Question

Calculate the pH of a \(2.0-M \mathrm{H}_{2} \mathrm{SO}_{4}\) solution.

Short answer

The pH of a \(2.0-M \mathrm{H}_{2} \mathrm{SO}_{4}\) solution can be calculated by first finding the concentration of H⁺ ions, which is \(4.0 M\). Then, we use the pH formula: pH = -log₁₀[H⁺] to get pH ≈ -0.60. Though unusual, pH values can go beyond the 0-14 range, indicating a very acidic solution in this case.

Step-by-step solution

Write the dissociation equation for sulfuric acid

In water, sulfuric acid dissociates as follows: H₂SO₄ → 2H⁺ + SO₄²⁻ This shows that 1 mole of H₂SO₄ will produce 2 moles of H⁺ ions.

Find the concentration of H⁺ ions

Since we know that 1 mole of H₂SO₄ produces 2 moles of H⁺ ions, we can calculate the concentration of H⁺ ions: Concentration of H⁺ ions = 2 × concentration of H₂SO₄ = 2 × 2.0 M = 4.0 M

Calculate the pH

The pH is calculated using the formula: pH = -log₁₀[H⁺] Where [H⁺] is the concentration of H⁺ ions. Using the concentration from Step 2: pH = -log₁₀(4.0)

Evaluate the expression and find the pH

Now, we evaluate the expression to find the pH: pH = -log₁₀(4.0) ≈ -0.60 However, note that the pH scale is typically considered to range from 0 to 14, so reporting a negative pH value may seem unusual. In this case, it indicates that the concentration of H⁺ is very high, and the solution is very acidic. It is vital to understand that the pH can go beyond the range of 0 to 14, even though such cases are uncommon.

Key concepts

Sulfuric Acid Dissociation

Sulfuric acid (\( \mathrm{H}_2\mathrm{SO}_4 \)) is a strong acid that dissociates completely in water, releasing hydrogen ions (\( \mathrm{H^+} \)) and sulfate ions (\( \mathrm{SO_4^{2-}} \)). The dissociation reaction can be represented as:

• \[ \mathrm{H}_2\mathrm{SO}_4 \rightarrow 2 \mathrm{H^+} + \mathrm{SO_4^{2-}} \]

This equation tells us that one mole of sulfuric acid yields two moles of \( \mathrm{H^+} \) ions. It is crucial to grasp this stoichiometry because it directly impacts calculations concerning acidity and pH. Knowing how many \( \mathrm{H^+} \) ions are produced allows us to determine the extent of acidity. Therefore, understanding this dissociation process is the first step in calculating the pH of a \(2.0-M\) solution of sulfuric acid.

Concentration of H⁺ Ions

Determining the concentration of hydrogen ions (\( \mathrm{H^+} \)) is essential for assessing the acidity of a solution. From sulfuric acid's dissociation, we know it produces two moles of \( \mathrm{H^+} \) for every mole of \( \mathrm{H}_2\mathrm{SO}_4 \). Therefore, to find the \( \mathrm{H^+} \) concentration:

• Multiply the concentration of \( \mathrm{H}_2\mathrm{SO}_4 \) by 2.
• In this exercise where \(2.0-M \mathrm{H}_2\mathrm{SO}_4\) was used, the calculation is:\[ 2 \text{ (moles } \mathrm{H^+}/\text{mole } \mathrm{H}_2\mathrm{SO}_4) \times 2.0 \text{ M} = 4.0 \text{ M} \]

So, there are \(4.0 \text{ M}\) of \( \mathrm{H^+} \) ions in the solution. This high concentration reflects the strong acidic nature of sulfuric acid when dissolved in water.

Acidic Solution

An acidic solution is one that releases hydrogen ions (\( \mathrm{H^+} \)) when dissolved in water, resulting in a low pH. Acids like sulfuric acid are classified based on their ability to release \( \mathrm{H^+} \) ions freely. Given the high concentration of \( \mathrm{H^+} \) ions in such solutions;

• More \( \mathrm{H^+} \) ions lead to lower pH values.
• This creates a more acidic environment.

The pH scale typically ranges from 0 (most acidic) to 14 (most basic), with 7 being neutral. In this context, the solution of sulfuric acid, being very acidic, significantly lowers the pH value. The understanding of an acidic solution is vital in chemistry, as it influences reaction conditions and the behavior of substances in the solution.

Negative pH Value

The occurrence of a negative pH might appear strange because we are accustomed to a pH scale between 0 and 14. However, for exceptionally acidic solutions with very high concentrations of hydrogen ions (\( \mathrm{H^+} \)), the pH can transcend the expected scale. Calculating pH involves the formula:

• \[ \text{pH} = -\log_{10}[\mathrm{H^+}] \]

For the \(4.0 \text{ M}\) concentration of \( \mathrm{H^+} \) in this exercise, solving results in a pH of approximately -0.60. Such a negative value indicates an intensely acidic solution, showcasing the sheer volume of hydrogen ions present. Although rare in everyday scenarios, negative pH values can occur in concentrated strong acids, illustrating the solution's potent acidity.