Question

A substance reacts according to the first order rate law and the specific reaction rate for the reaction is $1\times {10}^{-2}{s}^{-1}.$ If the initial concentration is 1.0 M. What is the reaction rate after 1 minute ?
${10}^{-0.26}\approx 5.5$

• A. $5.5\times {10}^{-6}\text{mol}{L}^{-1}{s}^{-1}$
• B. $5.5\times {10}^{-3}\text{mol}{L}^{-1}{s}^{-1}$
• C. $5.5\times {10}^{-1}\text{mol}{L}^{-1}{s}^{-1}$
• D. None of the above

Answer 1

The correct option is B $5.5\times {10}^{-3}\text{mol}{L}^{-1}{s}^{-1}$

Initial rate of a first order reaction = kC
$=1\times {10}^{-2}\times 1.0$
$=1\times {10}^{-2}\text{mol}{L}^{-1}{s}^{-1}$
Concentration after 60 seconds is calculated by applying first order kinetic equation,
$k=\frac{2.303}{60}lo{g}_{10}\frac{1}{(1-x)}$
or $1\times {10}^{-2}=\frac{2.303}{60}[-log(1-x\left)\right]$
or $\frac{60\times {10}^{-2}}{2.303}=-log(1-x)=0.2605$
$log(1-x)=-0.2605$

$(1-x)=\text{antilog}(-0.26)=0.55\text{mol L^{-1}}$
Rate of reaction after 1 minute $=k\times C$
$=1\times {10}^{-2}\times 0.55$
$=5.5\times {10}^{-3}\text{mol}{L}^{-1}{s}^{-1}$