When two reactants, A and B are mixed to give products C and D, the reaction quotient Q, at the initial stages of the reaction

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Prashant Kotian · Accepted Answer

Correct answer: D. Step 1 - Define the Reaction Quotient ($Q$) For a general reversible reaction where reactants $\ce{A}$ and $\ce{B}$ are mixed to yield products $\ce{C}$ and $\ce{D}$: $$\ce{aA + bB <=> cC + dD}$$ The reaction quotient ($Q$) at any arbitrary instant of time is defined as the ratio of the product of the instantaneous molar concentrations of the products to that of the reactants, with each concentration term raised to a power equal to its stoichiometric coefficient: $$Q = \frac{[\ce{C}]^c [\ce{D}]^d}{[\ce{A}]^a [\ce{B}]^b}$$ Step 2 - Analyze the System at the Initial Instant ($t = 0$) At the absolute beginning of the reaction, when the reactants are first mixed together at time $t = 0$: * The concentration of reactants $[\ce{A}]$ and $[\ce{B}]$ are at their maximum. * No products have been formed yet. Therefore, the instantaneous concentrations of the products are exactly zero: $$[\ce{C}] = 0 \text{ M}, \quad [\ce{D}] = 0 \text{ M}$$ Substituting these values into the reaction quotient expression: $$Q = \frac{(0)^c (0)^d}{[\ce{A}]^a [\ce{B}]^b} = 0$$ Thus, at the exact starting point of the reaction, the reaction quotient is zero. Step 3 - Analyze the Progress of the Reaction in the Initial Stages ($t > 0$) As the system moves forward during the initial stages of the reaction: * The forward reaction occurs spontaneously to produce the products $\ce{C}$ and $\ce{D}$ from the reactants. * Consequently, the product concentrations $[\ce{C}]$ and $[\ce{D}]$ start to increase continuously from zero ($[\ce{C}] \uparrow$ and $[\ce{D}] \uparrow$). * At the same time, reactants $\ce{A}$ and $\ce{B}$ are consumed, so their concentrations begin to decrease ($[\ce{A}] \downarrow$ and $[\ce{B}] \downarrow$). Because the numerator is continuously increasing while the denominator is simultaneously decreasing, the value of the reaction quotient $Q$ must continuously **increase with time** during the initial stages of the reaction. This trend continues until the system reaches dynamic chemical equilibrium, at which point the concentrations of all species become constant, and $Q$ reaches its maximum plateau value, becoming equal to the equilibrium constant ($Q = K$). Step 4 - Evaluate the Options * **Option (A) "is zero"**: Incorrect. While $Q$ is exactly equal to zero at the absolute starting instant ($t = 0$), the phrase "at the initial stages of the reaction" refers to the continuous time interval after the reaction starts. Once the reaction begins ($t > 0$), products form immediately, meaning $Q$ is no longer zero. * **Option (B) "decreases with time"**: Incorrect. For a forward reaction starting with only reactants, the concentration of products in the numerator increases and reactants in the denominator decrease, which mathematically forces $Q$ to increase over time. * **Option (C) "is independent of time"**: Incorrect. Since the concentrations of the reactants and products are continuously changing as the reaction proceeds towards equilibrium, $Q$ is a time-dependent variable. * **Option (D) "increases with time"**: Correct. As reactants are converted into products, the value of $Q$ continuously increases from its starting value of zero until it matches the equilibrium constant. $$\boxed{\text{D}}$$

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