For the given reaction.
`2A(s) +B(g) hArrC(g)+2D(s) +E(s)`
the degree of dissociation of B was found to be 20% at 300k and 24% at 500 k the rate of backward reaction

Options

A. increases with increase in pressure and temperature
B. increases with increases in pressure and decreases in temperature
C. depends on temperature only and decreases with increases in temperature
D. increases with increasing the concentration of B and increasing the temperature

Answer

To solve the question regarding the degree of dissociation of B and the rate of the backward reaction, we can follow these steps:

### Step 1: Understand the Reaction
The given reaction is:
\[ 2A(s) + B(g) \rightleftharpoons C(g) + 2D(s) + E(s) \]

In this reaction, B is a gaseous reactant, and its degree of dissociation is given at two different temperatures.

### Step 2: Define Degree of Dissociation
The degree of dissociation (α) is defined as the fraction of the original amount of a substance that has dissociated. For B, we have:
- At 300 K, α = 20% = 0.20
- At 500 K, α = 24% = 0.24

### Step 3: Analyze the Effect of Temperature
The degree of dissociation of B increases with temperature. This indicates that the forward reaction is favored at higher temperatures. According to Le Chatelier's principle, if the forward reaction is favored, the rate of the backward reaction will decrease as temperature increases.

### Step 4: Determine the Rate of Backward Reaction
The rate of the backward reaction is influenced by the concentration of products and the temperature. As the temperature increases, the rate of the forward reaction increases, leading to a decrease in the rate of the backward reaction.

### Step 5: Evaluate the Options
Now, we need to evaluate the options provided in the question regarding how the rate of the backward reaction changes with pressure and temperature.

1. **Option 1**: Increase with increase in pressure and temperature.
- Incorrect. The rate of reaction is independent of pressure in this case, and the backward reaction decreases with increasing temperature.

2. **Option 2**: Increase with increase in pressure.
- Incorrect. As established, the rate of reaction is independent of pressure.

3. **Option 3**: Depend on temperature only.
- Correct. The rate of the backward reaction decreases with an increase in temperature.

4. **Option 4**: Increase with increase in concentration of B.
- Incorrect. Increasing the concentration of B will favor the forward reaction, thus decreasing the rate of the backward reaction.

### Conclusion
The correct answer is **Option 3**: The rate of the backward reaction depends on temperature only and decreases with an increase in temperature.

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