For the given equilibrium
`L_((g)) hArr M_((g))`
The `K_f =5xx10^(-4)` mole /litre /seconds and `k_b=3 xx 10^(-2)` litre/mole /seconds
the equilibrium concentration of M is

Options

A. 0.13 M
B. 0.3 M
C. 0.8 M
D. can't be calculated

Answer

To solve the problem, we need to find the equilibrium concentration of M for the given equilibrium reaction:

\[ L_{(g)} \rightleftharpoons M_{(g)} \]

Given:
- \( K_f = 5 \times 10^{-4} \, \text{mol/L/s} \) (forward rate constant)
- \( K_b = 3 \times 10^{-2} \, \text{L/mol/s} \) (backward rate constant)

### Step 1: Calculate the equilibrium constant \( K_c \)

The equilibrium constant \( K_c \) can be calculated using the relationship between the forward and backward rate constants:

\[ K_c = \frac{K_f}{K_b} \]

Substituting the given values:

\[ K_c = \frac{5 \times 10^{-4}}{3 \times 10^{-2}} \]

### Step 2: Perform the calculation

Now, we perform the division:

\[ K_c = \frac{5 \times 10^{-4}}{3 \times 10^{-2}} = \frac{5}{3} \times 10^{-4 + 2} = \frac{5}{3} \times 10^{-2} \]

Calculating \( \frac{5}{3} \):

\[ K_c \approx 1.6667 \times 10^{-2} \]

### Step 3: Express \( K_c \) in decimal form

Converting \( K_c \) into decimal form:

\[ K_c \approx 0.01667 \]

### Step 4: Conclusion

Thus, the equilibrium constant \( K_c \) is approximately \( 0.01667 \). Since the question asks for the equilibrium concentration of \( M \), we can say that:

\[ \text{Equilibrium concentration of } M \text{ is related to } K_c. \]

In a simple equilibrium, if we assume that the initial concentration of \( L \) is \( [L]_0 \) and at equilibrium, \( x \) amount of \( L \) has converted to \( M \):

\[ K_c = \frac{[M]}{[L]_0 - [M]} \]

However, without the initial concentration of \( L \), we cannot find the exact concentration of \( M \). But we can conclude that the equilibrium concentration of \( M \) is related to \( K_c \).

### Final Answer

The equilibrium concentration of \( M \) can be expressed as:

\[ [M] = K_c \cdot ([L]_0 - [M]) \]

Since we don't have the initial concentration of \( L \), we cannot provide a numerical value for \( [M] \).

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