Solutions of two compounds, W and X, react together in the presence of a soluble catalyst, Y, as shown in the equation 2W + X → Z When the concentrations of W, X and Y are all doubled, the rate of reaction increases by a factor of four - AQA - A-Level Chemistry - Question 12 - 2018 - Paper 3

To determine the rate equation for the reaction, we need to consider how the rate of reaction is affected by the concentrations of the reactants.

From the information given, when the concentrations of W, X, and Y are all doubled, the rate of reaction increases by a factor of four. We will denote the rate of reaction as:

$ext{rate} = k[W]^m[X]^n[Y]^p$

Now, if we double the concentrations, our new rate will be:

$ext{rate}_{new} = k(2[W])^m(2[X])^n(2[Y])^p$

This simplifies to:

$ext{rate}_{new} = k imes 2^m[W]^m imes 2^n[X]^n imes 2^p[Y]^p = 2^{m+n+p} imes k[W]^m[X]^n[Y]^p$

According to the problem, this new rate is four times the original rate:

$ext{rate}_{new} = 4 imes ext{rate}_{original}$

This leads to:

$2^{m+n+p} = 4$

Since 4 can be expressed as $2^2$, we can equate the exponents:

$m + n + p = 2$

To find possible values for m, n, and p, we consider each reaction equation presented:

• For Option A: $rate = k[W]^2[X]$: Here, m=2, n=1 → $m + n = 3$ (not valid).
• For Option B: $rate = k[W]^2[Y]$: Here, m=2, p=1 → $m + p = 3$ (not valid).
• For Option C: $rate = k[X][Y]$: Here, n=1, p=1 → $m + n + p = 2$ (valid).
• For Option D: $rate = k[X][Z]$: This one is invalid as Z is a product (not applicable).

Thus, the valid answer based on the above analysis is:

C $rate = k[X][Y]$