Question

You have a solution of the weak acid HA and add some HCl to it. What are the major species in the solution? What do you need to know to calculate the pH of the solution, and how would you use this information? How does the pH of the solution of just the HA compare with that of the final mixture? Explain

Short answer

After adding HCl to the weak acid HA solution, the major species present are HA, A-, H3O+, Cl-, and H2O. To calculate the pH of the solution, we need the initial concentrations of HA and HCl, and the Ka of HA. We can use the Henderson-Hasselbalch equation \(pH = pKa + log(\frac{[A^-]}{[HA]})\) to calculate the pH. To compare the pH of the solution of just HA with the final mixture, calculate the pH of both solutions and compare the values. The pH of the final mixture is expected to be lower (more acidic) than the pH of the solution of just HA.

Step-by-step solution

Identify the major species

After adding HCl to the weak acid HA solution, we have the following species present in the solution: HA (weak acid), A- (conjugate base resulting from the ionization of HA), H3O+ (hydronium ions), Cl- (chloride ions from HCl), and H2O (water). HCl is a strong acid and it will dissociate completely, so the concentration of Cl- will be equal to the concentration of HCl added. The concentration of H3O+ will be the sum of the H3O+ generated by the dissociation of both HA and HCl.

Determine the information needed to calculate the pH

To calculate the pH of the solution, we need to know the initial concentrations of HA and HCl, as well as the acid dissociation constant (Ka) of HA. This information will be necessary to apply the Henderson-Hasselbalch equation, which is given by: \(pH = pKa + log(\frac{[A^-]}{[HA]})\) Where \(pH\) is the pH of the solution, \(pKa\) is the negative logarithm of the acid dissociation constant (Ka), \([A^-]\) is the concentration of the conjugate base, and \([HA]\) is the concentration of the undissociated weak acid.

Calculate the pH of the solution

Once we have the initial concentrations of HA and HCl and the Ka of HA, we can calculate the pH of the solution using the following procedure: 1. Calculate the initial concentration of H3O+ by considering the complete dissociation of HCl, which gives \([H3O+] = [HCl]\). 2. Calculate the pKa of HA using the equation \(pKa = -log(Ka)\). 3. Calculate the concentration of A- in the equilibrium using the following relationship: \([A^-] = \frac{[H3O+]}{10^{(pKa - pH)}}\) 4. Calculate the concentration of undissociated HA using the expression: \([HA] = [HA]_0 - [A^-]\) Where \([HA]_0\) is the initial concentration of HA before the addition of HCl. 5. Finally, use the obtained values of [A-] and [HA] in the Henderson-Hasselbalch equation to calculate the pH of the solution.

Compare the pH of the solution of just HA with the final mixture

In a solution containing just HA, we can calculate its pH using the Henderson-Hasselbalch equation as well with the initial concentrations of HA and A-. After computing the pH of the final mixture (after the addition of HCl), compare the two pH values to determine which solution is more acidic or alkaline. Since HCl is a strong acid, we can expect that the pH of the final mixture will be lower (more acidic) than the pH of the solution of just HA.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a powerful tool used to calculate the pH of a solution containing a weak acid and its conjugate base. It is derived from the dissociation equilibrium of the weak acid. The equation is expressed as:
\[pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right)\]
In this equation, \(pH\) represents the measure of acidity or alkalinity of the solution. The \(pKa\) is the negative logarithm of the acid dissociation constant (\(Ka\)) specific to the weak acid in question, serving as an indicator of the acid's strength.

• **\([A^-]\)** denotes the concentration of the conjugate base, which forms when the weak acid donates a proton.
• **\([HA]\)** indicates the concentration of the undissociated weak acid molecules present in the solution.

This equation helps bridge the understanding between concentration and pH. Knowing how to apply it allows students to predict the behavior of acid-base equilibrium in buffer solutions effectively.

Weak acid

A weak acid is one that does not fully dissociate into its ions in water. This partial dissociation means that in a solution, a significant proportion of the acid molecules remain intact as \([HA]\) while a smaller amount releases hydrogen ions \((H^+)\) or forms hydronium ions \((H_3O^+)\).

The behavior of weak acids is represented by their acid dissociation constant, \(Ka\), a value that reflects their tendency to lose protons in solution. A smaller \(Ka\) value suggests a weaker acid, having less capability to donate protons compared to strong acids like HCl.

• Common examples include acetic acid (vinegar) and citric acid (found in citrus fruits).
• Because weak acids do not completely ionize, their solutions have higher pH compared to strong acids at comparable concentrations.

Understanding weak acids is vital for comprehending buffer systems and their ability to maintain a stable pH in biological and chemical systems.

pH calculation

Calculating the pH of a solution is crucial for understanding its chemical behavior, particularly in reactions involving acids and bases. pH is a logarithmic scale used to measure the acidity or basicity of a solution. It is defined as the negative logarithm of the hydrogen ion concentration:
\[pH = -\log([H^+])\]
For solutions involving weak acids, the Henderson-Hasselbalch equation provides a convenient method to find the pH, especially when the acid is part of a buffer system.

• To determine the pH, start by obtaining the concentration of the hydronium ions, \([H_3O^+]\), in the solution.
• If a strong acid like HCl is added, its complete dissociation contributes additional hydronium ions, significantly affecting the pH.
• With the information of initial concentrations and the \(Ka\) of the weak acid, use these in the Henderson-Hasselbalch equation to determine the equilibrium pH.

Grasping pH calculations allow students to predict how a solution reacts chemically, which is a foundational skill in biochemistry and pharmacology, where the control of pH is often critical.