For the reaction P `to` 2Q, the rate of formation of Q is 0.50 moles per litre-hour. What is the rate of disappearance of P?

Options

A. `0.50 mol//l-hr`
B. `0.25 mol//l-hr`
C. `1.0 mol//l-hr`
D. `0.75 mol//l-hr`

Answer

To solve the problem, we need to determine the rate of disappearance of reactant P given the rate of formation of product Q in the reaction:

\[ P \rightarrow 2Q \]

### Step-by-Step Solution:

1. **Identify the Rate of Formation of Q**:
We are given that the rate of formation of Q is:
\[ \frac{d[Q]}{dt} = 0.50 \text{ moles per litre-hour} \]

2. **Understand the Stoichiometry of the Reaction**:
From the balanced equation, we can see that 1 mole of P produces 2 moles of Q. This means that for every mole of P that disappears, 2 moles of Q are formed.

3. **Relate the Rate of Disappearance of P to the Rate of Formation of Q**:
The relationship can be expressed as:
\[ -\frac{d[P]}{dt} = \frac{1}{2} \frac{d[Q]}{dt} \]
Here, the negative sign indicates the disappearance of P, and the factor of \( \frac{1}{2} \) accounts for the stoichiometric ratio.

4. **Substitute the Given Rate of Formation of Q**:
Substitute the known value of \(\frac{d[Q]}{dt}\) into the equation:
\[ -\frac{d[P]}{dt} = \frac{1}{2} \times 0.50 \text{ moles per litre-hour} \]

5. **Calculate the Rate of Disappearance of P**:
\[ -\frac{d[P]}{dt} = 0.25 \text{ moles per litre-hour} \]
Therefore, the rate of disappearance of P is:
\[ \frac{d[P]}{dt} = 0.25 \text{ moles per litre-hour} \]

### Final Answer:
The rate of disappearance of P is:
\[ 0.25 \text{ moles per litre-hour} \]