Question

Compare the pH of a \(0.040 \mathrm{M} \mathrm{HCl}\) solution with that of a \(0.040 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solution. (Hint: \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is a strong acid; \(K_{2}\) for \(\mathrm{HSO}_{4}^{-}=1.3 \times 10^{-2}\).)

Short answer

The H₂SO₄ solution is more acidic with a pH of 1.20 compared to HCl's pH of 1.40.

Step-by-step solution

Determine pH of HCl

HCl is a strong acid that fully dissociates in water. For a \(0.040\,\text{M}\) HCl solution, the concentration of \(\text{H}^+\) ions is \(0.040\,\text{M}\). The pH is calculated as follows: \[pH = -\log[\text{H}^+] = -\log(0.040) \approx 1.40\]

Determine Initial Dissociation of H₂SO₄

\(\text{H}_2\text{SO}_4\) is a strong acid that dissociates completely in its first step. For a \(0.040\,\text{M}\) \(\text{H}_2\text{SO}_4\) solution, the concentration of \(\text{H}^+\) ions after the first dissociation is \(0.040\,\text{M}\).

Account for Second Dissociation Step of H₂SO₄

The second dissociation of \(\text{HSO}_4^-\) is not complete and is represented by the reaction: \[\text{HSO}_4^- \rightleftharpoons \text{H}^+ + \text{SO}_4^{2-}\] With \(K_2 = 1.3 \times 10^{-2}\), solve for additional \([\text{H}^+]\) due to this dissociation:\[K_2 = \frac{[\text{H}^+][\text{SO}_4^{2-}]}{[\text{HSO}_4^-]} = 1.3 \times 10^{-2}\]

Calculate Additional [H⁺] from Second Dissociation

Assume \([\text{HSO}_4^-] \approx 0.040\,\text{M}\) initially. From this, \[x^2 / (0.040) \approx 1.3 \times 10^{-2}\] Solving for \(x\) (additional \([\text{H}^+]\)) gives: \[x \approx \sqrt{(0.040)(1.3 \times 10^{-2})} \approx 0.023\,\text{M}\]

Calculate Total [H⁺] and pH for H₂SO₄

Add the \([\text{H}^+]\) from both dissociation steps: \[ [\text{H}^+]_{\text{total}} = 0.040 + 0.023 = 0.063\,\text{M}\] Then, calculate the pH:\[pH = -\log(0.063) \approx 1.20\]

Compare Results

The pH of the \(0.040\,\text{M}\) HCl solution is approximately 1.40, while the pH of the \(0.040\,\text{M}\) \(\text{H}_2\text{SO}_4\) solution is approximately 1.20. The \(\text{H}_2\text{SO}_4\) solution is more acidic.

Key concepts

Strong Acids

When we talk about strong acids, we're referring to acids that dissociate completely in water, releasing all available hydrogen ions (H⁺) into the solution. This is a characteristic of strength because the acid's ability to donate its protons determines its impact on the solution's pH level.
Examples of strong acids include:

• Hydrochloric acid (HCl)
• Sulfuric acid (H₂SO₄)
• Nitric acid (HNO₃)

These acids are known for their aggressive behavior in chemical reactions due to their complete dissociation.
If you're comparing strong acids, it's important to consider their concentration and dissociation ability to fully grasp their potential acidity.

Dissociation

Dissociation is the process by which substances split into smaller particles or ions, typically in a solution. For acids, this means releasing hydrogen ions (H⁺) into the solution, defining its acidic properties.
This process is crucial when understanding acid behavior:

• Complete Dissociation: Strong acids dissociate fully in water. They donate all of their H⁺ ions.
• Partial Dissociation: Weak acids do not release all available H⁺ ions into the solution. Some of the original molecules remain intact.

By knowing the dissociation extent, one can predict the resulting pH of the solution. More dissociated H⁺ ions mean a lower (more acidic) pH value.

Acid Strength

Acid strength refers to the tendency of an acid to donate its protons to a base. This is measured by how completely the acid can dissociate in a given solution. Stronger acids dissociate more completely, thereby increasing the concentration of hydrogen ions in the solution.
Factors influencing acid strength include:

• Concentration: Higher concentration typically leads to a lower pH, indicating a stronger acid effect.
• Stability of Resulting Anion: The more stable the anion formed after the acid donates its proton, the stronger the acid.
• Polarity of the Bond: More polar bonds between hydrogen and the rest of the acid molecule make it easier for H⁺ to dissociate.

Understanding acid strength is crucial when comparing different acids such as HCl and H₂SO₄, where both dissociate completely but have different secondary dissociation events and concentration effects.

Sulfuric Acid Dissociation

Sulfuric acid (H₂SO₄) is unique among strong acids because it undergoes dissociation in two steps. Understanding each step sheds light on its acidic properties:
**First Step of Dissociation:**

• In water, H₂SO₄ dissociates completely to produce H⁺ ions and HSO₄⁻ ions.
• This initial step resembles the behavior of other strong acids like HCl, leading to an immediate increase in H⁺ ions.

**Second Step of Dissociation:**

• HSO₄⁻ further dissociates in water, although not completely, to give more H⁺ ions and SO₄²⁻ ions.
• This step is characterized by its equilibrium constant, K₂ = 1.3 × 10⁻², indicating it's not as strong as the first.
• Despite being a weaker dissociation step, this contributes additional H⁺, making the solution more acidic than an equivalent concentration of other strong acids like HCl.

These two steps lead to a greater overall concentration of hydrogen ions in solution, resulting in a lower pH level for sulfuric acid compared to a HCl solution of the same concentration.