Question

A solution of $A$ is mixed with an equal volume of a solution of $B$ containing the same number of moles, and the reaction $A+B⟶C$ occurs. At the end of 1 hour, $A$ is $75$% reacted. The amount of $A$ that will be left unreacted at the end of $2$ hours if the reaction is first order in $A$ and zero order in $B$ is:

• A. $6.25$
• B. $7.28$
• C. $8.43$
• D. $8.92$

Answer 1

Answer: (A)

$6.25$

The integrated rate law for the first order reaction is $k=\frac{2.303}{t}log\frac{[A{]}_0}{[A{]}_t}$.

For $t=1hr$,

$k=\frac{2.303}{1}log\frac{100}{(100-75)}$ -------- (1)

For $t=2hr$,

$k=\frac{2.303}{2}log\frac{100}{[A{]}_t}$ -------- (2)

From equations (1) and (2),

$\frac{2.303}{1}log\frac{100}{(100-75)}=\frac{2.303}{2}log\frac{100}{[A{]}_t}$

Hence, $[A{]}_t=6.25$