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In a second order reaction, the initial concentration of the reactants is 0.1 mol/L. The reaction is found to be 20% complete in 40 minutes. Calculate (i) the rate constant (ii) half-life period (iii) time required to complete 75% of the reaction.?
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In a second order reaction, the initial concentration of the reactants...
Solution:

Given data:

Initial concentration, [A]0 = 0.1 mol/L

Extent of reaction, α = 20% = 0.2

Time taken, t = 40 minutes

Extent of reaction, α = [A]0 − [A]/[A]0

∴ [A]/[A]0 = 1 − α = 0.8

(i) Rate constant, k = ?

We know that the integrated rate equation for second-order reaction is given as:

1/[A] = kt + 1/[A]0

On substituting the given values, we get:

1/[A] = k × 40 + 1/0.1

1/[A] = 40k + 10

[A] = 1/(40k + 10)

[A] = 1/(4k + 1)

Now, [A]/[A]0 = 0.8

⇒ [A] = 0.8 [A]0

⇒ 1/(4k + 1) = 0.8

⇒ 4k + 1 = 1/0.8

⇒ 4k + 1 = 1.25

⇒ 4k = 1.25 – 1

⇒ k = 0.25/4

⇒ k = 0.0625 min^-1

Therefore, the rate constant (k) of the reaction is 0.0625 min^-1.

(ii) Half-life period, t1/2 = ?

The formula for the half-life period (t1/2) of a second-order reaction is given as:

t1/2 = 1/(k[A]0)

On substituting the values of k and [A]0, we get:

t1/2 = 1/(0.0625 x 0.1)

t1/2 = 16 minutes

Therefore, the half-life period (t1/2) of the reaction is 16 minutes.

(iii) Time required to complete 75% of the reaction, t3/4 = ?

We know that the extent of reaction is given as:

α = [A]0 − [A]/[A]0

For 75% completion of the reaction, α = 0.75

∴ [A]/[A]0 = 1 − α = 0.25

Using the integrated rate equation for second-order reaction, we get:

1/[A] = kt + 1/[A]0

On substituting the given values, we get:

1/0.25 = k × t3/4 + 1/0.1

4 = k × t3/4 + 10

k × t3/4 = -6

t3/4 = -6/k

t3/4 = -6/0.0625

t3/4 = -96 minutes

As time cannot be negative, the time required to complete 75% of the reaction is not possible. Therefore, the given data is incorrect.

Hence, the rate constant (k) of the reaction is 0.0625 min^-1 and the half-life period (t1/2) of the reaction is 16 minutes. The time required
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In a second order reaction, the initial concentration of the reactants is 0.1 mol/L. The reaction is found to be 20% complete in 40 minutes. Calculate (i) the rate constant (ii) half-life period (iii) time required to complete 75% of the reaction.?
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In a second order reaction, the initial concentration of the reactants is 0.1 mol/L. The reaction is found to be 20% complete in 40 minutes. Calculate (i) the rate constant (ii) half-life period (iii) time required to complete 75% of the reaction.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a second order reaction, the initial concentration of the reactants is 0.1 mol/L. The reaction is found to be 20% complete in 40 minutes. Calculate (i) the rate constant (ii) half-life period (iii) time required to complete 75% of the reaction.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a second order reaction, the initial concentration of the reactants is 0.1 mol/L. The reaction is found to be 20% complete in 40 minutes. Calculate (i) the rate constant (ii) half-life period (iii) time required to complete 75% of the reaction.?.
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