Question

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is:
\(2 K_2Cr_2O_7 + 8 H_2SO_4 + 3 C_2H_6O \to 2 Cr_2(SO_4)_3 + 3 C_2H_4O_2 + 2 K_2SO_4 + 11 H_2O\)
If the rate of appearance of \(Cr_2(SO_4)_3\) is \(2.67 \, \text{mol min}^{-1}\) at a particular time, the rate of disappearance of \(C_2H_6O\) at the same time is _________ \(\text{mol min}^{-1}\). (Nearest integer)

Hint:

For any reaction \(aA \to bB\), the relationship between rates is \(\frac{1}{a}(\text{Rate of consumption of } A) = \frac{1}{b}(\text{Rate of production of } B)\).

Answer 1

Correct Answer: 4

Step 1: Understanding the Concept:
The relative rates of reaction are proportional to the stoichiometric coefficients of the balanced chemical equation.
Step 2: Detailed Explanation:
From the balanced equation:
Coefficient of \(C_2H_6O\) is 3.
Coefficient of \(Cr_2(SO_4)_3\) is 2.
Relation between rates:
\[ -\frac{1}{3} \frac{d[C_2H_6O]}{dt} = +\frac{1}{2} \frac{d[Cr_2(SO_4)_3]}{dt} \]
Given: \(\frac{d[Cr_2(SO_4)_3]}{dt} = 2.67 \, \text{mol min}^{-1}\).
Rate of disappearance of \(C_2H_6O\) (\(-\frac{d[C_2H_6O]}{dt}\)):
\[ \text{Rate} = \frac{3}{2} \times 2.67 = 1.5 \times 2.67 = 4.005 \, \text{mol min}^{-1} \]
Step 3: Final Answer:
Rounding to the nearest integer, the rate is 4.