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  • Consider the reaction <img alt="a \mathrm{~A}+b \mathrm{~B} \longrightarrow" src="https://entrancecorner.oncodecogs.com/gif.latex?a%20%5Cmathrm%7B%7EA%7D&plus;b%20%5Cmathrm%7B%7EB%7D%20%5Clongr

Consider the reaction a \mathrm{~A}+b \mathrm{~B} \longrightarrow Products. When the concentration of both the reactants \text{A and B} is doubled, the rate increases by sixteen times. However, when the concentration of \text{A} is doubled keeping the concentration of \mathrm{B} fixed, the rate is doubled. The overall order of reaction is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

To determine the overall order of the reaction, we can analyze the effect of concentration changes on the rate.

Let's start by considering the first scenario where the concentrations of both reactants A and B are doubled, and the rate increases by sixteen times. This information suggests that the rate equation for this reaction can be expressed as:

\text { Rate }=k[A]^m[B]^n

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

When both [A] and [B] are doubled, the new rate becomes 16 times the original rate:

(2[A])^m \cdot(2[B])^n=16 \cdot\left([A]^m \cdot[B]^n\right)

Simplifying, we have:

\begin{aligned} & 2^m \cdot 2^n=16 \\ & 2^{(m+n)}=16 \\ & 2^{(m+n)}=2^4 \quad\left(\text { since } 16=2^4\right) \end{aligned}

By comparing the exponents, we can conclude that:

m+n=4(\text { Equation } 1)

Now let's consider the second scenario where only the concentration of A is doubled while the concentration of B is fixed. The rate in this case is doubled. Using the rate equation, we have:

\text { Rate }=k[A]^m[B]^n

When [A] is doubled while [B] remains constant, the new rate becomes twice the original rate:

(2[A])^m \cdot[B]^n=2 \cdot\left([A]^m \cdot[B]^n\right)

Simplifying, we have:

\begin{aligned} & 2^m \cdot 1^n=2 \\ & 2^m=2 \\ & m=1(\text { Equation } 2) \end{aligned}

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

Overall order =m+n=1+3=4

Hence, the overall order of the reaction is 4.

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vinayak

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