JEE Main 2021: Rate of Appearance and Disappearance

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Daily Challenge JEE Main 2021 (27 Aug, Shift 1)

Rates of Appearance and Disappearance

Connect the rate of change of individual species to the overall reaction stoichiometry.

Question:

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is:

$$ 2K_2Cr_2O_7 + 8H_2SO_4 + 3C_2H_6O \rightarrow 2Cr_2(SO_4)_3 + 3C_2H_4O_2 + 2K_2SO_4 + 11H_2O $$

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)

Enter your integer answer:

Detailed Solution

Concept Check: The Rate of Reaction is constant for the whole equation. To equate the rates of individual components, you must divide the rate of disappearance (for reactants) or appearance (for products) by their respective stoichiometric coefficients.

Step 1: Write the Rate Expression

From the balanced chemical equation, look specifically at the two species in question: ethanol ($C_2H_6O$) and chromium(III) sulfate ($Cr_2(SO_4)_3$).

$$ \text{Rate of Reaction} = -\frac{1}{3} \frac{d[C_2H_6O]}{dt} = +\frac{1}{2} \frac{d[Cr_2(SO_4)_3]}{dt} $$

Note: The negative sign just indicates disappearance. The "rate of disappearance" itself is a positive quantity: $-\frac{d[C_2H_6O]}{dt}$.

Step 2: Substitute Known Values

We are given the rate of appearance of $Cr_2(SO_4)_3$:

$$ \frac{d[Cr_2(SO_4)_3]}{dt} = 2.67 \text{ mol min}^{-1} $$

Substitute this into our equated expression from Step 1:

$$ \frac{1}{3} \left(-\frac{d[C_2H_6O]}{dt}\right) = \frac{1}{2} (2.67) $$

Step 3: Solve for Rate of Disappearance

Isolate the term for the rate of disappearance of $C_2H_6O$:

$$ -\frac{d[C_2H_6O]}{dt} = \frac{3}{2} \times 2.67 $$ $$ -\frac{d[C_2H_6O]}{dt} = 1.5 \times 2.67 $$ $$ -\frac{d[C_2H_6O]}{dt} = 4.005 \text{ mol min}^{-1} $$

The question asks for the answer to the nearest integer.

$4.005$ rounds to $\mathbf{4}$.

Final Answer: 4

Exam Trap: Don't Confuse the Terms!

• Rate of Disappearance/Appearance: This is literally just how fast a specific chemical is vanishing or forming (e.g., $\frac{d[A]}{dt}$). It does not include the stoichiometric coefficient.
• Rate of Reaction: This is the standardized rate for the whole chemical equation. It does include dividing by the stoichiometric coefficient (e.g., $\frac{1}{a}\frac{d[A]}{dt}$).

Review Reaction Rates

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