Question

Consider a solution prepared by mixing a weak acid HA and \(\mathrm{HCl}\). What are the major species? Explain what is occurring in solution. How would you calculate the \(\mathrm{pH}\) ? What if you added NaA to this solution? Then added \(\mathrm{NaOH}\) ?

Short answer

The major species in a solution containing a weak acid HA and a strong acid HCl are HA, HCl, A-, H2O, and Cl-. HCl dissociates completely, while HA partially dissociates. To calculate the pH, find the total concentration of H+ ions from HCl and HA, then use the formula \( pH = -\log_{10}([H+]) \). Adding NaA increases A- concentration, suppressing HA dissociation and increasing pH. Adding NaOH reacts with H+ ions, decreasing their concentration, forming A- and water, and increasing pH.

Step-by-step solution

Identify the major species in the solution

When a weak acid HA and a strong acid HCl are present in a solution, the major species will be HA, HCl, A-, H2O, and Cl-. This is due to HCl dissociating completely, while weak acids such as HA do not dissociate completely, leading to the presence of both HA and A-.

Explain the interactions in the solution

Since HCl is a strong acid, it will dissociate completely into H+ and Cl-. The weak acid, HA, will partially dissociate into H+ and A-. The increase in H+ concentration in the solution will suppress the dissociation of HA, according to Le Chatelier's principle. Therefore, the major interaction occurring in the solution is the complete dissociation of HCl and the partial dissociation of HA.

Calculate the pH of the solution

To calculate the pH of the solution, first, find the total concentration of H+ ions in the solution. The H+ ions come from both the dissociation of HCl and the dissociation of the weak acid HA. Since HCl dissociates completely, the concentration of H+ from HCl will be equal to the initial concentration of HCl. The concentration of H+ ions from HA can be calculated from the dissociation constant (Ka) of HA. Then, use the formula for pH: \( pH = -\log_{10}([H+]) \)

Identify the effect of adding NaA to the solution

Adding NaA will increase the concentration of A- ions in the solution. The excess A- causes the equilibrium of the weak acid HA to shift towards the left, and it will further suppress the dissociation of HA. This effect would result in a decrease in the concentration of H+ ions and an increase in the pH of the solution.

Identify the effect of adding NaOH to the solution

Upon adding NaOH, a strong base, it will react with the H+ ions present in the solution, decreasing their concentration. The reaction between the strong base NaOH and the weak acid HA will form A- and water. As the concentration of H+ ions decreases, the pH of the solution will increase.

Key concepts

pH Calculation

Understanding how to calculate the pH value of a solution is essential for analyzing its acidity or basicity. To calculate the pH of a solution, one must first understand the concentration of hydrogen ions \( [H^+] \). The pH is then found using the formula \( pH = -\textrm{log}_{10}([H^+]) \). The logarithmic scale is used because the range of hydrogen ion concentrations in solutions can be very broad, and the logarithm helps to simplify this into a manageable scale.

For a solution containing a strong acid like HCl, which dissociates completely, the pH calculation is straightforward because every molecule of HCl contributes a hydrogen ion. However, if a weak acid like HA is present, its partial dissociation must be considered. We calculate the contribution of \( [H^+] \) ions from HA using its dissociation constant (Ka) and the initial concentration. Thus, the total \( [H^+] \) used in the pH calculation equals the sum of \( [H^+] \) from both HCl and HA. When dealing with mixed acid solutions, the understanding of acid dissociation, as discussed later, is necessary to perform an accurate pH calculation.

Acid-Base Equilibrium

Acid-base equilibrium involves the balance between acid and base species in a solution. For a weak acid HA, this equilibrium can be represented as \( HA \leftrightarrow H^+ + A^- \). At equilibrium, the rates of the forward and reverse reactions are equal. The ratio of concentration of the products to reactants is expressed by the equilibrium constant, Ka, which is unique for each weak acid.

The position of the equilibrium can be altered by changes in the concentration of the reactants or products as per Le Chatelier's principle. For instance, if the concentration of \( A^- \) is increased by adding a salt like NaA, the equilibrium shifts to the left, reducing the dissociation of HA and decreasing the concentration of \( H^+ \), which in turn affects the pH. Conversely, adding a strong base like NaOH shifts the equilibrium by removing \( H^+ \) ions, forming water and \( A^- \) ions, thus increasing the pH. Both these alterations to the equilibrium play a significant role in pH control and buffer solutions.

Le Chatelier's Principle

Le Chatelier's principle is a vital concept that predicts the response of an equilibrium system to disturbances. It posits that if an external change is imposed on a system at equilibrium, the system adjusts itself to counteract the change and re-establish equilibrium. This principle applies to acid-base reactions, temperature, pressure, and concentration changes.

In the context of our exercise, when the strong acid HCl is added to a solution with a weak acid HA, the large increase in \( H^+ \) concentration suppresses the dissociation of HA due to the common ion effect. When NaA is added, it contributes additional \( A^- \) ions to the solution, which in turn shifts the equilibrium to the left, following Le Chatelier's principle, leading to less dissociation of HA and an increased pH. Each reaction adjustment serves to minimize the impact of the added substances and maintain the equilibrium of the solution, reflecting the essence of Le Chatelier's principle.

Dissociation of Acids

The dissociation of acids in solution is a critical aspect of their chemistry. A strong acid like HCl dissociates completely in water to form \( H^+ \) and \( Cl^- \) ions. On the other hand, a weak acid like HA dissociates only partially, leading to an equilibrium between undissociated acid \( HA \) and its ions \( H^+ \) and \( A^- \).

The extent of dissociation is governed by the acid dissociation constant (Ka), which provides a measure of the acid's strength. Weak acids have smaller Ka values, indicating less dissociation. The concept of acid dissociation is essential when calculating pH and understanding buffer solutions, as it determines the concentrations of various ions in solution, which in turn control the solution's acidity. The proper assessment of dissociation is key to accurate predictions of pH and understanding the system's response to different types of stresses, such as adding more acid, base, or a conjugate component of the weak acid.