**Rate Expression and Reaction Order**

The rate expression of a chemical reaction represents the relationship between the rate of the reaction and the concentrations of the reactants. In this case, the rate expression for the reaction A + B → products is given as:

rate = k[A]^2[B]^3

Here, k is the rate constant, [A] is the concentration of A, and [B] is the concentration of B. The exponents of [A] and [B] represent the order of the reaction with respect to A and B, respectively.

**Doubling Concentrations**

When the concentrations of both A and B are doubled, the new concentrations are 2[A] and 2[B]. We need to determine the factor by which the rate will increase.

**Effect on Rate**

To determine the effect on the rate, we substitute the new concentrations into the rate expression:

rate' = k(2[A])^2(2[B])^3

Simplifying the expression:

rate' = k(4[A]^2)(8[B]^3)
rate' = 32k[A]^2[B]^3

Comparing this with the original rate expression:

rate' = 32(rate)

Therefore, when the concentrations of both A and B are doubled, the rate of the reaction increases by a factor of 32.

**Explanation**

The reason the rate increases by a factor of 32 is due to the relationship between concentration and reaction rate. In this reaction, the order of A is 2, which means that doubling the concentration of A will result in a rate increase of 2^2 = 4. Similarly, the order of B is 3, so doubling the concentration of B will result in a rate increase of 2^3 = 8.

Since both A and B are present in the rate expression, doubling the concentrations of both will result in a combined rate increase of 4 x 8 = 32.

This demonstrates the importance of the reaction order in determining the effect of concentration changes on the rate of the reaction. The reaction order reflects the sensitivity of the reaction rate to changes in the concentration of each reactant.

R =K [A]^p[B]^q
=k[A]^2[B]^3

if it's doubled r =([A]^2)^2([B]^3)^2
=32k [A][B]
r'/r=32

rate increases by factor of 32