Question

If $50\%$ of the reactant is converted into a product in a first order reaction in $25$ minutes, how much of it would react in $100$ minutes ?

• A. $93.75\%$
• B. $87.5\%$
• C. $75\%$
• D. $100\%$

Answer 1

Answer: (A)

Number of half-lives $=\frac{100}{25}=4$ i.e., $n=4$

Amount of the substance left after 4 half-lives

$=\frac{A^0}{2^n}(\because n=4)$

$=\frac{A^0}{2^4}=\frac{A^0}{16}=\frac{100}{16}=6.25\%$

$\therefore$ Amount of the substance converted into the product in $100\min =100-6.25=93.75\%$