Equilibrium concentrations of A and B involved in following equilibrium are 0.01 M and 0.02 M respectively: `[A(g)implies B(g)]` If 0.01 M of A is added at equilibrium, then at new equilibrium concentration of B will be

Options

A. `6.67` x `10^-2` M
B. `2.67` x `10^-2` M
C. `1.33` x `10^-2` M
D. `1.33` x `10^-1` M

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the equilibrium concentrations
We are given the equilibrium concentrations of A and B:
- \([A]_{eq} = 0.01 \, M\)
- \([B]_{eq} = 0.02 \, M\)

### Step 2: Write the equilibrium expression
The equilibrium expression for the reaction \( A(g) \rightleftharpoons B(g) \) is given by:
\[ K_c = \frac{[B]}{[A]} \]
Substituting the equilibrium concentrations:
\[ K_c = \frac{0.02}{0.01} = 2 \]

### Step 3: Add 0.01 M of A to the system
When we add 0.01 M of A to the system, the new concentration of A becomes:
\[ [A]_{new} = 0.01 + 0.01 = 0.02 \, M \]
The concentration of B remains the same initially at 0.02 M.

### Step 4: Set up the reaction shift
According to Le Chatelier's principle, adding more reactant (A) will shift the equilibrium to the right (towards the products, B). Let \( x \) be the amount of A that reacts to form B.

At the new equilibrium:
- \([A] = 0.02 - x\)
- \([B] = 0.02 + x\)

### Step 5: Write the new equilibrium expression
The equilibrium expression remains the same:
\[ K_c = \frac{[B]}{[A]} = 2 \]
Substituting the new concentrations:
\[ 2 = \frac{0.02 + x}{0.02 - x} \]

### Step 6: Solve for \( x \)
Cross-multiplying gives:
\[ 2(0.02 - x) = 0.02 + x \]
Expanding and rearranging:
\[ 0.04 - 2x = 0.02 + x \]
\[ 0.04 - 0.02 = 2x + x \]
\[ 0.02 = 3x \]
\[ x = \frac{0.02}{3} = 0.00667 \, M \]

### Step 7: Calculate the new concentration of B
Now, substituting \( x \) back to find the new concentration of B:
\[ [B]_{new} = 0.02 + x = 0.02 + 0.00667 = 0.02667 \, M \]

### Step 8: Final answer
The new concentration of B at equilibrium is approximately:
\[ [B]_{new} \approx 0.02667 \, M \text{ or } 0.0267 \, M \]