The 1st order reaction is 60% complete in 20 minutes. How long will the reaction take to be 84% complete?

• A. 54
• B. 68
• C. 40
• D. 76

To determine how long it will take for a first-order reaction to reach 84% completion, we can use the first-order kinetics equation. The equation is:

First-Order Reaction Formula

The formula for a first-order reaction is:

ln([A]₀/[A]) = kt

Where:

• [A]₀ = initial concentration
• [A] = concentration at time t
• k = rate constant
• t = time

Step 1: Calculate the Rate Constant (k)

Given that the reaction is 60% complete in 20 minutes, this means 40% of the reactant remains. We can set up the equation:

ln(1/0.4) = k * 20

Calculating this gives:

ln(2.5) ≈ 0.9163

Now, solving for k:

k ≈ 0.9163 / 20 ≈ 0.0458 min⁻¹

Step 2: Calculate Time for 84% Completion

For 84% completion, 16% of the reactant remains. We set up the equation:

ln(1/0.16) = kt

Calculating this gives:

ln(6.25) ≈ 1.8325

Now, substituting k into the equation:

1.8325 = 0.0458 * t

Solving for t:

t ≈ 1.8325 / 0.0458 ≈ 39.98 minutes

Final Answer

Therefore, the time required for the reaction to be 84% complete is approximately 40 minutes. The correct option is C.