For a reversible reaction if the concentrations of the reactants are doubled, the equilibrium constant will be

Options

A. doubled
B. halved
C. one-fourth
D. the same

Answer

To solve the question regarding the effect of doubling the concentrations of reactants on the equilibrium constant for a reversible reaction, we can follow these steps:

### Step 1: Understand the Concept of Equilibrium Constant (K)
The equilibrium constant (K) for a reversible reaction is defined as the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. For a general reaction:

\[ aA + bB \rightleftharpoons cC + dD \]

The equilibrium constant (K) is given by:

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

### Step 2: Analyze the Effect of Changing Concentrations
If we double the concentrations of the reactants A and B, the new concentrations will be:

\[ [A]_{new} = 2[A] \]
\[ [B]_{new} = 2[B] \]

### Step 3: Substitute the New Concentrations into the Equilibrium Expression
Now, we can substitute the new concentrations into the equilibrium expression:

\[ K' = \frac{[C]^c [D]^d}{[A]_{new}^a [B]_{new}^b} \]

Substituting the new values:

\[ K' = \frac{[C]^c [D]^d}{(2[A])^a (2[B])^b} \]

### Step 4: Simplify the New Equilibrium Constant Expression
This can be simplified as follows:

\[ K' = \frac{[C]^c [D]^d}{2^a [A]^a \cdot 2^b [B]^b} \]
\[ K' = \frac{[C]^c [D]^d}{2^{(a+b)} [A]^a [B]^b} \]

### Step 5: Relate the New Equilibrium Constant to the Original
Since the original equilibrium constant \( K \) is:

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

We can express \( K' \) in terms of \( K \):

\[ K' = \frac{K}{2^{(a+b)}} \]

### Step 6: Conclusion
From this expression, we can see that the new equilibrium constant \( K' \) will be equal to the original equilibrium constant \( K \) divided by \( 2^{(a+b)} \). Therefore, if the concentrations of the reactants are doubled, the equilibrium constant will not change in value; it remains constant because it is only dependent on the temperature and not on the concentrations of reactants or products.

### Final Answer
The equilibrium constant will remain unchanged (K' = K).

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