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At $T(\mathrm{~K})$, the following data were obtained for a general reaction, $A+B+C \longrightarrow$ products
\begin{array}{ccccc}
\hline Expt. & \begin{array}{c}
Initial \\
{[A]}
\end{array} & \begin{array}{c}
Initial \\
{[B]}
\end{array} & \begin{array}{c}
Initial \\
{[C]}
\end{array} & Initial rate \\
\hline 1. & 0.02 \mathrm{M} & 0.1 \mathrm{M} & 0.03 \mathrm{M} & 2.4 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline 2. & 0.02 \mathrm{M} & 0.2 \mathrm{M} & 0.03 \mathrm{M} & 4.8 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline 3. & 0.02 \mathrm{M} & 0.2 \mathrm{M} & 0.06 \mathrm{M} & 9.6 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline 4. & 0.04 \mathrm{M} & 0.2 \mathrm{M} & 0.06 \mathrm{M} & 9.6 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline
\end{array}
The rate constant for the above reaction is
Options:
\begin{array}{ccccc}
\hline Expt. & \begin{array}{c}
Initial \\
{[A]}
\end{array} & \begin{array}{c}
Initial \\
{[B]}
\end{array} & \begin{array}{c}
Initial \\
{[C]}
\end{array} & Initial rate \\
\hline 1. & 0.02 \mathrm{M} & 0.1 \mathrm{M} & 0.03 \mathrm{M} & 2.4 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline 2. & 0.02 \mathrm{M} & 0.2 \mathrm{M} & 0.03 \mathrm{M} & 4.8 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline 3. & 0.02 \mathrm{M} & 0.2 \mathrm{M} & 0.06 \mathrm{M} & 9.6 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline 4. & 0.04 \mathrm{M} & 0.2 \mathrm{M} & 0.06 \mathrm{M} & 9.6 \times 10^{-6} \mathrm{~ms}^{-1} \\
\hline
\end{array}
The rate constant for the above reaction is
Solution:
2694 Upvotes
Verified Answer
The correct answer is:
$8.0 \times 10^{-4} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
Comparing expt. (1) and expt. (2).
When $[B]$ is doubled rate of reaction doubles.
$\therefore$ Reaction is first order is $B$.
Comparing expt. (2) and expt (3).
When $[C]$ is doubled rate of reaction doubles.
$\therefore$ Reaction is first order in $C$.
Comparing expt. [3] and expt [4]. When $[A]$ is doubled rate of reaction remains unchanged.
$\therefore$ Reaction is zero order in $A$.
Rate law $=K[A]^0[B]^{\prime}[C]^{\prime}$
Using data of expt. (1) we get
$$
\begin{aligned}
& 2.4 \times 10^{-6}=K[0.02]^0[0.1]^1[0.03]^1 \\
& 2.4 \times 10^{-6}=K \times 1 \times 0.1 \times 0.03 \\
& K=\frac{2.4 \times 10^{-6}}{3 \times 10^{-3}}=0.8 \times 10^{-3}=8.0 \times 10^{-4} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}
\end{aligned}
$$
When $[B]$ is doubled rate of reaction doubles.
$\therefore$ Reaction is first order is $B$.
Comparing expt. (2) and expt (3).
When $[C]$ is doubled rate of reaction doubles.
$\therefore$ Reaction is first order in $C$.
Comparing expt. [3] and expt [4]. When $[A]$ is doubled rate of reaction remains unchanged.
$\therefore$ Reaction is zero order in $A$.
Rate law $=K[A]^0[B]^{\prime}[C]^{\prime}$
Using data of expt. (1) we get
$$
\begin{aligned}
& 2.4 \times 10^{-6}=K[0.02]^0[0.1]^1[0.03]^1 \\
& 2.4 \times 10^{-6}=K \times 1 \times 0.1 \times 0.03 \\
& K=\frac{2.4 \times 10^{-6}}{3 \times 10^{-3}}=0.8 \times 10^{-3}=8.0 \times 10^{-4} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}
\end{aligned}
$$
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