Question

The half life of a $1^{st}$ order reaction is $1$min $40$ seconds. Calculate its rate constant.

• A. $6.9\times {10}^{-3}mi{n}^{-1}$
• B. $6.9\times {10}^{-3}{s}^{-1}$
• C. $6.9\times {10}^{-3}$s
• D. $100$s

Answer 1

Answer: (B)

$6.9\times {10}^{-3}{s}^{-1}$

The half life of a $1^{st}$ order reaction is $1$min $40$ seconds.
Convert minutes into seconds.
$1min=60s$

$t_{1/2}=1min+40s$

$t_{1/2}=60s+40s$

$t_{1/2}=100s$
$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{100s}$

The rate constant is $k=6.9\times {10}^{-3}{s}^{-1}$