The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a per

Question

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is\ $2 \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}+8 \mathrm{H}_{2} \mathrm{SO}_{4}+3 \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} ightarrow 2 \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}ight)_{3}+$ $$ 3 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}+2 \mathrm{~K}_{2} \mathrm{SO}_{4}+11 \mathrm{H}_{2} \mathrm{O} $$ If the rate of appearance of $\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}ight)_{3}$ is $2.67 \mathrm{~mol} \mathrm{~min}^{-1}$ at a particular time, the rate of disappearance of $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}$ at the same time is _______ $\mathrm{mol} \mathrm{min}{ }^{-1}$. (Nearest integer)\

Professor PC Thomas Classes · Answer

(4): The rate law for the given reaction will be,\ $2 \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}+8 \mathrm{H}_{2} \mathrm{SO}_{4}+3 \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} \longrightarrow$ $$ \begin{aligned} & 2 \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}ight)_{3}+3 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}+2 \mathrm{~K}_{2} \mathrm{SO}_{4} \ &+11 \mathrm{H}_{2} \mathrm{O} \end{aligned}, \begin{aligned} & \Rightarrow-\frac{1}{3} \frac{d\left[\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}ight]}{d t}=\frac{1}{2} \frac{d\left[\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}ight)_{3}ight]}{d t} \ & \Rightarrow \ & = \ & -\frac{d\left[\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}ight]}{d t}=\frac{3}{2} 	imes \frac{d\left[\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}ight)_{3}ight]}{d t} \end{aligned} $$