The degree of dissociation `(alpha)` can be calculated using the formula,
`alpha=(dt-d_(0))/((n-1)d_(0))`
This formula is applicable at

Options

A. constant volume and constant temperature
B. constant volume and variable temperature
C. constant pressure and constant temperature
D. all the above conditions

Answer

To solve the question regarding the applicability of the formula for calculating the degree of dissociation (alpha), we will analyze the given formula and the conditions under which it is valid.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The formula for the degree of dissociation is given by:
\[ \alpha = \frac{d_t - d_0}{(n - 1)d_0} \]
where:
- \(d_t\) = final density of the gaseous mixture after dissociation
- \(d_0\) = initial density of the reactant before dissociation
- \(n\) = number of moles of products formed from one mole of reactant.

2. **Analyzing the Reaction**:
Consider a reaction where a reactant A dissociates into products B. For every mole of A that dissociates, \(N\) moles of B are produced. This means that the total number of moles changes as the reaction proceeds.

3. **Volume and Pressure Changes**:
- When the reactant dissociates, the total number of moles in the system changes, which affects the volume of the gas mixture.
- If the number of moles increases, the volume must also increase if the pressure is to remain constant.

4. **Identifying Conditions**:
- The formula is applicable under conditions where the pressure is constant and the temperature is also constant. This is because:
- At constant pressure, the volume can change as the number of moles changes.
- Temperature being constant ensures that the gas behaves ideally, allowing us to use the density relationship.

5. **Evaluating Options**:
- **Option 1**: Constant volume and constant temperature - Incorrect, as volume cannot remain constant when moles change.
- **Option 2**: Constant volume and variable temperature - Incorrect for the same reason as above.
- **Option 3**: Constant pressure and constant temperature - Correct, as this allows for volume changes due to varying moles.
- **Option 4**: All of the above - Incorrect, as not all conditions are valid.

6. **Conclusion**:
The formula for calculating the degree of dissociation (alpha) is applicable under the condition of constant pressure and constant temperature.

### Final Answer:
The formula is applicable at **constant pressure and constant temperature**.