The equation `alpha=(D-d)/((n-1)d)` is correctly matched for: (`alpha` is the degree of dissociation, D and d are the vapour densities before and after dissociation, respectively).

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding the equation \(\alpha = \frac{D - d}{(n - 1)d}\), we need to understand the components involved in this equation and how they relate to the degree of dissociation in a chemical reaction.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- \(\alpha\) is the degree of dissociation, which indicates the fraction of the original substance that has dissociated into products.
- \(D\) is the vapor density of the gas before dissociation.
- \(d\) is the vapor density of the gas after dissociation.
- \(n\) is the sum of the stoichiometric coefficients of the products formed in the reaction.

2. **Setting Up the Equation**:
- The equation given is \(\alpha = \frac{D - d}{(n - 1)d}\).
- This equation is derived based on the changes in vapor density before and after the dissociation of a substance.

3. **Analyzing the Stoichiometric Coefficients**:
- To use this equation, we need to determine the value of \(n\) for the specific reaction we are analyzing.
- The value of \(n\) is crucial because it represents how many moles of products are formed from the dissociation of one mole of reactant.

4. **Evaluating the Options**:
- We will evaluate each option provided (A, B, C, D) to find the correct value of \(n\) that satisfies the equation.
- For each option, calculate the sum of the stoichiometric coefficients of the products.

5. **Calculating for Each Option**:
- **Option A**: If the products have stoichiometric coefficients of \( \frac{n}{2} \) and \( \frac{n}{3} \), then \(n = \frac{n}{2} + \frac{n}{3} = \frac{5n}{6}\), which is not equal to \(n\).
- **Option B**: If the products have stoichiometric coefficients of \( \frac{n}{3} \) and \( \frac{2n}{3} \), then \(n = \frac{n}{3} + \frac{2n}{3} = 2n\), which is valid.
- **Option C**: If the products have stoichiometric coefficients of \( \frac{3n}{4} \), then \(n = \frac{3n}{4}\), which is not equal to \(n\).
- **Option D**: If the products have stoichiometric coefficients of \( \frac{n}{2} \) and \( n \), then \(n = \frac{n}{2} + n = \frac{3n}{2}\), which is again not equal to \(n\).

6. **Conclusion**:
- The only option that satisfies the equation is **Option B**, where the sum of the stoichiometric coefficients equals \(n\).

### Final Answer:
The equation \(\alpha = \frac{D - d}{(n - 1)d}\) is correctly matched for **Option B**.