Problem 114 - Chemistry: The Central Science

Question

A hypothetical acid \(\mathrm{H}_{2} \mathrm{X}\) is both a strong acid and a diprotic acid. (a) Calculate the pH of a \(0.050 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{X}\), assuming that only one proton ionizes peracid molecule. (b) Calculate the \(\mathrm{pH}\) of the solution from part (a), now assuming that both protons of each acid molecule completely ionize. (c) In an experiment it is observed that the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{X}\) is \(1.27 .\) Comment on the relative acid strengths of \(\mathrm{H}_{2} \mathrm{X}\) and \(\mathrm{H} \mathrm{X}^{-}\). (d) Would a solution of the salt \(\mathrm{NaH} \mathrm{X}\) be acidic, basic, or neutral? Explain.

Step-by-Step Solution

Answer

The pH of a 0.050 M solution of H2X, assuming that only one proton ionizes per acid molecule, is 1.30. However, considering both protons ionized, the pH would be 1.00. The experimentally observed pH is 1.27, which suggests that H2X is a stronger acid than HX⁻. A solution of NaHX would be acidic, as HX⁻, the conjugate base of the strong acid H2X, can donate a proton to water and increase the concentration of H⁺ ions.

Step 1: Ionization equation of H2X with one proton ionizing

H2X → H⁺ + HX⁻ #Step 2: Calculate the concentration of H⁺ ions#

Step 2: Concentration of H⁺ ions when only one proton ionizes

As it is assumed that only one proton ionizes per acid molecule and H2X is a strong acid, the concentration of H⁺ ions would be equal to the initial concentration of H2X, which is 0.050 M. #Step 3: Calculate the pH of the solution#

Step 3: pH calculation for one proton ionization

The pH of the solution is given by pH = -log[H⁺] Substitute the value of H⁺ concentration: pH = -log(0.050) = 1.30 #b) Calculate the pH of the solution from part (a), now assuming that both protons of each acid molecule completely ionize.# #Step 1: Write the ionization equation#

Step 4: Ionization equation of H2X with both protons ionizing

H2X → 2H⁺ +X²⁻ #Step 2: Calculate the concentration of H⁺ ions#

Step 5: Concentration of H⁺ ions when both protons ionize

As both protons ionize per acid molecule and H2X is a strong acid, the concentration of H⁺ ions would be twice the initial concentration of H2X, which is (2 × 0.050) M = 0.100 M. #Step 3: Calculate the pH of the solution#

Step 6: pH calculation for both proton ionization

The pH of the solution is given by pH = -log[H⁺] Substitute the value of H⁺ concentration: pH = -log(0.100) = 1.00 #c) Comment on the relative acid strengths of H2X and HX¯.#

Step 7: Relative acid strengths

The experimentally observed pH is 1.27, which indicates that the ionization of one proton occurs more easily and the actual dissociation is somewhere in between one and two protons ionizing. Therefore, H2X is a stronger acid than HX¯. #d) Would a solution of the salt NaHX be acidic, basic, or neutral? Explain.# #Step 1: Write the ionization equation of NaHX#

Step 8: Ionization equation of NaHX

NaHX → Na⁺ + HX⁻ #Step 2: Determine if the solution of NaHX will be acidic, basic, or neutral#

Step 9: Acidic, basic, or neutral solution

Since HX⁻ is the conjugate base of the strong acid H2X, the solution of NaHX would be acidic due to the presence of HX⁻ which can donate a proton to water and increase the concentration of H⁺ ions.

Key Concepts

Diprotic Acid

A diprotic acid is a type of acid that can donate two protons (hydrogen ions, H⁺) per molecule during the process of ionization. These acids undergo ionization in multiple steps, each releasing a proton. The first ionization usually occurs more readily compared to the second, because removing the first proton often causes the acid to become a less negatively charged species.

• Example: Sulfuric acid ( H₂SO₄ ) is a well-known diprotic acid and can ionize in the following sequence:
• H₂SO₄ → H⁺ + HSO₄⁻ (first ionization)
• HSO₄⁻ → H⁺ + SO₄²⁻ (second ionization)

Diprotic acids are common in chemistry and play a critical role in acid-base equilibria, as they can affect the pH and the acidity of solutions significantly.

pH Calculation

Calculating the pH of a solution is essential for understanding its acidity. The pH is defined as the negative logarithm ( -log ) of the hydrogen ion concentration [ H⁺ ] in a solution.
This means:

pH = -log([ H⁺ ])
To compute the pH correctly, it's necessary to know the concentration of hydrogen ions.
For strong acids, such as a hypothetical strong diprotic acid H₂X , the calculation assumes full ionization:

• For single proton ionization: Assume [ H⁺ ] = initial concentration of H₂X (0.050 M in this problem).
• For both protons ionizing completely: Assume [ H⁺ ] = 2 × initial concentration of H₂X , hence 0.100 M in this scenario.

Efficient pH calculation is indispensable for understanding chemical reactivity and health of systems involving acids.

Conjugate Base

The conjugate base of an acid is what remains after the acid has donated a proton. Once an acid releases a proton, it transforms into its conjugate base. The strength and behavior of the conjugate base can significantly influence the resulting pH of a solution.

• For H₂X , the conjugate base after losing one proton is HX⁻
• And after losing two protons, it is X²⁻
• The conjugate base HX⁻ can sometimes re-gain a proton to revert back to the acid form, especially in weak acids where equilibrium is significant.
• Given the problem, the observation in part (c) suggests HX⁻ is weaker than H₂X , as it does not fully ionize in the provided 0.050 M solution scenario.

Conjugate bases form an integral part of buffer systems affecting the acidity or basicity of solutions.

Strong Acids

Strong acids are fully ionized in solution, meaning they release all their available protons. This complete ionization characterizes acids such as hydrochloric acid HCl and sulfuric acid H₂SO₄ .
When a strong acid such as a hypothetical H₂X is in solution:

• All H₂X molecules dissociate into H⁺ ions and HX⁻ .
• If both protons are released, resulting X²⁻ forms.
• Resulting pH is more acidic compared to weak acids, given complete dissociation.

Understanding strong acids is vital in predicting reactions and preparing chemical solutions, especially in industrial and research contexts.

Ionization

Ionization of an acid involves the liberation of protons ( H⁺ ) into the solution, converting the acid into its corresponding conjugate base. This ionization process directly influences the pH and reactivity of the solution.
There are different degrees of ionization:

• Partial Ionization characterizes weak acids that do not fully dissociate in solution.
• Complete Ionization relates to strong acids where dissociation is total.
• For a diprotic acid such as H₂X , ionization can happen in successive phases – first releasing one proton, then the other, influencing calculations like those in the exercise.

The level of ionization provides insights into an acid's strength and helps in predicting chemical behavior, especially when forming salts or reacting with bases.