Question

$$K=\frac{\left[\mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}\right]}{\left[\mathrm{Mn}^{2+}\right]\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right]^{2}}$$

Short answer

The equilibrium constant expression for the reaction between manganese(II) ions and oxalate ions forming manganese(II) tartrate ion is given by: \[K=\frac{\left[\mathrm{Mn}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}^{2-}\right]}{\left[\mathrm{Mn}^{2+}\right]\left[\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\right]^{2}}\] The value of K helps us understand the position of the chemical equilibrium, indicating whether the reaction favors the formation of manganese(II) tartrate ion, manganese(II) ions, and oxalate ions, or if the concentrations of reactants and products are equal at equilibrium.

Step-by-step solution

Understand the equilibrium constant expression

The equilibrium constant, K, is used to describe the relationship between the concentrations of reactants and products at equilibrium for a chemical reaction. It is an important parameter that helps us evaluate how "far" a reaction proceeds or how "favorable" the reaction is based on the concentrations of the species involved. In this expression, K is defined as the ratio of the concentration of manganese(II) tartrate ion to the concentrations of manganese(II) ions and oxalate ions squared.

Identify the chemical species involved in the expression

We have three chemical species involved in the expression: 1) Manganese(II) tartrate ion, \(\mathrm{Mn}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}^{2-}\), 2) Manganese(II) ions, \(\mathrm{Mn}^{2+}\), and 3) Oxalate ions, \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\).

Write the balanced chemical equation for the reaction

Based on the K expression, it can be concluded that this is a reaction involving one manganese(II) ion and two oxalate ions forming one manganese(II) tartrate ion. The balanced chemical equation can be written as follows: \[\mathrm{Mn}^{2+} + 2\mathrm{C}_{2}\mathrm{O}_{4}^{2-} \rightleftharpoons \mathrm{Mn}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}^{2-}\]

Apply the Law of Mass Action to the balanced chemical equation

According to the law of mass action, the equilibrium constant expression K is defined as the product of the concentrations of the products, raised to their stoichiometric coefficients, divided by the product of the concentrations of the reactants, raised to their stoichiometric coefficients. For our balanced chemical equation, the expression for K can be written as: \[K=\frac{\left[\mathrm{Mn}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}^{2-}\right]}{\left[\mathrm{Mn}^{2+}\right]\left[\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\right]^{2}}\]

Interpret the meaning of K

The value of K gives us information about the position of the chemical equilibrium. If K is greater than 1, the reaction favors the formation of the manganese(II) tartrate ion. If K is less than 1, the reaction favors the formation of manganese(II) ions and oxalate ions. A K value equal to 1 indicates that the reaction is equally favorable in both the forward and reverse directions, i.e., the concentrations of reactants and products are equal at equilibrium.

Key concepts

Chemical Equilibrium

Chemical equilibrium refers to the state of a reversible 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, although they are not necessarily equal. This balance is a dynamic condition where both reactions continuously occur without any net change in the concentrations of the reactants and products. Understanding chemical equilibrium is crucial as it explains how reactions reach a stable state under given conditions.

• In a closed system, equilibrium shifts depend on factors like temperature, pressure, and concentration.
• When a reaction reaches equilibrium, any disturbance (like a change in concentration or temperature) will shift the equilibrium position, as described by Le Chatelier's Principle.

Grasping the concept of chemical equilibrium allows us to understand various biological and industrial processes where maintaining a stable concentration of substances is essential.

Law of Mass Action

The Law of Mass Action provides a mathematical framework to understand the relationship between the concentrations of reactants and products in a chemical system at equilibrium. This law states that for a general reversible reaction \[ aA + bB \rightleftharpoons cC + dD \]The equilibrium constant expression, K, is given by \[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]Here, the square brackets denote molarity, or concentration, and each concentration is raised to a power equal to its stoichiometric coefficient in the balanced chemical equation.Application of the Law of Mass Action helps in determining the equilibrium constant, which is an exceptional tool to predict the extent of a reaction. When the law is applied to an equilibrium system,

• It helps in predicting the yield of chemical processes.
• Provides insights into how changes in reaction conditions will affect reaction dynamics.

Moreover, understanding this concept facilitates a deep comprehension of myriad scientific and engineering problems related to chemical reactions.

Reaction Quotient

The reaction quotient, Q, serves as an indicator to predict the direction in which a reaction will proceed to reach equilibrium. It is calculated using the same formula as the equilibrium constant, K.It provides a snapshot of the system's current state and is represented by the following expression for a reaction: \[ Q = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]By comparing Q to K, you can determine whether a reaction is at equilibrium:

• If \( Q < K \), the reaction will shift towards the products to reach equilibrium.
• If \( Q > K \), the reaction will shift towards the reactants.
• If \( Q = K \), the system is at equilibrium.

This concept is pivotal in monitoring reactions to ascertain how factors such as concentration changes can drive the system towards equilibrium, enabling more efficient and effective chemical process management.