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Order of Reaction Determination

For a rxn A+B-----> P if conc. of A is increased by 3 times, then the rate becomes √3 times and if conc. of B is increased by 2 times, rate of rxn becomes 4√2 times. Find the order of reaction and order of individual reactant?????

To determine the order of reaction and the order of individual reactants, we can use the given information and the concept of rate equations.

Let's assume the rate equation for the reaction is:

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

Where:

Rate is the rate of the reaction,

k is the rate constant,

[A] is the concentration of reactant A,

[B] is the concentration of reactant B,

m is the order of reactant A, and

n is the order of reactant B.

From the given information, we have two sets of conditions:

Condition 1:

[A] increases by 3 times, and the rate becomes √3 times.

Condition 2:

[B] increases by 2 times, and the rate becomes 4√2 times.

Let's analyze each condition separately:

Condition 1:

If [A] increases by 3 times and the rate becomes √3 times, we can write the following relationship:

Rate₁ = k[A]₁^m[B]₁^n

Rate₂ = k[A]₂^m[B]₂^n

Rate₂/Rate₁ = (√3) / 1

(Assuming [B] remains constant)

Substituting the values, we get:

(k[A]₂^m[B]₂^n) / (k[A]₁^m[B]₁^n) = (√3) / 1

([A]₂ / [A]₁)^m = (√3) / 1

Since [A]₂ is 3 times [A]₁, we can substitute that in:

(3)^m = (√3) / 1

3^m = √3

Taking the square of both sides:

(3^m)^2 = (√3)^2

3^(2m) = 3

2m = 1

m = 1/2

So, the order of reactant A (m) is 1/2.

Condition 2:

If [B] increases by 2 times and the rate becomes 4√2 times, we can write the following relationship:

Rate₃ = k[A]₃^m[B]₃^n

Rate₃/Rate₁ = (4√2) / (√3)

(Assuming [A] remains constant)

Substituting the values, we get:

(k[A]₃^m[B]₃^n) / (k[A]₁^m[B]₁^n) = (4√2) / (√3)

([B]₃ / [B]₁)^n = (4√2) / (√3)

Since [B]₃ is 2 times [B]₁, we can substitute that in:

(2)^n = (4√2) / (√3)

2^n = 2√2 / √3

(2^n)^2 = (2√2 / √3)^2

2^(2n) = 8(2) / 3

2^(2n) = 16 / 3

2n = log₂(16 / 3)

2n ≈ 2.415

So, the order of reactant B (n) is approximately 1.208.

Therefore, the overall order of the reaction is the sum of the individual reactant orders:

Overall order = m + n

Overall order ≈ 1/2 + 1.208

Overall order ≈ 1.708

To summarize:

The order of reactant A is approximately 1/2.

The order of reactant B is approximately 1.208.

The overall