`xA+yBrarrzC`. If `-(d[A])/(dt)=-(d[B])/(dt)=1.5(d[C])/(dt)`, then x, y and z are :

Options

A. `1, 1, 1`
B. `3, 2, 3`
C. `3, 3, 2`
D. `2, 2, 3`

Answer

To solve the problem, we need to determine the stoichiometric coefficients \( x \), \( y \), and \( z \) in the reaction \( xA + yB \rightarrow zC \) based on the given rate relationship:

\[ -\frac{d[A]}{dt} = -\frac{d[B]}{dt} = 1.5 \frac{d[C]}{dt} \]

### Step 1: Write the Rate Expressions
From the reaction \( xA + yB \rightarrow zC \), we can express the rates of change of the concentrations as follows:

- For \( A \):
\[ -\frac{d[A]}{dt} = \frac{1}{x} \frac{d[A]}{dt} \]

- For \( B \):
\[ -\frac{d[B]}{dt} = \frac{1}{y} \frac{d[B]}{dt} \]

- For \( C \):
\[ \frac{d[C]}{dt} = \frac{1}{z} \frac{d[C]}{dt} \]

### Step 2: Set Up the Relationships
According to the problem, we have:

\[ -\frac{d[A]}{dt} = -\frac{d[B]}{dt} = 1.5 \frac{d[C]}{dt} \]

This means we can equate the rates:

1. From \( A \) and \( C \):
\[ -\frac{d[A]}{dt} = \frac{1}{x} \frac{d[A]}{dt} = 1.5 \frac{1}{z} \frac{d[C]}{dt} \]

2. From \( B \) and \( C \):
\[ -\frac{d[B]}{dt} = \frac{1}{y} \frac{d[B]}{dt} = 1.5 \frac{1}{z} \frac{d[C]}{dt} \]

### Step 3: Solve for Ratios
From the first relationship, we can derive:

\[ \frac{1}{x} = 1.5 \frac{1}{z} \implies x = \frac{z}{1.5} \]

From the second relationship, we have:

\[ \frac{1}{y} = 1.5 \frac{1}{z} \implies y = \frac{z}{1.5} \]

### Step 4: Express \( x \) and \( y \) in Terms of \( z \)
From the equations derived, we can express \( x \) and \( y \):

\[ x = 1.5z \quad \text{and} \quad y = 1.5z \]

### Step 5: Substitute Values
To find specific values, we can assume \( z = 1 \) (as it is often convenient to set one stoichiometric coefficient to 1):

\[ x = 1.5 \times 1 = 1.5 \quad \text{and} \quad y = 1.5 \times 1 = 1.5 \]

However, we need to find integer values. If we multiply through by 2 to eliminate the fraction:

\[ x = 3, \quad y = 3, \quad z = 2 \]

### Conclusion
Thus, the stoichiometric coefficients are:

\[ x = 3, \quad y = 3, \quad z = 2 \]

### Final Answer
The values of \( x \), \( y \), and \( z \) are:

\[ x = 3, \quad y = 3, \quad z = 2 \]