Question

A substance A decomposes in solution following the first order kinetics. Flask I contains 1 L of 1 M solution of A and flask II contains 100 mL of 0.6 M solution. After 8 hr, the concentration, of A in the flask I becomes 0.25 M. What will be the time for the concentration of A in flask II to become 0.3 M?

• A. 0.4 hr
• B. 2.4 hr
• C. 4.0 hr
• D. Unpredictable as rate constant is not given

Answer 1

The correct option is C 4.0 hr

For $1^{st}$ order reaction.

$k=\frac{2.303}{t}log\frac{\left[A_0\right]}{\left[A\right]}$

For flask I

$k=\frac{2.303}{8}log\frac{\left[1\right]\left[4\right]}{\left[0.25\right]}$ _____ (1)

for flask II

$k=\frac{2.303}{t}log\frac{0.62}{0.3}$ ______ (2)

From (1) and (2)

$\frac{2.303}{8}log4=\frac{2.303}{t}log2$

$t=\frac{8log2}{log4}=\frac{8log2}{2log2}=4$

$\therefore$ time = 4 hours.