Problem 19 - Chemistry: The Central Science in SI Units, Global Edition

Question

Which of the following statements are true and which are false? (a) The equilibrium constant can never be a negative number. (b) In reactions that we draw with a single-headed arrow, the equilibrium constant has a value that is very close to zero. (c) As the value of the equilibrium constant increases, the speed at which a reaction reaches equilibrium increases.

Step-by-Step Solution

Answer

(a) True: The equilibrium constant can never be a negative number since it's calculated using the concentrations of products and reactants which are always positive values. (b) False: In reactions with single-headed arrows, the equilibrium constant has a value that is exceedingly large, not close to zero, as they are practically irreversible. (c) False: The equilibrium constant doesn't influence the speed at which a reaction reaches equilibrium. The rate of reaction is dictated by the rate constant, which depends on activation energy and temperature.

Step 1: Statement (a): The equilibrium constant can never be a negative number.

To determine the truth of this statement, recall that the equilibrium constant (K) for a reaction is calculated using the concentrations of products and reactants raised to the power of their stoichiometric coefficients in the balanced chemical equation. Since concentrations can never be negative, it's impossible for the equilibrium constant to be a negative number. Therefore, statement (a) is true.

Step 2: Statement (b): In reactions that we draw with a single-headed arrow, the equilibrium constant has a value that is very close to zero.

Reactions drawn with a single-headed arrow are generally considered to be irreversible or practically irreversible, meaning they essentially proceed in only one direction, from reactants to products. This means that the concentration of reactants decreases to an extremely low value while the concentration of products increases until the reaction is almost complete. With little to no reactants remaining at equilibrium, the value of the equilibrium constant (K) will be exceedingly large, not close to zero. Thus, statement (b) is false.

Step 3: Statement (c): As the value of the equilibrium constant increases, the speed at which a reaction reaches equilibrium increases.

The equilibrium constant (K) is related to the concentrations of products and reactants at equilibrium and does not provide information about the speed at which equilibrium is reached. The rate of the reaction is dictated by the rate constant, which depends on the activation energy and temperature. Therefore, there is no direct correlation between the equilibrium constant value and the speed at which a reaction reaches equilibrium. Statement (c) is false. In summary: - Statement (a) is true. - Statement (b) is false. - Statement (c) is false.

Key Concepts

Reversible and Irreversible Reactions

Chemical reactions are often categorized into reversible and irreversible types based on their ability to proceed in either direction. Reversible reactions can proceed in both forward and backward directions. In a reversible reaction, the products formed can react together to form the original reactants. These reactions are denoted using a double-headed arrow (⇌). For example, in the process of ammonia synthesis, the following reversible reaction occurs: \[ N_2(g) + 3H_2(g) ⇌ 2NH_3(g) \] Irreversible reactions, on the other hand, proceed primarily in one direction, from reactants to products. They are typically represented with a single-headed arrow (→). In these reactions, products do not readily revert to reactants, usually because the products are very stable or escape from the reaction mixture. A common example is combustion: \[ C(s) + O_2(g) → CO_2(g) \] Understanding the nature of a reaction as reversible or irreversible is important in predicting the concentration of reactants and products in the reaction mixture.

Chemical Equilibrium

Chemical equilibrium is the state in which both reactants and products are present in concentrations that have no further tendency to change over time. This happens when the rates of the forward and backward reactions are equal. As a result, the quantities of reactants and products remain constant, though not necessarily equal, hence dynamically balanced.At equilibrium, the equilibrium constant \( K \) gives a quantitative measure of the concentrations of products and reactants:\[ K = \frac{{[Products]}^{c}}{[Reactants]^{d}} \] Where \( c \) and \( d \) represent the stoichiometric coefficients in the balanced equation. The equilibrium constant is a crucial concept, as it indicates the extent to which reactions proceed to form products. A high \( K \) value means a reaction strongly favors the formation of products at equilibrium, while a low \( K \) value indicates equilibrium lies more towards the reactants.

Reaction Rate

The reaction rate measures how quickly reactants are converted into products in a chemical reaction. It is influenced by several factors including concentration, temperature, and the presence of a catalyst. Each reaction has its own rate law, which describes how the concentration of reactants affects the reaction rate:\[ Rate = k[A]^m[B]^n \] Where:

• \( k \) is the rate constant, unique to each reaction at a given temperature.
• \( [A] \) and \( [B] \) are the concentrations of the reactants.
• \( m \) and \( n \) are the reaction orders, which must be determined experimentally.

Contrary to what some might assume, the equilibrium constant \( K \) does not affect the rate of attaining equilibrium. Instead, the reaction rate is determined by its kinetics, which involve the specific path the reaction takes and the energy barrier that must be overcome, known as activation energy. Understanding the reaction rate is crucial for controlling industrial processes, increasing yields, and ensuring safety in chemical manufacturing.