Question

Calculate the time taken for $90\%$ completion of a first order reaction if the same reaction takes $69.3\text{minutes}$ for $50\%$ completion.

• A. $230.3\text{minutes}$
• B. $115.15\text{minutes}$
• C. $460.6\text{minutes}$
• D. None of these

Answer 1

The correct option is A $230.3\text{minutes}$

For a first order reaction,
Rate constant, $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{69.3}=0.01mi{n}^{-1}$
$k=\frac{2.303}{t}lo{g}_{10}\frac{a}{a-x}$
where, $a=$ initial amount of reactant
$(a-x)=$amount of reactant remaining after time t
${}^{\prime }{t}^{\prime }=0.1a$ for $90\%$ completion
$0.01=\frac{2.303}{t}lo{g}_{10}\frac{a}{0.1a}$
$t=\frac{2.303}{0.01}=230.3\text{min}$
Hence, (a) option is correct.