For a first order reaction, the half life is 60 minutes. In how many time reaction will completed 90%?

Question

Answer

Answer

Answer

H

Answer

Time for 90% completion of reaction

Given:

Half-life of the reaction = 60 minutes

To find:

Time taken for 90% completion of the reaction

Formula:

For a first order reaction, the fraction of reactant remaining after time t is given by:

$$ \frac{[A]}{[A]_0} = e^{-kt} $$

where [A] is the concentration of reactant at time t, [A]₀ is the initial concentration of reactant, k is the rate constant, and t is the time.

Solution

Calculate the rate constant (k):

Since the half-life of the reaction is 60 minutes, we can use the formula for half-life of a first order reaction:

$$ t_{1/2} = \frac{0.693}{k} $$

Substituting the given half-life value:

$$ 60 = \frac{0.693}{k} $$

Solving for k, we get:

$$ k = 0.693/60 = 0.01155 \, min^{-1} $$
Calculate the time for 90% completion:

We need to find the time at which 10% of the reaction is remaining. This is equivalent to 90% completion of the reaction.

Using the formula for a first order reaction:

$$ \frac{[A]}{[A]_0} = e^{-kt} $$

Substituting the values:

$$ 0.1 = e^{-0.01155 \times t} $$

Taking natural logarithm on both sides:

$$ ln(0.1) = -0.01155 \times t $$

Solving for t, we get:

$$ t = \frac{ln(0.1)}{-0.01155} \approx 167.8 \, minutes $$

Therefore, the time taken for 90% completion of the reaction is approximately 167.8 minutes.

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