For the reaction `2X+3Y to 4Z + 6Q`

Options

A. rate of consumption of X is 3 times the rate of formation of Q
B. rate of formation of Q is twice the rate of consumption of Y
C. rate of formation of Z is half of the rate of the consumption of X.
D. rate of consumption of X is thrice the rate of consumption of Y

Answer

To solve the problem regarding the reaction \(2X + 3Y \rightarrow 4Z + 6Q\) and the rates of consumption and formation of the substances involved, we can follow these steps:

### Step 1: Write the Rate Expressions
For the reaction \(2X + 3Y \rightarrow 4Z + 6Q\), we can express the rates of consumption and formation based on the stoichiometry of the reaction.

- Rate of consumption of \(X\) is given as:
\[ -\frac{1}{2} \frac{d[X]}{dt} \]

- Rate of consumption of \(Y\) is:
\[ -\frac{1}{3} \frac{d[Y]}{dt} \]

- Rate of formation of \(Z\) is:
\[ \frac{1}{4} \frac{d[Z]}{dt} \]

- Rate of formation of \(Q\) is:
\[ \frac{1}{6} \frac{d[Q]}{dt} \]

### Step 2: Relate the Rates
From the problem, we know that the rate of consumption of \(X\) is 3 times the rate of formation of \(Q\). Thus, we can write:
\[ -\frac{1}{2} \frac{d[X]}{dt} = 3 \left(\frac{1}{6} \frac{d[Q]}{dt}\right) \]

### Step 3: Simplify the Expression
Simplifying the equation from Step 2:
\[ -\frac{1}{2} \frac{d[X]}{dt} = \frac{1}{2} \frac{d[Q]}{dt} \]
This implies:
\[ -\frac{d[X]}{dt} = \frac{d[Q]}{dt} \]

### Step 4: Analyze the Rate of Consumption of \(Y\)
Next, we need to relate the rate of formation of \(Q\) to the rate of consumption of \(Y\):
\[ \frac{1}{6} \frac{d[Q]}{dt} = -\frac{1}{3} \frac{d[Y]}{dt} \]

### Step 5: Solve for the Rates
From the equation in Step 4, we can rearrange to find:
\[ \frac{d[Y]}{dt} = -2 \frac{d[Q]}{dt} \]

### Step 6: Analyze the Rate of Formation of \(Z\)
Now, we can relate the rate of formation of \(Z\) to the rate of consumption of \(X\):
\[ \frac{1}{4} \frac{d[Z]}{dt} = \frac{1}{2} \left(-\frac{d[X]}{dt}\right) \]

### Step 7: Final Relationships
From the above, we can conclude:
- The rate of formation of \(Z\) is half the rate of consumption of \(X\).
- The rate of consumption of \(X\) is twice the rate of consumption of \(Y\).

### Summary of Results
1. Rate of consumption of \(X\) is 3 times the rate of formation of \(Q\).
2. Rate of formation of \(Z\) is half the rate of consumption of \(X\).
3. Rate of consumption of \(X\) is twice the rate of consumption of \(Y\).