Question

The bromination of acetone that occurs in acid solution is represented by this equation.
$CH _{3} COCH _{3}( aq )+ Br _{2}( aq ) \rightarrow CH _{3} COCH _{2} Br ( aq )+ H ^{+}( aq )+ Br ^{-}( aq )$
These kinetic data were obtained for given reaction concentrations.

Based on given data, the rate equations is:

• A. Rate $=k\left[ CH _{3} COCH _{3}\right]\left[ H ^{+}\right]$
• B. Rate $=k\left[ CH _{3} COCH _{3}\right]\left[ Br _{2}\right]$
• C. Rate $=k\left[ CH _{3} COCH _{3}\right]\left[ Br _{2}\right]\left[ H ^{+}\right]^{2}$
• D. Rate $=k\left[ CH _{3} COCH _{3}\right]\left[ Br _{2}\right]\left[ H ^{+}\right]$

Answer 1

Answer: (A)

Rewriting the given data for the reaction
$CH _{3} COCH _{3}( aq ) + Br _{2}( aq ) \xrightarrow{ H ^{+}} CH _{3} COCH _{2} Br ( aq )+ H ^{+}( aq )+ Br ^{-}( aq )$
Actually this reaction is autocatalyzed and involves complex calculation for concentration terms.
We can look at the above results in a simple way to find the dependence of reaction rate (i.e., rate of disappearance of $Br_2)$
From data (1) and (2) in which concentration of $CH _{3} COCH _{3}$ and $H ^{+}$remain unchanged and only the concentration of $Br _{2}$ is doubled, there is no change in rate of reaction. It means the rate of reaction is independent of concentration of $Br _{2}$
Again from (2) and (3) in which $\left( CH _{3} COCH _{3}\right)$ and $\left( Br _{2}\right)$ remain constant but $H ^{+}$increases from $0.05 M$ to $0.10$ i.e. doubled, the rate of reaction changes from $5.7 \times 10^{-5}$ to $1.2 \times$ $10^{-4}$ (or $12 \times 10^{-5}$ ), thus it also becomes almost doubled. It shows that rate of reaction is directly proportional to $\left[ H ^{+}\right]$. From (3) and (4), the rate should have doubled due to increase in conc of $\left[ H ^{+}\right]$from $0.10 \,M$ to $0.20\, M$ but the rate has changed from $1.2 \times 10^{-4}$ to $3.1 \times 10^{-4}$. This is due to change in concentration of $CH _{3} COCH _{3}$ from $0.30\, M$ to $0.40$ $M$. Thus the rate is directly proportional to $\left[ CH _{3} COCH _{3}\right]$. We now get
rate $=k\left[ CH _{3} COCH _{3}\right]^{1}\left[ Br _{2}\right]^{0}\left[ H ^{+}\right]^{1}$
$=k\left[ CH _{3} CCH _{3}\right]\left[ H ^{+}\right]$
Trick : only option (a) can be correct if rate does not depend on $\left[ Br _{2}\right]$.