For the reaction `, XA + YB to ZC`
If `(-d[A])/( dt) = (-d[B])/(dt) = (1.5 d [C])/(dt)`. then the correct statements among the following is:

Options

A. The value of `Y=2`
B. The value of `X=Y=Z=3`
C. The value of `X=Y=3`
D. The value of `X=2`

Explanation

To solve the problem, we need to analyze the given reaction and the relationships between the rates of disappearance of reactants and the rate of appearance of the product.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction is given as:
\[ \text{XA} + \text{YB} \rightarrow \text{ZC} \]

2. **Write the Rate Expressions**:
The rate of disappearance of reactants and the rate of appearance of products can be expressed as:
\[ -\frac{d[A]}{dt} = \frac{1}{X} \cdot \text{Rate} \]
\[ -\frac{d[B]}{dt} = \frac{1}{Y} \cdot \text{Rate} \]
\[ \frac{d[C]}{dt} = \frac{1}{Z} \cdot \text{Rate} \]

3. **Given Relationship**:
We are given that:
\[ -\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{1.5}{dt} \cdot \frac{d[C]}{dt} \]

4. **Set Up the Equations**:
From the given relationship, we can express:
\[ -\frac{d[A]}{dt} = k \quad \text{and} \quad -\frac{d[B]}{dt} = k \]
where \( k \) is a constant representing the rate of disappearance of A and B.

From the relationship with C, we can write:
\[ k = \frac{1.5}{Z} \cdot \frac{d[C]}{dt} \]

5. **Equate and Solve for X, Y, Z**:
From the equations:
\[ -\frac{d[A]}{dt} = \frac{1}{X} \cdot k \]
\[ -\frac{d[B]}{dt} = \frac{1}{Y} \cdot k \]
\[ \frac{d[C]}{dt} = \frac{1}{Z} \cdot k \]

Since both A and B have the same rate of disappearance, we can equate:
\[ \frac{1}{X} = \frac{1}{Y} \]
Thus, \( X = Y \).

6. **Substituting Values**:
From the earlier relationships, we can express:
\[ k = \frac{1.5}{Z} \cdot \frac{d[C]}{dt} \]
By substituting \( k \) into the equations, we can find the values of X, Y, and Z.

7. **Final Values**:
After comparing coefficients, we find:
\[ X = 3, \quad Y = 3, \quad Z = 2 \]

### Conclusion:
The correct statements based on the values of X, Y, and Z are:
- \( X = Y = 3 \)
- \( Z = 2 \)