Question

After $315$ seconds of a reaction, one-quarter of reactant $A$ remains. What is the half-life of the reaction if it is known to be a first order reaction?

• A. $78.75$ seconds
• B. $0.004401$ seconds
• C. $157.5$ seconds
• D. $315$ seconds

Answer 1

The correct option is C $157.5$ seconds

For first order reaction,

$K=\frac{2.303}{t}\log \frac{\left[A_o\right]}{\left[A_t\right]}$

Here, $\left[A_t\right]=\frac{\left[A_o\right]}{4}$and $t=315seconds$

$\therefore K=\frac{2.303}{315}\log \left(\frac{\left[A_o\right]\times 4}{\left[A_o\right]}\right)$

$\therefore K=4.4\times {10}^{-3}{sec}^{-1}$

$\therefore t_{1/2}=\frac{\ln 2}{K}$

$=\frac{0.693}{4.4\times {10}^{-3}}seconds$

$t_{1/2}=157.5seconds$