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The following data are obtained for a reaction, $\mathrm{X}+\mathrm{Y} \rightarrow$ Products.
$\begin{array}{llll}\text { Expt. } & {\left[\mathrm{X}_{0}\right] / \mathrm{mol}} & {\left[\mathrm{Y}_{0}\right] / \mathrm{mol}} & \text { rate } / \mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1} \\ 1 & 0.25 & 0.25 & 1.0 \times 10^{-6} \\ 2 & 0.50 & 0.25 & 4.0 \times 10^{-6} \\ 3 & 0.25 & 0.50 & 8.0 \times 10^{-6}\end{array}$
The overall order of the reaction is
Options:
$\begin{array}{llll}\text { Expt. } & {\left[\mathrm{X}_{0}\right] / \mathrm{mol}} & {\left[\mathrm{Y}_{0}\right] / \mathrm{mol}} & \text { rate } / \mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1} \\ 1 & 0.25 & 0.25 & 1.0 \times 10^{-6} \\ 2 & 0.50 & 0.25 & 4.0 \times 10^{-6} \\ 3 & 0.25 & 0.50 & 8.0 \times 10^{-6}\end{array}$
The overall order of the reaction is
Solution:
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Verified Answer
The correct answer is:
5
$\mathrm{r}=\mathrm{K}[\mathrm{X}]^{\mathrm{x}}[\mathrm{Y}]^{\mathrm{y}}$
Total order $=\mathrm{n}=\mathrm{x}+\mathrm{y}$
By exp. (1) \& (2)
$\begin{array}{l}
\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{\mathrm{K}[.25]^{\mathrm{x}}[.25]^{\mathrm{y}}}{\mathrm{K}[.50]^{\mathrm{x}}[.25]^{\mathrm{y}}}=\frac{1.0 \times 10^{-6}}{4.0 \times 10^{-6}} \\
\frac{1}{(2)^{\mathrm{x}}}=\frac{1}{4}, \mathrm{x}=2
\end{array}$
By exp. (1) \& (3)
$\begin{array}{l}
\frac{r_{1}}{r_{3}}=\frac{K[.25]^{x}[.25]^{y}}{K[.25]^{x}[.50]^{y}}=\frac{1 \times 10^{-6}}{8 \times 10^{-6}} \\
\frac{1}{(2)^{y}}=\frac{1}{8}, y=3
\end{array}$
So Total order $=2+3=5$
Total order $=\mathrm{n}=\mathrm{x}+\mathrm{y}$
By exp. (1) \& (2)
$\begin{array}{l}
\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{\mathrm{K}[.25]^{\mathrm{x}}[.25]^{\mathrm{y}}}{\mathrm{K}[.50]^{\mathrm{x}}[.25]^{\mathrm{y}}}=\frac{1.0 \times 10^{-6}}{4.0 \times 10^{-6}} \\
\frac{1}{(2)^{\mathrm{x}}}=\frac{1}{4}, \mathrm{x}=2
\end{array}$
By exp. (1) \& (3)
$\begin{array}{l}
\frac{r_{1}}{r_{3}}=\frac{K[.25]^{x}[.25]^{y}}{K[.25]^{x}[.50]^{y}}=\frac{1 \times 10^{-6}}{8 \times 10^{-6}} \\
\frac{1}{(2)^{y}}=\frac{1}{8}, y=3
\end{array}$
So Total order $=2+3=5$
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