For the reaction `X+3Y rarrZ`, which form of differential rate law is incorrect?

Options

A. `dX//dt = dY//3dt`
B. `3dZ//dt = -dY//dt`
C. `dZ//dt = -dX//dt`
D. `dX//dt = dZ//dt`

Explanation

To determine which form of the differential rate law is incorrect for the reaction \( X + 3Y \rightarrow Z \), we need to analyze the rate expressions based on the stoichiometry of the reaction.

### Step-by-Step Solution:

1. **Write the Rate of Reaction**:
The rate of reaction can be expressed in terms of the change in concentration of reactants and products. For the given reaction, we can write:
\[ \text{Rate} = -\frac{1}{1} \frac{d[X]}{dt} = -\frac{1}{3} \frac{d[Y]}{dt} = \frac{d[Z]}{dt} \]

2. **Analyze Each Expression**:
- For \( X \): The rate is given by \( -\frac{d[X]}{dt} \).
- For \( Y \): The rate is given by \( -\frac{1}{3} \frac{d[Y]}{dt} \).
- For \( Z \): The rate is given by \( \frac{d[Z]}{dt} \).

3. **Establish Relationships**:
From the rate expressions, we can establish relationships:
- From \( -\frac{d[X]}{dt} = -\frac{1}{3} \frac{d[Y]}{dt} \), we can derive that \( \frac{d[Y]}{dt} = 3 \frac{d[Z]}{dt} \).
- From \( -\frac{d[X]}{dt} = \frac{d[Z]}{dt} \), we can see that the change in concentration of \( X \) is directly related to the formation of \( Z \).

4. **Evaluate Given Options**:
- **Option A**: \( -\frac{d[X]}{dt} = -\frac{1}{3} \frac{d[Y]}{dt} \) (Correct)
- **Option B**: \( -\frac{1}{3} \frac{d[Y]}{dt} = \frac{d[Z]}{dt} \) (Correct)
- **Option C**: \( -\frac{d[X]}{dt} = \frac{d[Z]}{dt} \) (Correct)
- **Option D**: \( \frac{d[X]}{dt} = \frac{d[Z]}{dt} \) (Incorrect, as it does not account for the negative sign)

5. **Identify the Incorrect Statement**:
The incorrect form of the differential rate law is found in **Option D**. The correct relationship should include a negative sign since the concentration of reactants decreases while the concentration of products increases.

### Final Answer:
The incorrect form of the differential rate law is **Option D**.