Question

(a) How is a reaction quotient used to determine whether a system is at equilibrium? (b) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (c) 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?

Short answer

(a) A reaction quotient (\(Q_c\)) is used to determine if the system is at equilibrium by comparing it to the equilibrium constant (\(K_c\)). If \(Q_c = K_c\), the system is at equilibrium. If \(Q_c \neq K_c\), the system is not at equilibrium and must proceed in a specific direction. (b) When \(Q_c > K_c\), the reaction must proceed in the reverse direction, converting products back into reactants, until \(Q_c = K_c\) and equilibrium is reached. (c) If only reactants are present in a reaction and no products have been formed, the reaction quotient \(Q_c = 0\).

Step-by-step solution

(a) Relationship between Reaction Quotient and Equilibrium

The reaction quotient (\(Q_c\)) is a value that compares the relative amounts of products and reactants in a reaction at any given point. At equilibrium, the reaction quotient is equal to the equilibrium constant (\(K_c\)). If \(Q_c = K_c\), the system is at equilibrium, meaning the relative concentrations of reactants and products will not change anymore. If \(Q_c \neq K_c\), the system is not at equilibrium and the reaction must proceed in a specific direction to reach equilibrium.

(b) Reaction Direction for \(Q_c > K_c\)

If the reaction quotient \(Q_c\) is greater than the equilibrium constant \(K_c\) (\(Q_c > K_c\)), it means there are more products relative to the reactants than there would be at equilibrium. To reach equilibrium, the reaction must proceed in the reverse direction, converting products back into reactants. This will cause the concentrations of products to decrease and the concentrations of reactants to increase, ultimately lowering \(Q_c\) until it becomes equal to \(K_c\).

(c) Value of \(Q_c\) with Only Reactants Present

When there are no products present and only reactants exist in the reaction, their concentrations will have non-zero values. In contrast, the concentrations of the products will be equal to zero. Since the reaction quotient \(Q_c\) involves the multiplication of product concentrations divided by the multiplication of reactant concentrations, the value of \(Q_c\) in this case would be zero. In other words, when only reactants are present in a reaction, the reaction quotient \(Q_c = 0\).

Key concepts

Equilibrium Constant

The equilibrium constant, denoted by \(K_c\), is a crucial concept in chemistry that helps us understand the balance of chemical reactions. It is a number that represents the ratio of the concentrations of products to the concentrations of reactants at chemical equilibrium. This means that when a reaction reaches a state where it appears to stop changing, the values of these concentrations stay constant, and their specific ratio is the equilibrium constant.

\(K_c\) is specific to a particular reaction at a given temperature. Changing the temperature can alter \(K_c\), because the reaction can shift in either the forward or the reverse direction. This can either increase or decrease the amount of products compared to reactants.

In summary, the equilibrium constant tells us where the balance of a reaction lies. If \(K_c\) is a large number, the reaction likely favors the formation of products, whereas a smaller \(K_c\) typically indicates that reactants are favored at equilibrium. It's a reliable indicator of the tendencies of chemical reactions under specified conditions.

Chemical Equilibrium

Chemical equilibrium refers to the state in a chemical reaction where the rates of the forward and reverse reactions are equal. At this point, the concentrations of the reactants and products remain constant over time, though both reactions continue to occur.

• The system is dynamic, meaning that even at equilibrium, molecules don't stop reacting; they just do so at balanced rates.
• Equilibrium isn't static. In practical terms, it’s the condition where the macroscopic properties like concentration, pressure, and color become constant.

To determine if a system is at equilibrium, compare the reaction quotient \(Q_c\) to the equilibrium constant \(K_c\). When \(Q_c = K_c\), the system is at equilibrium. Any deviation, where \(Q_c eq K_c\), indicates that the reaction will shift in the direction that helps achieve equilibrium, ensuring that the concentrations adjust accordingly.

Reaction Direction

The direction in which a reaction proceeds to reach equilibrium depends on the comparison between the reaction quotient \(Q_c\) and the equilibrium constant \(K_c\). This concept is pivotal in predicting which way a reaction will shift in order to achieve balance.

• If \(Q_c < K_c\), more reactants are present than at equilibrium, requiring the formation of more products. The reaction will proceed in the forward direction to reach equilibrium.
• If \(Q_c > K_c\), there are more products than at equilibrium, leading the reaction to proceed in the reverse direction to convert some products back into reactants.
• When \(Q_c = K_c\), the system is already at equilibrium, and no net change occurs in the concentrations of reactants and products.

Understanding the reaction direction aids in controlling chemical processes, predicting outcomes, and designing systems in fields like chemical engineering and biochemistry.