‹ Back to the paper
Solve the following.
25% of a first order reaction is completed in 30 minutes. Calculate the time taken in minutes for…
$25\%$ of a first order reaction is completed in $30\text{ minutes}$. Calculate the time taken in minutes for the reaction to go to $90\%$ completion.
Answer
Answer
Formulas used: First-order integrated rate law: k = 2.303/t*log10(A0/A) with A = 75, t = 30 min, A0 = 100, so k = 0.00959 min^-1 First-order integrated rate law: k = 2.303/t*log10(A0/A) with A = 10, k = 0.00959 min^-1, A0 = 100, so t = 240 min
Formula: $k = \dfrac{2\cdot303}{t}\log\dfrac{[\mathrm{A}]_0}{[\mathrm{A}]}$
For $25\%$ completion in $30\text{ min}$: $[\mathrm{A}]_0 = 100$, $[\mathrm{A}] = 75$
$k = \dfrac{2\cdot303}{30\text{ min}}\log\dfrac{100}{75} = 9\cdot59\times10^{-3}\text{ min}^{-1}$
For $90\%$ completion: $[\mathrm{A}] = 10$
$t = \dfrac{2\cdot303}{9\cdot59\times10^{-3}\text{ min}^{-1}}\log\dfrac{100}{10} = 240\text{ min}$
Final answer: 240 min