Problem 21 - A Complete Resource Book in Chemistry for JEE Main

Question

When two reactants \(\mathrm{A}\) and are mixed to give products and \(D\), the reaction quotient \(Q\), at the initial stages of the reaction (a) is zero (b) decreases with time (c) is independent of time (d) increases with time

Step-by-Step Solution

Answer

The reaction quotient \( Q \) is zero initially and increases with time.

Step 1: Understand the Reaction Quotient

The reaction quotient, denoted as \( Q \), is a measure of the relative amounts of products and reactants during a reaction at a particular point in time. It is similar in form to the equilibrium constant \( K \), but unlike \( K \), \( Q \) can be used at any time before the system reaches equilibrium.

Step 2: Consider Initial Reaction Condition

At the initial stages of the reaction, the reactants are just starting to form products. If the reaction starts with only reactants and no products, initially there are zero products present. Thus, the concentration terms for products in the expression for \( Q \) are initially zero.

Step 3: Apply the Definition of Reaction Quotient

The reaction quotient \( Q \) is calculated using the expression:\[ Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]where \([A], [B], [C], [D]\) are the concentrations of reactants and products, and \(a, b, c, d\) are the stoichiometric coefficients. At the start, the concentrations of \( C \) and \( D \) (products) are zero.

Step 4: Evaluate the Initial Value of Q

Since the initial concentrations of the products \( C \) and \( D \) are zero, the numerator of the expression for \( Q \) becomes zero:\[ Q = \frac{0 \, (0)}{[A]^a[B]^b} = 0 \]This implies that at the very beginning of the reaction, \( Q = 0 \).

Step 5: Analyze Change Over Time

As the reaction proceeds, products \( C \) and \( D \) begin to form, increasing their concentrations. Consequently, the numerator of the reaction quotient expression increases, indicating that \( Q \) will increase as time progresses and more products are formed.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry that describes the state a reversible reaction reaches when the rates of the forward and reverse reactions are equal. At this point, the concentrations of both reactants and products remain constant over time. However, equilibrium does not mean the reactions have stopped; they continue to occur, but their effects cancel each other out.
At equilibrium, the system's reaction quotient (Q) equals the equilibrium constant (K). The expression for chemical equilibrium involves products divided by reactants, with each concentration raised to the power of its respective stoichiometric coefficient:\[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] Here, [A], [B], [C], [D] are the concentrations of the chemical species, while a, b, c, d are the stoichiometric coefficients from the balanced chemical equation. Depending on the value of K, the equilibrium can lie towards the reactants or products side, indicating which species are in greater concentration at equilibrium.
In practice, shifts in equilibrium can occur if the system experiences changes in concentration, temperature, or pressure, highlighting the dynamic nature of chemical reactions.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It helps us understand how much of each substance we need or can expect to get from a reaction.
The balanced chemical equation plays a crucial role in stoichiometry. For example, if you have a reaction: \[ aA + bB \rightarrow cC + dD \] The coefficients a, b, c, and d tell you how many moles of reactants are needed to produce a specific amount of products. This allows chemists to convert between masses, moles, and units of concentration.
Using stoichiometry, you can calculate the amount of reactant needed or product formed. For instance, if you know the amount of A, you can use the molar ratio between A and C (given by their coefficients) to find how much C will be produced. This quantitative information is critical not just for chemical reactions in a lab but also for industrial processes and environmental systems.

Initial Reaction Conditions

In any chemical reaction, initial conditions are critical as they determine the starting point for calculating changes over time. These include the concentrations of the reactants and products at the very beginning before the reaction has proceeded.
Understanding initial reaction conditions is key to analyzing how a reaction will unfold. Usually, reactions start with a certain amount of reactants and possibly some products. Often at these initial stages, the reaction quotient (Q) becomes crucial as it provides insight into how the reaction is progressing compared to its equilibrium state.
For instance, in a reaction starting with only reactants A and B, the initial concentration of products C and D is zero. Thus, Q is zero as the product side of the reaction quotient expression involves zero concentrations:\[ Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} = \frac{0 \cdot 0}{[A]^a[B]^b} = 0 \] As time passes, reactants are converted into products, and this change increases Q. Analyzing how Q changes from the initial state helps predict whether the reaction is approaching equilibrium or moving towards a change in direction.