If the forward rate constant of reversible reaction is 0.16 and backward rate constant is `4xx10^(4)` , then the equilibrum constant will be .

Options

A. `2.25xx10^(-6)`
B. `2.5xx10^(-5)`
C. `4xx10^(-6)`
D. `4xx10^(-5)`

Answer

To find the equilibrium constant (K) for a reversible reaction given the forward and backward rate constants, we can follow these steps:

### Step 1: Identify the given values
- Forward rate constant (k_f) = 0.16
- Backward rate constant (k_b) = 4 × 10^4

### Step 2: Write the formula for the equilibrium constant
The equilibrium constant (K) for a reversible reaction is given by the ratio of the forward rate constant to the backward rate constant:
\[ K = \frac{k_f}{k_b} \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ K = \frac{0.16}{4 \times 10^4} \]

### Step 4: Perform the calculation
To simplify the calculation, we can express 0.16 in a form that makes it easier to divide:
\[ K = \frac{0.16}{4 \times 10^4} = \frac{0.16}{4} \times 10^{-4} \]

Calculating \( \frac{0.16}{4} \):
\[ \frac{0.16}{4} = 0.04 \]

So now we have:
\[ K = 0.04 \times 10^{-4} \]

### Step 5: Express in scientific notation
Now, we can express \( 0.04 \times 10^{-4} \) in scientific notation:
\[ K = 4 \times 10^{-6} \]

### Final Answer
Thus, the equilibrium constant (K) is:
\[ K = 4 \times 10^{-6} \]