Read the following paragraph and answer the questions given below,
for a general reaction, `aA+bB hArr cC+dD`, equilibrium constant `K_c` is given by `K_c=([C]^c[D]^d)/([A]^a[B]^b)` However, when all reactants and products are gases the equilibrium constant is generally expressed in terms of partial pressure.
`K_p=(P_C^cxx P _D^d)/(P_A^axxP_B^b)`
For a reversible reaction , if concentration of the reactants are doubled, the equilibrium constant will be

Options

A. `1/2` times
B. `1/4` times
C. 2 times
D. remain same

Answer

To solve the question regarding the effect of doubling the concentration of reactants on the equilibrium constant \( K_c \), we can follow these steps:

### Step 1: Understand the Definition of Equilibrium Constant
The equilibrium constant \( K_c \) for a general reaction \( aA + bB \rightleftharpoons cC + dD \) is defined as:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
This equation shows the ratio of the concentrations of the products to the reactants at equilibrium.

### Step 2: Write the Expression for \( K_c \)
For simplicity, consider a reaction where \( A \) converts to \( B \):
\[ A \rightleftharpoons B \]
The equilibrium constant \( K_c \) can be expressed as:
\[ K_c = \frac{[B]}{[A]} \]

### Step 3: Analyze the Effect of Doubling Reactant Concentration
If we double the concentration of the reactant \( A \), the new concentration of \( A \) becomes \( 2[A] \). The equilibrium expression now becomes:
\[ K_{c1} = \frac{[B]}{[2A]} = \frac{[B]}{2[A]} \]

### Step 4: Relate the New Equilibrium Constant to the Original
We can relate \( K_{c1} \) to the original \( K_c \):
\[ K_{c1} = \frac{[B]}{2[A]} = \frac{1}{2} \cdot \frac{[B]}{[A]} = \frac{K_c}{2} \]

### Step 5: Conclusion
From the above analysis, we see that when the concentration of the reactants is doubled, the new equilibrium constant \( K_{c1} \) becomes half of the original equilibrium constant \( K_c \). Therefore, the equilibrium constant remains unchanged in terms of its value; it is simply expressed in a different way due to the change in concentration.

Thus, the answer is that the equilibrium constant will be:
\[ \text{remains the same} \]