In which statement is true ?

Options

A. Reaction `A + B rarr Q` is faster.
B. Reaction `Q rarr C` is faster.
C. Reaction in (a) and (b) are equal.
D. Unpredictable.

Explanation

To solve the question regarding the activation energy in a multi-step reaction and determine which statement is true, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Reactions**:
We have two reactions:
- Reaction 1: \( A + B \rightarrow Q \)
- Reaction 2: \( Q \rightarrow C \)

2. **Understand Activation Energy**:
Activation energy (Ea) is the minimum energy required for a reaction to occur. It can be visualized as the height of the energy barrier that the reactants must overcome.

3. **Analyze the Potential Energy Diagram**:
From the video transcript, we know that:
- The total energy for the formation of \( Q \) from \( A + B \) is 25 kcal/mol.
- The energy level of \( Q \) is at 7 kcal/mol.
- The energy level of \( C \) is at 20 kcal/mol.

4. **Calculate Activation Energy for Each Reaction**:
- **For Reaction 1 (\( A + B \rightarrow Q \))**:
\[ \text{Ea}_{A+B \rightarrow Q} = \text{Total Energy} - \text{Energy of Q} = 25 \text{ kcal/mol} - 7 \text{ kcal/mol} = 18 \text{ kcal/mol} \]

- **For Reaction 2 (\( Q \rightarrow C \))**:
\[ \text{Ea}_{Q \rightarrow C} = \text{Energy of C} - \text{Energy of Q} = 20 \text{ kcal/mol} - 7 \text{ kcal/mol} = 3 \text{ kcal/mol} \]

5. **Compare Activation Energies**:
- \( \text{Ea}_{A+B \rightarrow Q} = 18 \text{ kcal/mol} \)
- \( \text{Ea}_{Q \rightarrow C} = 3 \text{ kcal/mol} \)

Since \( 18 \text{ kcal/mol} > 3 \text{ kcal/mol} \), the activation energy for the first reaction is greater than that for the second reaction.

6. **Determine Reaction Rates**:
According to the principle that lower activation energy leads to a faster reaction, we conclude:
- The reaction \( Q \rightarrow C \) is faster than \( A + B \rightarrow Q \).

7. **Select the True Statement**:
The correct statement is that the reaction \( Q \rightarrow C \) is faster than \( A + B \rightarrow Q \).

### Final Answer:
The true statement is: "The reaction \( Q \rightarrow C \) is faster than \( A + B \rightarrow Q \)."