Problem 19 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

What will be the effect of adding \(100 \mathrm{ml}\) of \(0.001 \mathrm{M}-\mathrm{HCl}\) solution to \(100 \mathrm{ml}\) of a solution having \(0.1 \mathrm{M}-\mathrm{HA}\) ? The acid dissociation constant of \(\mathrm{HA}\) is \(10^{-5}\). (a) The degree of dissociation of HA will decrease but the \(\mathrm{pH}\) of solution remains unchanged. (b) The degree of dissociation of \(\mathrm{HA}\) remains unchanged but the \(\mathrm{pH}\) of solution decreases. (c) Neither degree of dissociation nor pH of solution will change. (d) The degree of dissociation as well as pH of solution will decrease.

Step-by-Step Solution

Answer

The degree of dissociation of HA will decrease and the pH of the solution will decrease as well, so the correct answer is (d).

Step 1: Calculate Mole of HCl Added

First, calculate the number of moles of HCl added to the solution. Since the volume of HCl solution is 100 ml and the concentration is 0.001 M, the moles of HCl are calculated as moles = concentration * volume. Here, volume must be converted from ml to liters by dividing by 1000.

Step 2: Calculate Initial Moles of HA

Find the initial number of moles of HA in the 100 ml solution before adding HCl. This is done by multiplying the concentration of HA by the volume of the solution, remembering to convert the volume from ml to liters.

Step 3: Find New Concentration of HA

After mixing the two solutions, we have a total volume of 200 ml. The new concentration of HA can be calculated based on the initial moles of HA and the new volume (in liters).

Step 4: Analyze the Change in Degree of Dissociation and pH

The added HCl will provide free H+ ions, which will suppress the dissociation of HA due to the common ion effect. The pH of the solution will decrease because the concentration of H+ ions in the solution increases with the addition of HCl. The degree of dissociation of HA will decrease as well, since the equilibrium will shift to compensate for the increased H+ ions.

Key Concepts

Acid Dissociation Constant

The acid dissociation constant, often denoted as Ka, is a quantitative measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid into its ions. For a generic acid HA, which dissociates into H+ (hydrogen ion) and A- (the conjugate base), the reaction can be written as:
\[HA \rightleftharpoons H+ + A-\]
The Ka is then defined by the equation:
\[ K_a = \frac{[H+][A-]}{[HA]} \]
where the square brackets denote the concentration of each species at equilibrium. A larger Ka value indicates a stronger acid, since it implies a greater concentration of H+ ions. In the context of the common ion effect, when additional HCl is added to the solution of HA, the dissociation of HA is suppressed, because the system shifts to maintain equilibrium by favoring the reactant side to reduce the concentration of H+ ions. This is due to the Le Chatelier's Principle, where the system responds to an external change to re-establish equilibrium.

pH Calculation

pH calculation is the process of determining the acidity or basicity of a solution. The pH is defined as the negative logarithm (base 10) of the concentration of hydrogen ions (H+):
\[ pH = -\log[H+] \]
In an acid-base chemistry context, the pH helps to understand the extent of acid or base dissociation. When HCl is added to the HA solution, the H+ ion concentration increases, leading to a lower pH value. Thus, the pH will decrease, indicating that the solution becomes more acidic. While calculating pH, it's crucial to consider ionization constants and the concentrations of all species in the solution.

Degree of Dissociation

The degree of dissociation, represented by the symbol 'α', is a measure of the extent to which a compound (usually an acid or a base) separates into its ions in a given solvent. It is defined by the fraction of the original substance that has dissociated at equilibrium:
\[\alpha = \frac{\text{Moles of substance dissociated}}{\text{Total moles of substance initially present}}\]
The presence of a common ion, in our example, H+ from HCl, affects the equilibrium of the reaction by decreasing the dissociation of HA. Here, Le Chatelier's Principle is at play again, where the acid HA is less dissociated because the increased concentration of H+ ions effectively drives the reaction towards the left, reducing α.

Chemical Equilibrium

Chemical equilibrium refers to the state of a chemical reaction where the forward and reverse reaction rates are equal, resulting in no overall change in the concentrations of reactants and products over time. It is a dynamic balance, not a static one, as the molecules are constantly reacting, but at a rate that keeps the concentration steady. The equilibrium can be disturbed by changing conditions such as concentration, temperature, and pressure.
When HCl is added to the HA solution, equilibrium is temporarily disturbed. According to Le Chatelier's Principle, the equilibrium will shift to reduce the effect of this disturbance – in this case, by favoring the formation of HA from H+ and A-. Therefore, equilibrium plays a pivotal role in understanding the behavior of the reaction when the external conditions are altered, such as by adding a strong acid like HCl to a weak acid like HA.