Solve an equilibrium problem (using an ICE table) to calculate the pH of each solution. a. 0.18 M CH3NH2 b. 0.18 M CH3NH3Cl c. a mixture that is 0.18 M in CH3NH2 and 0.18 M in CH3NH3Cl

The ICE (Initial, Change, Equilibrium) table is a valuable tool for solving equilibrium problems in chemistry. It helps us to visually organize and understand changes in concentrations of reactants and products over the course of a reaction. Initially, you list the initial concentrations of the reactants and products, which, for weak base and acid reactions, typically means the reactants are present and the products are not. During the reaction, the concentrations of the reactants decrease and those of the products increase by a certain amount, which we often denote as 'x'. At equilibrium, you then express the new concentrations of all species.

When setting up an ICE table, careful attention must be paid to stoichiometry and to using proper equilibrium constants. For instance, a reaction starting with 0.18 M CH3NH2 would have an initial concentration of 0.18 M for CH3NH2 and 0 M for CH3NH3+ and OH−. As the reaction proceeds to equilibrium, 'x' amount of CH3NH2 is converted into 'x' amount of CH3NH3+ and OH−, showing the stoichiometric relationship. Understanding this concept is critical in correctly calculating the changes in species concentrations and eventually determining the pH.

The Henderson-Hasselbalch equation is a simplified method to calculate the pH of a solution when dealing with weak acids or bases, especially when they exist in a buffer system as conjugate pairs. It relates the pH of a solution to the pKa (the negative logarithm of the acid dissociation constant, Ka) and the ratio of the concentrations of the conjugate base and the conjugate acid. The equation is given by:
\[ pH = pKa + \log\left(\frac{[\text{Conjugate Base}]}{[\text{Conjugate Acid}]}\right) \].

For example, when you have a mixture of a weak base and its conjugate acid in equal concentrations, as we do with CH3NH2 and CH3NH3Cl, the logarithmic term becomes zero because the log of 1 is 0. This results in the pH being equal to the pKa. This property of buffers is what makes them so vital in biological systems and industrial processes, where maintaining a stable pH is crucial.

The behavior of weak bases and acids in water is quintessential for understanding pH calculations. Unlike strong acids and bases, which dissociate completely in water, weak acids and bases only partially dissociate. This partial dissociation creates an equilibrium condition in the solution. For instance, when CH3NH2 (a weak base) reacts with water, it produces CH3NH3+ and OH− ions, but not all CH3NH2 molecules convert into products. Similarly, the conjugate acid, CH3NH3+, partially dissociates into CH3NH2 and H3O+ ions in water.

Crucially, for weak bases and their corresponding acids, we use the equilibrium constants Kb and Ka, respectively, to quantify how far the reaction proceeds towards the products. These constants are essential parameters that need to be known or calculable in order to find the pH of the solutions concerned. It's important to grasp this concept of partial dissociation because it influences how we set up ICE tables and apply the Henderson-Hasselbalch equation.

The equilibrium expression for a chemical reaction allows us to relate the concentrations of reactants and products at equilibrium. For weak acid and base reactions, we have the acid dissociation constant (Ka) or the base dissociation constant (Kb). These constants are derived from the ratio of the concentrations of the products to the reactants at equilibrium, raised to the power of their stoichiometric coefficients.

For example, with a weak base like CH3NH2, the equilibrium expression using Kb would be \[ Kb = \frac{[CH3NH3+][OH−]}{[CH3NH2]} \].
Understanding this expression is vital as it enables us to solve for the variables that represent the concentration changes in the ICE table. Also, it is directly involved in the process of calculating pOH and subsequently pH. Equilibrium expressions can vary based on the reaction, but they all follow the same principle of quantifying the position of equilibrium. Bearing in mind how these expressions are constructed and manipulated provides a basis for successfully solving equilibrium problems and calculating pH in various chemical scenarios.