A first order reaction takes 40 min for 30% decomposition. W... | CHEMISTRY - INTEGRATED RATE EQUATIONS | SolveeIt

A first order reaction takes 40 min for 30% decomposition. What will be $t_{1/2}$ ?

$77.7min.$

$52.5\min$

$46.2min.$

$22.7min.$

Answer

$77.7min.$

Explanation

30% decomposition means X = 30% of $R_{0}$ or

$R = R_{0} - 0.3R_{0} = 0.7R_{0}$

For first order, $k = \frac{2.303}{t}\log\frac{R_{0}}{R}$

$= \frac{2.303}{40}\log\frac{10}{7}\min^{- 1} = 8.918 \times 10^{- 3}\min^{- 1}{}$

$t_{1/2} = \frac{0.693}{k} = \frac{0.693}{8.918 \times 10^{- 3}\min^{- 1}} = 77.7\min$

Question: A first order reaction takes 40 min for 30% decomposition. What will be \(t_{1/2}\)?...