- The equilibrium constant \(K\) is defined by thermodynamic properties and depends exclusively on temperature.
- Le Chatelier's principle explains that while systems adjust their equilibrium position in response to pressure changes, these shifts are designed to keep the ratio of products to reactants equal to the constant \(K\).
- Changes in concentration or pressure do not change the value of \(K\).
- Therefore, the correct statement is that the value of \(K\) does not change, making the correct option \(\boxed{c}\).
Explanation
- Understanding the Equilibrium Constant \(K\)
The chemical equilibrium constant, denoted by \(K\), is a fundamental parameter that characterizes a chemical reaction at a specific temperature. It quantifies the relationship between the concentrations (or partial pressures) of the products and reactants once the system has reached a state of dynamic equilibrium.
The thermodynamic definition of the equilibrium constant is derived from the standard Gibbs free energy change of the reaction, \(\Delta G^\circ\), according to the equation:
\[\Delta G^\circ = -RT \ln K\]
where \(R\) is the universal gas constant and \(T\) is the absolute temperature. Since \(\Delta G^\circ\) is a property that depends solely on the nature of the reactants and products and the temperature at which the reaction occurs, it follows that the equilibrium constant \(K\) is also a function of temperature alone.
- Distinguishing Equilibrium Position from Equilibrium Constant
Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions (such as concentration, pressure, or temperature), the system will shift its position to counteract the change and re-establish equilibrium.
While changes in concentration or pressure do affect the position of the equilibrium—meaning the relative amounts (concentrations) of reactants and products shift to maintain the value of \(Q\) equal to \(K\)—these changes do not alter the value of the equilibrium constant \(K\) itself. The constant \(K\) is only altered if the temperature of the system is changed. Therefore, an increase in pressure will cause the system to shift towards the side with fewer moles of gas (or aqueous species, depending on the phase) to relieve the pressure, but the value of \(K\) will remain constant.
- Final Conclusion
Based on the thermodynamic definition, the equilibrium constant \(K\) depends exclusively on temperature. Consequently, changes in pressure do not influence the numerical value of \(K\). Therefore, the statement that correctly completes the table for an increase in pressure is that the value of \(K\) does not change. This corresponds to option (c).
Examples
Think of the equilibrium constant \(K\) like a specific "recipe ratio" for a dish that only changes if you decide to cook at a different altitude (temperature). If you add more ingredients (concentrations) or squeeze the cooking pot (pressure), you might move things around to keep the meal consistent, but the "perfect recipe ratio" itself remains the same unless you change the heat! This principle helps chemists predict how chemical plants should be operated efficiently without unnecessarily changing temperatures.