Question

In a reaction 2A + B \(\rightarrow\) 3C, the concentration of A decreases from 0.5 mol L\textsuperscript{--1 to 0.3 mol L\textsuperscript{--1} in 10 minutes. The rate of production of 'C' during this period is}

• A. 0.01 mol L\textsuperscript{--1} min\textsuperscript{--1}
• B. 0.04 mol L\textsuperscript{--1} min\textsuperscript{--1}
• C. 0.05 mol L\textsuperscript{--1} min\textsuperscript{--1}
• D. 0.03 mol L\textsuperscript{--1} min\textsuperscript{--1}
• E. 0.02 mol L\textsuperscript{--1} min\textsuperscript{--1}

Hint:

Always remember to multiply the overall rate of reaction by the target species' coefficient to get its specific rate of production. Here, the overall rate is 0.01, so for C (coefficient 3), the rate is 0.03.

Answer 1

The Correct Option is D

Concept: The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time, adjusted for its stoichiometric coefficient.
• Rate of Reaction: For the reaction \(aA + bB \rightarrow cC\), the average rate is: \[ \text{Rate} = -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t} = +\frac{1}{c}\frac{\Delta [C]}{\Delta t} \]
• Rate of Disappearance: This is simply \(\frac{-\Delta [A]}{\Delta t}\).
• Rate of Production: This is simply \(\frac{\Delta [C]}{\Delta t}\).

Step 1: Calculate the rate of disappearance of A. Initial concentration \([A]_1 = 0.5\) mol L\textsuperscript{--1} Final concentration \([A]_2 = 0.3\) mol L\textsuperscript{--1} Time interval \(\Delta t = 10\) minutes \[ \text{Rate of disappearance of A} = \frac{- (0.3 - 0.5)}{10} = \frac{0.2}{10} = 0.02 \text{ mol L}^{-1} \text{ min}^{-1} \]

Step 2: Relate the rate of A to the rate of C. From the stoichiometry \(2A \rightarrow 3C\): \[ -\frac{1}{2} \frac{\Delta [A]}{\Delta t} = \frac{1}{3} \frac{\Delta [C]}{\Delta t} \] \[ \frac{\Delta [C]}{\Delta t} = \frac{3}{2} \left( -\frac{\Delta [A]}{\Delta t} \right) \] \[ \frac{\Delta [C]}{\Delta t} = \frac{3}{2} \times (0.02) = 3 \times 0.01 = 0.03 \text{ mol L}^{-1} \text{ min}^{-1} \]