Question

$80\%$ of a first order reaction was completed in $70min$. How much time will take for $90\%$ completion of a reaction?

• A. $114min$
• B. $100min$
• C. $140min$
• D. $70min$

Answer 1

The correct option is B $100min$

For a first order reaction we have:

$k=\frac{1}{t}ln\frac{a}{a-x}\left(i\right)$

where, $k=$rate constant of reaction
$t$ = time
$a$ = initial concentration of the reactant
$x$ = amount of reactant reacted in time t

Since, the reactant has reacted $80\%$ in $70min$, the remaining reactant is $20\%$

At $t=70min$,
$k=\frac{1}{70}ln\frac{100}{20}$
$k=0.023$

Time required for 90% completion of reaction is,
$k=\frac{1}{t}ln\frac{100}{100-90}$

$0.023=\frac{1}{t}ln\frac{100}{10}$

$0.023=\frac{2.303}{t}log\frac{100}{10}$

$t=\frac{2.303}{0.023}log\frac{100}{10}$
$t\approx 100min$

Hence, (b) is the correct option.