Question

Explain the difference between \(K_{c}\) and \(K_{\mathrm{p}}\) . For a given reaction, how are the two constants related?

Short answer

\(K_{c}\) is based on the concentration of substances in solution while \(K_{\mathrm{p}}\) is based on the partial pressures of gaseous substances. They are related for reactions involving gases by the equation \(K_{\mathrm{p}} = K_{c}(RT)^{\Delta n}\).

Step-by-step solution

Explain the difference between the equilibrium constants

The equilibrium constant, denoted as \(K_{c}\), is defined for a chemical equilibrium involving substances in a solution and is based on the concentration of the reactants and products. In contrast, \(K_{\mathrm{p}}\) is used for reactions involving gases and is based on the partial pressures of the reactants and products. Both constants provide a measure of the extent of the reaction at equilibrium but are based on different properties of the reactants and products.

Relating the two constants

For a given reaction where the number of moles of gaseous reactants and products are different, \(K_{\mathrm{p}}\) and \(K_{c}\) are related by the equation \(K_{\mathrm{p}} = K_{c}(RT)^{\Delta n}\) where \(R\) is the gas constant, \(T\) is the temperature in kelvins, and \(\Delta n\) is the difference in moles of gas products and reactants (products minus reactants). This equation shows that while the two constants are conceptually similar, they can numerically differ if the reaction results in a change in the number of moles of gas.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the backward reaction. At this point, the concentration of reactants and products remains constant over time, though both reactions still occur. An important aspect of understanding chemical equilibrium is recognizing that it is a dynamic balance, meaning compounds are continuously reacting and forming, but without any net change in concentration.

To illustrate, consider a simple reaction where substance A and substance B react to form substance C and substance D. At equilibrium, A and B are turning into C and D at the same rate that C and D are changing back into A and B. The equilibrium constant, denoted as either Kc for concentrations or Kp for partial pressures, quantifies the ratio of products to reactants in a chemical reaction at this stable state.

Reaction Quotient

The reaction quotient, Q, is a measure that compares the relative amounts of products and reactants at any point during a reaction, not just at equilibrium. Like the equilibrium constants, Q can also be expressed in terms of concentration (Qc) or partial pressure (Qp).

Q can be used to predict which direction a reaction will shift to reach equilibrium. If Q is less than K, the forward reaction is favored, and the concentration of products will increase until equilibrium is reached. Conversely, if Q is greater than K, the reaction will shift in reverse, increasing the concentration of reactants until equilibrium is achieved.

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemical equilibrium that describes how a system at equilibrium responds to external changes in order to maintain its equilibrium state. If a system is subjected to a change in concentration, temperature, or pressure, the system will adjust by shifting the equilibrium position to counteract the imposed change.

For example, adding more reactant to a system at equilibrium will cause the system to shift towards the formation of more products. Conversely, increasing the temperature of an exothermic reaction will shift the equilibrium towards the reactants to absorb the added heat. Le Chatelier's principle allows us to predict the behavior of a reaction under stress, providing invaluable insight into the design of chemical processes and the optimization of reaction conditions.

Partial Pressure

Partial pressure is a term used to describe the pressure exerted by a single gas component in a mixture of gases. Each gas in a mixture exerts pressure independently, and the total pressure of the mixture is the sum of the partial pressures of all the gases present. This concept is crucial for understanding gas-phase reactions.

The partial pressure of a gas can be used in the context of equilibrium constants as Kp. In the case of a reaction involving gases, equilibrium constants can be expressed in terms of partial pressures. Kp is particularly useful because it directly correlates to the pressures measured in a container, making it easy to calculate and apply in laboratory settings for reactions where gases are involved.