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The problem presented is a typical acid-base problem involving perchloric acid (HClO₄), which is a strong acid that completely dissociates in water.

**Given:**
- Mass of perchloric acid (HClO₄): 722 mg
- Volume of the solution: 140 mL

**Step 1: Convert mass of HClO₄ to moles.**

First, we need to convert the given mass of perchloric acid from milligrams to grams:
\[
722 \, \text{mg} = 0.722 \, \text{g}
\]

Next, we use the molar mass of perchloric acid (HClO₄), which is approximately:
\[
M(\text{HClO₄}) = 100.46 \, \text{g/mol}
\]
Now, we calculate the number of moles of HClO₄:
\[
\text{moles of HClO₄} = \frac{0.722 \, \text{g}}{100.46 \, \text{g/mol}} \approx 0.00719 \, \text{mol}
\]

**Step 2: Find the concentration of H⁺ ions (since HClO₄ is a strong acid, it fully dissociates).**

The concentration of H⁺ ions is the same as the concentration of HClO₄, which can be found by dividing the number of moles by the volume of the solution (converted to liters):
\[
\text{Volume of solution} = 140 \, \text{mL} = 0.140 \, \text{L}
\]
\[
\text{Concentration of H⁺} = \frac{0.00719 \, \text{mol}}{0.140 \, \text{L}} \approx 0.0514 \, \text{mol/L}
\]

**Step 3: Calculate the pH.**

Since the concentration of H⁺ ions is equal to the concentration of HClO₄, we can calculate the pH using the formula:
\[
\text{pH} = -\log [\text{H⁺}]
\]
\[
\text{pH} = -\log(0.0514) \approx 1.29
\]

Thus, the pH of the solution is approximately **1.29**.

Would you like more details on any step or have further questions?

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Here are 5 related questions to deepen your understanding:
1. How does the concentration of a strong acid differ from that of a weak acid?
2. What is the role of the molar mass in calculating the moles of a substance?
3. Why is the concentration of H⁺ equal to the concentration of HClO₄ for strong acids?
4. How would the pH change if the solution volume increased but the mass of acid stayed the same?
5. Can you explain the logarithmic relationship used in pH calculations?

**Tip:** When dealing with strong acids, remember that they dissociate completely in water, simplifying pH calculations.

A chemist dissolves 722 mg of pure perchloric acid in enough water to make up 140 mL of solution. Calculate the pH of the solution. Be sure your answer has the correct number of significant digits.

Learn how to calculate the pH of a perchloric acid solution using 722 mg of HClO₄ dissolved in 140 mL of solution. This step-by-step guide covers mass to moles conversion, concentration calculation, and pH determination. Suitable for Grades 11-12.

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