To determine which solution has the lowest pH value, we need to understand how to calculate the pH of each solution based on the concentration of hydrochloric acid (HCl) in moles per liter (M). The pH of a solution is a measure of its acidity, and it is calculated using the formula: \[ \text{pH} = -\log[\text{H}^+] \] Where \([\text{H}^+]\) is the concentration of hydrogen ions in moles per liter. ### Step-by-Step Explanation 1. **Understanding the Concentration of HCl Solutions**: - HCl is a strong acid, which means it completely dissociates in water: \[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \] - Therefore, the concentration of hydrogen ions \([\text{H}^+]\) in the solution is equal to the concentration of HCl. 2. **Calculating the Concentration of Each Option**: - **Option A**: 5 ml of (m/10) HCl - Concentration = \( \frac{1}{10} \) M - Moles of HCl in 5 ml = \( \frac{1}{10} \times 0.005 \) L = \( 5 \times 10^{-6} \) moles - Total volume = 0.005 L - Concentration of HCl = \( \frac{5 \times 10^{-6}}{0.005} = 0.1 \) M - \([\text{H}^+] = 0.1\) M - pH = \(-\log(0.1) = 1\) - **Option B**: 10 ml of (m/10) HCl - Concentration = \( \frac{1}{10} \) M - Moles of HCl in 10 ml = \( \frac{1}{10} \times 0.01 \) L = \( 1 \times 10^{-5} \) moles - Total volume = 0.01 L - Concentration of HCl = \( \frac{1 \times 10^{-5}}{0.01} = 0.1 \) M - \([\text{H}^+] = 0.1\) M - pH = \(-\log(0.1) = 1\) - **Option C**: 15 ml of (m/5) HCl - Concentration = \( \frac{1}{5} \) M - Moles of HCl in 15 ml = \( \frac{1}{5} \times 0.015 \) L = \( 3 \times 10^{-5} \) moles - Total volume = 0.015 L - Concentration of HCl = \( \frac{3 \times 10^{-5}}{0.015} = 0.2 \) M - \([\text{H}^+] = 0.2\) M - pH = \(-\log(0.2) \approx 0.70\) - **Option D**: 20 ml of (m/8) HCl - Concentration = \( \frac{1}{8} \) M - Moles of HCl in 20 ml = \( \frac{1}{8} \times 0.02 \) L = \( 2.5 \times 10^{-5} \) moles - Total volume = 0.02 L - Concentration of HCl = \( \frac{2.5 \times 10^{-5}}{0.02} = 0.125 \) M - \([\text{H}^+] = 0.125\) M - pH = \(-\log(0.125) \approx 0.90\) 3. **Comparing pH Values**: - Option A: pH = 1 - Option B: pH = 1 - Option C: pH ≈ 0.70 - Option D: pH ≈ 0.90 From the calculations, we see that **Option C** has the lowest pH value (approximately 0.70), not Option A as previously recorded. ### Why Other Options Are Incorrect or Weaker: - **Option A** and **Option B** both yield a pH of 1, which is higher than the pH of Option C. - **Option D** has a pH of approximately 0.90, which is also higher than that of Option C. ### Revision Summary: - pH is calculated using the formula \(\text{pH} = -\log[\text{H}^+]\). - Strong acids like HCl completely dissociate, so \([\text{H}^+]\) equals the concentration of the acid. - The solution with the highest concentration of HCl will have the lowest pH. - In this case, Option C (15 ml of (m/5) HCl) has the lowest pH value of approximately 0.70.