In a hypothetical reaction `2X+Y rarr M+N`. If the concentration of `Y` is kept constant but that of `X` is tripled, the rate of reaction then will be

Options

A. Increased by `3` times
B. Increased by `6` times
C. Increased by `9` times
D. Unpredictable

Explanation

To solve the problem step by step, we need to analyze the given reaction and how the rate of reaction is affected by changes in concentration.

### Step 1: Write the Rate Law Expression
For the reaction \( 2X + Y \rightarrow M + N \), we can express the rate of reaction using the rate law. The general form of the rate law is:

\[ \text{Rate} = k [X]^a [Y]^b \]

where:
- \( k \) is the rate constant,
- \( [X] \) is the concentration of reactant \( X \),
- \( [Y] \) is the concentration of reactant \( Y \),
- \( a \) and \( b \) are the orders of the reaction with respect to \( X \) and \( Y \), respectively.

### Step 2: Analyze the Given Conditions
According to the problem, the concentration of \( Y \) is kept constant, and the concentration of \( X \) is tripled.

Let’s denote the initial concentration of \( X \) as \( [X] \) and the concentration of \( Y \) as \( [Y] \).

### Step 3: Calculate the New Rate
If the concentration of \( X \) is tripled, the new concentration of \( X \) becomes \( 3[X] \). The rate of the reaction with the new concentration of \( X \) can be expressed as:

\[ \text{New Rate} = k (3[X])^a [Y]^b \]

### Step 4: Simplify the New Rate Expression
Now, we can simplify the new rate expression:

\[ \text{New Rate} = k \cdot 3^a \cdot [X]^a \cdot [Y]^b \]

### Step 5: Compare the New Rate with the Original Rate
The original rate of the reaction is:

\[ \text{Original Rate} = k [X]^a [Y]^b \]

Now, we can express the new rate in terms of the original rate:

\[ \text{New Rate} = 3^a \cdot \text{Original Rate} \]

### Step 6: Determine the Effect of Tripling \( X \)
The factor \( 3^a \) indicates how the rate changes based on the order of the reaction with respect to \( X \).

- If \( a = 1 \), the rate increases by a factor of 3.
- If \( a = 2 \), the rate increases by a factor of 9.
- If \( a = 0 \), the rate remains unchanged.
- If \( a \) is unknown, we cannot predict the exact change in rate.

### Conclusion
Since we do not know the value of \( a \), we cannot determine the exact factor by which the rate increases. Therefore, the correct answer is that the change in rate is unpredictable.

### Final Answer
The rate of reaction will be **unpredictable**.

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