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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

01

Ionization equation of H2X with one proton ionizing

H2X 鈫� H鈦� + HX鈦� #Step 2: Calculate the concentration of H鈦� ions#

02

Concentration of H鈦� 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鈦� ions would be equal to the initial concentration of H2X, which is 0.050 M. #Step 3: Calculate the pH of the solution#

03

pH calculation for one proton ionization

The pH of the solution is given by pH = -log[H鈦篯 Substitute the value of H鈦� 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#

04

Ionization equation of H2X with both protons ionizing

H2X 鈫� 2H鈦� +X虏鈦� #Step 2: Calculate the concentration of H鈦� ions#

05

Concentration of H鈦� ions when both protons ionize

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

06

pH calculation for both proton ionization

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

07

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炉. #d) Would a solution of the salt NaHX be acidic, basic, or neutral? Explain.# #Step 1: Write the ionization equation of NaHX#

08

Ionization equation of NaHX

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

09

Acidic, basic, or neutral solution

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Diprotic Acid

A diprotic acid is a type of acid that can donate two protons (hydrogen ions, H鈦�) 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 ( H鈧係O鈧� ) is a well-known diprotic acid and can ionize in the following sequence:
• H鈧係O鈧� 鈫� H鈦� + HSO鈧勨伝 (first ionization)
• HSO鈧勨伝 鈫� H鈦� + SO鈧劼测伝 (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鈦� ] in a solution.
This means:

pH = -log([ H鈦� ])
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 H鈧俋 , the calculation assumes full ionization:

• For single proton ionization: Assume [ H鈦� ] = initial concentration of H鈧俋 (0.050 M in this problem).
• For both protons ionizing completely: Assume [ H鈦� ] = 2 脳 initial concentration of H鈧俋 , 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 H鈧俋 , the conjugate base after losing one proton is HX鈦�
• And after losing two protons, it is X虏鈦�
• The conjugate base HX鈦� 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鈦� is weaker than H鈧俋 , 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 H鈧係O鈧� .
When a strong acid such as a hypothetical H鈧俋 is in solution:

• All H鈧俋 molecules dissociate into H鈦� ions and HX鈦� .
• If both protons are released, resulting X虏鈦� 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鈦� ) 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 H鈧俋 , ionization can happen in successive phases 鈥� 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.