H}_2] = 0.2$ M, $[\text{NH}_3] = 0.3$ M.

Calculate $Q$ :

Q = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} = \frac{(0.3)^2}{(0.1)(0.2)^3} = \frac{0.09}{0.0008} = 112.5

Since $Q = 112.5 > K = 0.50$ , the reaction shifts backward (to the left) — NH₃ will decompose into N₂ and H₂ until equilibrium is reached.

$K$ changes ONLY with temperature:

Exothermic reaction: increasing T decreases K (shifts backward)
Endothermic reaction: increasing T increases K (shifts forward)

$Q$ changes whenever concentrations change — by adding/removing reactants or products, changing volume, etc.

graph TD
    A["Calculate Q from current concentrations"] --> B{"Compare Q with K"}
    B -->|"Q < K"| C["Forward shift →"]
    B -->|"Q = K"| D["At equilibrium — no shift"]
    B -->|"Q > K"| E["Backward shift ←"]
    C --> F["More products formed"]
    E --> G["More reactants formed"]
    F --> H["Q increases toward K"]
    G --> I["Q decreases toward K"]
    style A fill:#fbbf24,stroke:#000,stroke-width:2px
    style C fill:#86efac,stroke:#000
    style E fill:#fca5a5,stroke:#000
    style D fill:#93c5fd,stroke:#000

Why This Works

The equilibrium constant $K$ represents the “target” ratio of products to reactants that a reaction naturally settles at. The reaction quotient $Q$ is the “current” ratio. If $Q < K$ , there are not enough products yet — so the forward reaction speeds up. If $Q > K$ , there are too many products — so the reverse reaction speeds up. The system always adjusts to make $Q = K$ .

This is essentially Le Chatelier’s principle expressed mathematically.

Common Mistake

Students often confuse Q and K as the same thing. K is a CONSTANT at a given temperature — it does not change when you add more reactant or change the volume. Q is VARIABLE — it changes with every concentration change. When a question says “the equilibrium constant changes,” it means temperature changed. When Q changes, it just means concentrations changed (perhaps due to adding a substance or changing volume).

Memory aid: Q is the Question (“Where am I now?”), K is the Key (“Where should I end up?”). If Q is less than K, you have not reached the destination — move forward. If Q is more than K, you have overshot — move backward. This analogy works for every equilibrium problem.

Question

Solution — Step by Step

Why This Works

Common Mistake

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