Question

Which of the following statements is true regarding the general equilibrium expression? (a) \(K_{\text {eq }}\) can be determined experimentally. (b) \(K_{\text {eq }}\) can be determined theoretically.

Short answer

Statement (a) is true: \( K_{\text{eq}} \) is determined experimentally.

Step-by-step solution

Understanding the Equilibrium Constant

The equilibrium expression, denoted as \( K_{\text{eq}} \), represents the ratio of the concentrations of products to reactants at equilibrium. It is unique for a given reaction at a specified temperature.

Experimental Determination

\( K_{\text{eq}} \) is determined experimentally by measuring the concentrations of reactants and products at equilibrium under controlled conditions. This experimental data is used to calculate the equilibrium constant.

Theoretical Calculation

While theoretical models and thermodynamic data can estimate \( K_{\text{eq}} \), the exact value is most accurately determined through experimental measurements. Theoretical methods generally provide an approximation.

Evaluating the Statements

Statement (a) is true because \( K_{\text{eq}} \) is determined through experimental data. Statement (b) is somewhat misleading because while theoretical estimations are possible, they rely on approximations and are not as precise as experimental determination.

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to no net change in the concentrations of reactants and products. At this point, the reaction is said to be at equilibrium. The equilibrium constant, represented as \( K_\text{eq} \), describes the ratio of the concentrations of products to reactants at equilibrium, reflecting that balance between forward and reverse reactions. This constant is crucial because it signifies the extent to which a reaction will proceed.

• If \( K_\text{eq} \) is large, more products are present at equilibrium, indicating the reaction favors product formation.
• If \( K_\text{eq} \) is small, more reactants are present, and the reaction favors reactants.

The value of \( K_\text{eq} \) is influenced by temperature, meaning that for each unique temperature, there is a specific equilibrium constant. This helps chemists predict how changing conditions will impact the position of equilibrium and the concentrations of the involved chemical species.

Experimental Measurements

Determining the equilibrium constant \( K_\text{eq} \) hinges on experimental measurements. During an experiment, the concentrations of both reactants and products are measured once the system has reached equilibrium. All measurements must be conducted under controlled conditions to ensure accuracy. From these concentration values, the equilibrium constant can be calculated using the general equilibrium expression for the reaction, which relates these concentrations to \( K_\text{eq} \).
Accurate experimental determination is essential because \( K_\text{eq} \) varies with conditions and is not theoretically derived with precision. The process includes careful consideration of experimental parameters like temperature, pressure, and concentration, as even slight variations can affect the equilibrium state. Scientists often use tools such as spectrophotometry, calorimetry, or chromatography to gather necessary concentration data. These tools help ensure that the measured values are reliable and reproducible, contributing to more accurate and precise calculations of \( K_\text{eq} \).

Thermodynamic Data

Thermodynamic data provides a theoretical approach to estimating the equilibrium constant \( K_\text{eq} \). This involves analyzing the standard Gibbs free energy change, \( \Delta G^\circ \), for a reaction. The relationship between \( \Delta G^\circ \) and the equilibrium constant is given by:\[ \Delta G^\circ = -RT \ln K_\text{eq} \]where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin. Using thermodynamic data, chemists can estimate whether a reaction is spontaneous and the probable position of equilibrium.
However, these calculations are approximations. They rely on standard conditions and often cannot capture the full complexity of real experimental settings. While useful for predictive purposes, these theoretical values generally do not match the precision achievable through direct experimental measurements. Actual experimental data provide the most reliable source for determining \( K_\text{eq} \) because they account for all variables at play in the reaction environment, offering a comprehensive view beyond theoretical approximations.