Calculate the order of reaction A+B gives p in the terms of A and B. If the concentration of reactants are doubled the rate becomes 2times the initial rate and if rate get tripled rate becomes three times the initial rate?

To determine the order of the reaction A + B → P in terms of reactants A and B, we can use the information provided about how the rate changes with varying concentrations of the reactants. Let's break this down step by step.

Understanding Reaction Rates

The rate of a chemical reaction can be expressed using the rate law, which relates the rate of the reaction to the concentrations of the reactants. For a reaction like A + B → P, the rate law can be written as:

Rate = k[A]^m[B]^n

Here, k is the rate constant, [A] and [B] are the concentrations of reactants A and B, and m and n are the orders of the reaction with respect to A and B, respectively.

Analyzing the Given Information

You mentioned that when the concentrations of A and B are doubled, the rate becomes twice the initial rate. This can be expressed mathematically:

If we double the concentrations:

• New concentration of A = 2[A]
• New concentration of B = 2[B]

The new rate becomes:

New Rate = k(2[A])^m(2[B])^n = k(2^m[A]^m)(2^n[B]^n) = k(2^(m+n)[A]^m[B]^n

Since this new rate is twice the initial rate, we can set up the equation:

k(2^(m+n)[A]^m[B]^n) = 2(k[A]^m[B]^n)

By simplifying, we find:

2^(m+n) = 2

This implies:

m + n = 1

Considering the Tripling of the Rate

If we triple the concentrations:

• New concentration of A = 3[A]
• New concentration of B = 3[B]

The new rate becomes:

New Rate = k(3[A])^m(3[B])^n = k(3^m[A]^m)(3^n[B]^n) = k(3^(m+n)[A]^m[B]^n)

Setting this equal to three times the initial rate gives us:

k(3^(m+n)[A]^m[B]^n) = 3(k[A]^m[B]^n)

By simplifying, we find:

3^(m+n) = 3

This implies:

m + n = 1

Determining the Individual Orders

From both scenarios, we have established that:

m + n = 1

Now, we need to find specific values for m and n. One common way to do this is to assume a simple case where both reactants contribute equally to the rate. If we assume:

m = 1 and n = 0 (first order with respect to A and zero order with respect to B), or

m = 0 and n = 1 (zero order with respect to A and first order with respect to B),

Both cases satisfy the equation m + n = 1. However, without additional information, we cannot definitively determine the individual orders.

Final Thoughts

In summary, the overall order of the reaction A + B → P is 1, but the specific contributions of A and B (the values of m and n) could be either (1, 0) or (0, 1) based on the information provided. Further experimental data would be needed to clarify the individual orders.