QuestionSeptember 20, 2025

If a reaction is first order with a rate constant of 0.0450 s^-1 how much time is required for 75% of the initial quantity of reactant to be consumed? Answer: square S

If a reaction is first order with a rate constant of 0.0450 s^-1 how much time is required for 75% of the initial quantity of reactant to be consumed? Answer: square S
If a reaction is first order with a rate constant of 0.0450 s^-1 how much time is required for 75% of the initial quantity of reactant to be consumed? Answer: square S

Solution
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Answer

30.8 s Explanation 1. Write the first-order decay formula Use [A] = [A]_0 e^{-kt}, where k = 0.0450\, s^{-1}. 2. Set up for 75% consumption 75\% consumed means [A] = 0.25[A]_0. 3. Solve for time t 0.25 = e^{-0.0450 t} \implies \ln(0.25) = -0.0450 t \implies t = \frac{\ln(0.25)}{-0.0450}. 4. Calculate value \ln(0.25) = -1.3863, so t = \frac{-1.3863}{-0.0450} = 30.8 s.

Explanation

1. Write the first-order decay formula<br /> Use $[A] = [A]_0 e^{-kt}$, where $k = 0.0450\, s^{-1}$.<br />2. Set up for 75% consumption<br /> $75\%$ consumed means $[A] = 0.25[A]_0$.<br />3. Solve for time $t$<br /> $0.25 = e^{-0.0450 t} \implies \ln(0.25) = -0.0450 t \implies t = \frac{\ln(0.25)}{-0.0450}$.<br />4. Calculate value<br /> $\ln(0.25) = -1.3863$, so $t = \frac{-1.3863}{-0.0450} = 30.8$ s.
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