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 problem, we need to analyze the given reaction and the information about the degree of dissociation of B at two different temperatures. The reaction is:

\[ 2A(s) + B(g) \rightleftharpoons C(g) + 2D(s) + E(s) \]

### Step 1: Understand the Degree of Dissociation
The degree of dissociation (α) of B is given as:
- At 300 K, α = 20% = 0.2
- At 500 K, α = 24% = 0.24

This means that at higher temperatures, a greater fraction of B dissociates into products, indicating that the forward reaction is favored at higher temperatures.

### Step 2: Analyze the Effect of Temperature
From the information provided:
- As the temperature increases, the degree of dissociation of B increases.
- This implies that the rate of the forward reaction increases with temperature.

Since the forward reaction is favored with increased temperature, the rate of the backward reaction (which is the recombination of products back into reactants) must decrease.

### Step 3: Relationship Between Temperature and Backward Reaction
We conclude that:
- **Rate of backward reaction decreases with an increase in temperature.**
- Conversely, the rate of the backward reaction increases with a decrease in temperature.

### Step 4: Analyze the Effect of Pressure
In this reaction, we note that:
- The only gaseous reactant is B, and the gaseous product is C.
- The number of moles of gas on both sides of the reaction is equal (1 mole of B and 1 mole of C).

Since the number of moles of gas does not change, the pressure has no effect on the equilibrium position of this reaction.

### Step 5: Evaluate the Options
Now, we can evaluate the options given in the question:
- **Option A:** Increases with increase in pressure and temperature. (Incorrect)
- **Option B:** Increases with increase in pressure and decreases in temperature. (Incorrect)
- **Option C:** Depends on temperature only and decreases with increase in temperature. (Correct)
- **Option D:** Increases with increase in concentration of B and increasing temperature. (Incorrect)

### Conclusion
The correct answer is **Option C**, which states that the rate of the backward reaction depends on temperature only and decreases with an increase in temperature.

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