pH value of which one of the following is NOT equal to one? (A) 0.1 M HNO3 (B) 0.1 M CH3 COOH (C) 50 cm3 0.4 M HCl + 50 cm3 0.2 M NaOH (D) 0.05 M H2SO4

To determine which of the given options does not have a pH value equal to one, we need to analyze the pH of each solution based on their concentrations and the nature of the acids or bases involved. Let's break down each option step by step.

Understanding pH and Acid Concentration

The pH scale ranges from 0 to 14, where a pH of 7 is neutral. A pH less than 7 indicates acidity, while a pH greater than 7 indicates alkalinity. Strong acids, like hydrochloric acid (HCl), dissociate completely in water, while weak acids, like acetic acid (CH3COOH), do not.

Analyzing Each Option

• (A) 0.1 M HNO3: Nitric acid (HNO3) is a strong acid that fully dissociates in solution. Therefore, a 0.1 M solution will have a pH calculated as follows:
  • pH = -log[H⁺] = -log(0.1) = 1
• (B) 0.1 M CH3COOH: Acetic acid is a weak acid and does not fully dissociate. Its dissociation constant (K_a) is approximately 1.8 x 10^-5. To find the pH, we can use the formula:
  • For weak acids: [H⁺] = √(K_a × C) where C is the concentration.
  • [H⁺] = √(1.8 x 10^-5 × 0.1) ≈ 0.00134 M
  • pH = -log(0.00134) ≈ 2.87
• (C) 50 cm³ 0.4 M HCl + 50 cm³ 0.2 M NaOH: This is a neutralization reaction. First, we calculate the moles of HCl and NaOH:
  • Moles of HCl = 0.4 M × 0.050 L = 0.02 moles
  • Moles of NaOH = 0.2 M × 0.050 L = 0.01 moles

  Since HCl is in excess, the remaining moles of HCl after neutralization will be 0.02 - 0.01 = 0.01 moles. The total volume of the solution is 100 cm³ or 0.1 L.

  • [H⁺] = 0.01 moles / 0.1 L = 0.1 M
  • pH = -log(0.1) = 1
• (D) 0.05 M H2SO4: Sulfuric acid (H2SO4) is a strong acid that dissociates completely in its first step and partially in its second step. For the first dissociation:
  • H2SO4 → H⁺ + HSO₄^-
  • pH from first dissociation: [H⁺] = 0.05 M

  For the second dissociation, HSO₄^- is also a weak acid, contributing additional H⁺ ions, but for simplicity, we can estimate that the total [H⁺] will be slightly more than 0.05 M. Thus, the pH will be less than 1.

Conclusion

From our analysis, we see that:

• 0.1 M HNO3 has a pH of 1.
• 0.1 M CH3COOH has a pH of approximately 2.87.
• The mixture of HCl and NaOH results in a pH of 1.
• 0.05 M H2SO4 has a pH less than 1.

Thus, the answer to your question is (B) 0.1 M CH3COOH, as it does not have a pH equal to one.