Problem 42 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (b) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of \(Q_{c}\) at this point in the reaction?

Step-by-Step Solution

Answer

(a) If \(Q_c > K_c\), the reaction must proceed in the reverse direction to reach equilibrium, converting some products back into reactants until \(Q_c = K_c\). (b) At the start of a reaction with only reactants present and no products formed, the value of \(Q_c\) is 0.

Step 1: (a) Analyzing the reaction when \(Q_c > K_c\)

To determine how a reaction will proceed when \(Q_c > K_c\), we need to examine the definition of the reaction quotient, which is given by: $$Q_c = \frac{[\text{Products}]}{[\text{Reactants}]}$$ When \(Q_c > K_c\), it means that the concentration of the products is greater than their concentration at equilibrium. To reach equilibrium, the reaction needs to proceed in the reverse direction, converting some of the products back into reactants. This will decrease the product concentration and increase the reactant concentration until \(Q_c = K_c\).

Step 2: (b) Calculating \(Q_c\) at the start of a reaction with only reactants present

At the beginning of a reaction, when only reactants are present and no products have been formed, the concentration of products is essentially zero. Therefore, using the definition of the reaction quotient, we have: $$Q_c = \frac{[\text{Products}]}{[\text{Reactants}]} = \frac{0}{[\text{Reactants}]} = 0$$ So, at the start of the reaction with only reactants present and no products formed, the value of \(Q_c\) is 0.

Key Concepts

Chemical Equilibrium

Chemical equilibrium refers to the state in a chemical reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of the reactants and products remain constant over time, though the chemical reactions are still occurring. The system is not static but rather in a state of dynamic balance.
The concept of chemical equilibrium is fundamental in understanding various reactions in chemistry. It helps explain why some reactions yield more products, while others seem to come to a halt.
When a reaction reaches equilibrium, it doesn't mean that the reactants and products are in equal amounts. Rather, it indicates that their concentrations stop changing as the forward and reverse reactions proceed at the same rate.

• Static equilibrium means that nothing seems to be happening and concentrations are constant.
• Dynamic equilibrium indicates that reactions continue to occur, but without net change in concentrations.

Recognizing these two aspects of equilibrium is crucial for predicting how changes in conditions, like temperature or concentration, could affect a reaction.

Equilibrium Constant

The equilibrium constant, denoted as \( K_c \), is a crucial value for understanding the extent of a reaction at equilibrium. It is calculated using the concentrations of the products and reactants raised to the power of their stoichiometric coefficients from the balanced chemical equation.
The formula is given by:\[K_c = \frac{[\text{Products}]^m}{[\text{Reactants}]^n}\]where \(m\) and \(n\) represent the coefficients of the products and reactants respectively in the balanced equation.
A high \( K_c \) value means the reaction favors the formation of products at equilibrium, while a low \( K_c \) value indicates that reactants are favored.

• If \( K_c \) is much greater than 1, the reaction proceeds nearly to completion.
• If \( K_c \) is much less than 1, the reaction scarcely occurs.
• If \( K_c \) is close to 1, significant amounts of both reactants and products are present at equilibrium.

This key value helps chemists predict the behavior of reactions under different conditions and is an essential part of reaction quotient analysis.

Reactants and Products Concentration

In chemical reactions, the concentration of reactants and products plays a vital role in determining how a reaction proceeds. This involves the use of the Reaction Quotient \( Q_c \) and its comparison to the equilibrium constant \( K_c \).
At any given point in a reaction, \( Q_c \) is calculated using the same formula as \( K_c \), based on current concentrations, not those at equilibrium.

• If \( Q_c < K_c \), the reaction will proceed forward, producing more products.
• If \( Q_c > K_c \), the reaction will reverse, forming more reactants.
• If \( Q_c = K_c \), the system is at equilibrium, and no net change occurs.

The initial concentrations of reactants and products determine the direction and extent of the shift in the reaction. At the beginning of a reaction, where no products are present, \( Q_c = 0 \), which propels the reaction forward to produce products and reach equilibrium.