Reactions: `2A+B+2C to D` follows three mechanistic steps: `2A+B to X (slow)` `X+C to Y` (fast) `Y+C to D` (fast)
What is the molecularity of the rate determining step and the total order of the reaction?

Options

A. 3,2
B. 3,3
C. 5,2
D. 5,3

Answer

To solve the problem, we need to analyze the given reaction and its mechanistic steps to determine the molecularity of the rate-determining step and the total order of the reaction.

### Step-by-Step Solution:

1. **Identify the Rate-Determining Step:**
The first step of the reaction is given as:
\[ 2A + B \rightarrow X \quad (\text{slow step}) \]
Since this is the slow step, it is the rate-determining step.

2. **Determine the Molecularity of the Rate-Determining Step:**
Molecularity is defined as the number of reactant molecules involved in an elementary reaction. In the rate-determining step:
- There are 2 molecules of A.
- There is 1 molecule of B.

Therefore, the molecularity of the rate-determining step is:
\[ \text{Molecularity} = 2 \, (\text{from } A) + 1 \, (\text{from } B) = 3 \]

3. **Write the Rate Law for the Reaction:**
The rate law can be derived from the rate-determining step. Since the rate-determining step is:
\[ 2A + B \rightarrow X \]
The rate law can be expressed as:
\[ \text{Rate} = k [A]^2 [B]^1 \]
where \( k \) is the rate constant.

4. **Calculate the Total Order of the Reaction:**
The total order of a reaction is the sum of the powers of the concentration terms in the rate law. From the rate law:
- The order with respect to A is 2.
- The order with respect to B is 1.

Therefore, the total order of the reaction is:
\[ \text{Total Order} = 2 + 1 = 3 \]

### Final Answers:
- **Molecularity of the Rate-Determining Step:** 3
- **Total Order of the Reaction:** 3