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Half-life period of a first-order reaction is 10 minutes. Starting with 10 mol L−1, rate after 20 minutes will be

Question

Half-life period of a first-order reaction is 10 minutes. Starting with 10 mol L−1, rate after 20 minutes will be

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Solution

To find the rate after 20 minutes, we need to use the concept of half-life in a first-order reaction.

The half-life of a first-order reaction is the time it takes for the concentration of the reactant to decrease by half. In this case, the half-life period is given as 10 minutes.

Since the initial concentration is 10 mol L−1, after one half-life (10 minutes), the concentration will be reduced to 5 mol L−1.

Now, we need to determine how many half-lives have passed in 20 minutes. Since each half-life is 10 minutes, we can divide the total time (20 minutes) by the half-life period (10 minutes) to find the number of half-lives.

20 minutes / 10 minutes = 2 half-lives

Therefore, after 20 minutes, two half-lives have passed.

To find the rate after 20 minutes, we need to determine the concentration after two half-lives.

After the first half-life, the concentration is reduced to 5 mol L−1. After the second half-life, the concentration is reduced by half again:

5 mol L−1 / 2 = 2.5 mol L−1

So, the rate after 20 minutes will be 2.5 mol L−1.

This problem has been solved

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Rate of Reaction: Rate = - Δ[Reactant]/Δt = Δ[Product]/Δt Rate Law: Rate = k[A]^x[B]^y First Order Reaction: ln[A]t = -kt + ln[A]0 Second Order Reaction: 1/[A]t = kt + 1/[A]0 Zero Order Reaction: [A]t = -kt + [A]0 Half-Life (t1/2) for First Order Reaction: t1/2 = 0.693/k Half-Life (t1/2) for Second Order Reaction: t1/2 = 1/(k[A]0) Half-Life (t1/2) for Zero Order Reaction: t1/2 = [A]0/2k Arrhenius Equation: k = Ae^(-Ea/RT) where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Integrated Rate Law for First Order Reaction: ln([A]0/[A]t) = kt Integrated Rate Law for Second Order Reaction: 1/[A]t - 1/[A]0 = kt Integrated Rate Law for Zero Order Reaction: [A]0 - [A]t = kt

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