Question

Calculate the change in pH that results from adding (a) \(0.100 \mathrm{mol} \mathrm{NaNO}_{2}\) to \(1.00 \mathrm{L}\) of \(0.100 \mathrm{M} \mathrm{HNO}_{2}(\mathrm{aq})\) (b) \(0.100 \mathrm{mol} \mathrm{NaNO}_{3}\) to \(1.00 \mathrm{L}\) of \(0.100 \mathrm{M} \mathrm{HNO}_{3}(\mathrm{aq})\) Why are the changes not the same? Explain.

Short answer

The changes in pH are not the same because the addition of NaNO_2 to HNO_2 introduces a common ion that affects the equilibrium of the weak acid, thereby lowering the concentration of H+ ions and increasing pH. However, the addition of NaNO_3 to HNO_3 does not affect the pH as NO₃- ions do not react with water.

Step-by-step solution

Identify the Chemical Reactions

For the addition of NaNO_2 to HNO_2, the weak acid dissociation reaction can be written as: HNO_2(aq) ⇌ H+(aq) + NO_2-(aq). For the addition of NaNO_3 to HNO_3, it is important to remember that HNO_3 is a strong acid and completely dissociates into ions as HNO_3 → H+ + NO₃-. Adding NaNO₃ will result in the release of NO₃- ions, which do not affect the pH.

Calculate for Part (a)

By using the formula for the acid dissociation constant (Ka) which is [H+][NO_2⁻]/[HNO_2], and the concentrations of each species from the reaction with NaNO_2, the ionization of HNO_2 can be calculated. Adding NaNO_2 to HNO_2 introduces common ion NO_2-, and causes a shift in equilibrium left because of Le Chatelier's principle. This in turn decreases [H+] and as a result the pH increases.

Calculate for Part (b)

NO₃- ions do not react with water. Therefore, the addition of NaNO₃ does not cause any changes to the pH level of the HNO_3 solution.

Compare the Results

The pH change from adding NaNO_2 to HNO_2 will be different to that of adding NaNO₃ to HNO_3 because of the difference in the reaction of the added species with water. The former adds a common ion which suppress the ionization of HNO_2, thereby lowering [H+] and increasing the pH value. The latter, however, does not affect the pH as NO₃- ions do not react with water.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps us understand how a chemical equilibrium responds to changes in concentration, pressure, or temperature. According to this principle, if a system at equilibrium is subjected to a change, it will respond by shifting in a direction that counteracts the effect of the change.

In the context of pH and acid-base equilibria, Le Chatelier's Principle can help us understand how the addition of ions can affect the ion concentrations and thus the pH of a solution. For example, when NaNO₂ is added to a solution containing HNO₂, the common ion NO₂⁻ is introduced. Le Chatelier's principle predicts that the equilibrium will shift to the left, reducing the ionization of HNO₂—a weak acid.

To maintain equilibrium, the system decreases the concentration of hydrogen ions, [H⁺], which leads to an increase in pH. This is an example of how added species can systematically influence a chemical equilibrium, leading to noticeable changes in the pH of a solution.

Acid-Base Equilibria

Understanding acid-base equilibria is crucial for grasping how pH changes occur in solution. Equilibrium in an acid-base reaction is established when the rate of the forward reaction (acid dissociation into ions) equals the rate of the reverse reaction (recombination into the acid).

In our exercise scenario, HNO₂—a weak acid—partially dissociates in water according to the reaction: HNO₂(aq) ⇌ H⁺(aq) + NO₂⁻(aq). This equilibrium situation allows us to apply the expression for the acid dissociation constant, Ka. The equilibrium constant (Ka) provides a measure of the strength of the acid in solution, informing us of the equilibrium concentrations of the ions and the undissociated acid.

When comparing this with HNO₃, a strong acid, it dissociates completely: HNO₃ → H⁺ + NO₃⁻. Because HNO₃ dissociates fully, the equilibrium concept seems less relevant, as there is almost no undissociated HNO₃ left in solution. This stark difference is why adding NaNO₃ doesn't change the pH of the solution—it doesn't affect this complete ionization process.

Common Ion Effect

The "common ion effect" is an important concept in acid-base chemistry. It refers to the decrease in the ionization of a weak acid or base when a salt containing an ion already present in the equilibrium is added. This effect is directly related to Le Chatelier’s principle and acid-base equilibria.

For example, when NaNO₂ is added to the HNO₂ solution, it provides a source of NO₂⁻ ions. Since NO₂⁻ is already a product of the dissociation of HNO₂, its addition shifts the equilibrium position to the left according to Le Chatelier's principle. This suppresses further ionization of the HNO₂, reducing the concentration of H⁺ ions and increasing the pH.

In contrast, adding NaNO₃ to a solution of HNO₃ does not result in a common ion effect. This is because HNO₃ is a strong acid that is fully ionized in water, so additions of NO₃⁻ have no effect on the equilibrium of HNO₃—there's no further ionization to suppress. Therefore, the pH remains unchanged.