For a reaction, X + Y + Z ? Products the concentration of X is doubled keeping that of Y and Z constant. The rate of the reaction increases by four times. What is the order of the reaction? a) 2 b) 4 c) 1 d) 0

To determine the order of the reaction based on the information provided, we can use the rate law concept. The rate of a reaction is often expressed in terms of the concentrations of the reactants raised to their respective powers, which correspond to the order of the reaction with respect to each reactant.

Understanding the Rate Law

The general form of the rate law for a reaction involving reactants X, Y, and Z can be expressed as:

Rate = k [X]^m [Y]^n [Z]^p

Here, k is the rate constant, and m, n, and p represent the orders of the reaction with respect to reactants X, Y, and Z, respectively.

Analyzing the Given Information

In your scenario, we know that:

• The concentration of X is doubled: [X] becomes 2[X].
• The concentrations of Y and Z remain constant.
• The rate of the reaction increases by four times.

Setting Up the Equation

Let's denote the initial rate of the reaction as Rate₁ and the new rate after doubling the concentration of X as Rate₂. According to the information provided:

Rate₂ = 4 × Rate₁

Expressing Rates in Terms of Concentrations

Initially, the rate can be expressed as:

Rate₁ = k [X]ⁿ [Y]ⁿ [Z]ⁿ

After doubling the concentration of X, the new rate becomes:

Rate₂ = k (2[X])ⁿ [Y]ⁿ [Z]ⁿ

This simplifies to:

Rate₂ = k (2ⁿ [X]ⁿ) [Y]ⁿ [Z]ⁿ = 2ⁿ × Rate₁

Relating the Rates

Since we know that Rate₂ = 4 × Rate₁, we can set the two expressions equal to each other:

2ⁿ × Rate₁ = 4 × Rate₁

Dividing both sides by Rate₁ (assuming it is not zero), we get:

2ⁿ = 4

Solving for n

Now, we can solve for n:

2ⁿ = 2²

This implies that:

n = 2

Conclusion

The order of the reaction with respect to reactant X is 2. Therefore, the correct answer is a) 2.