Acids, Bases, and the pH Scale: Calculations and Relationships

Acids, Bases, and the pH Scale

Introduction to pH and pOH

The pH scale is a logarithmic scale used to express the concentration of hydrogen ions ([H+]) and hydroxide ions ([OH-]) in aqueous solutions. It allows chemists to easily compare the acidity or basicity of solutions, especially when dealing with very small concentrations.

• pH is a measure of the hydrogen ion concentration: $\text{pH} = -\log[\text{H}^+]$

• pOH is a measure of the hydroxide ion concentration: $\text{pOH} = -\log[\text{OH}^-]$

• The pH and pOH scales typically range from 0 to 14 under normal conditions.

Key Relationships and Formulas

• The relationship between pH and pOH is given by: $\text{pH} + \text{pOH} = 14$

• To find [H+] from pH: $[\text{H}^+] = 10^{-\text{pH}}$

• To find [OH-] from pOH: $[\text{OH}^-] = 10^{-\text{pOH}}$

• The ion product constant for water at 25°C: $K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$

Classifying Solutions by pH

• Acidic solution: pH < 7 [H+] > [OH-]

• Neutral solution: pH = 7 [H+] = [OH-]

• Basic solution: pH > 7 [H+] < [OH-]

Summary Table: pH, pOH, and Ion Concentrations

Type of Solution	pH	[H+]	[OH-]
Acidic	< 7	> 1.0 × 10-7 M	< 1.0 × 10-7 M
Neutral	= 7	= 1.0 × 10-7 M	= 1.0 × 10-7 M
Basic	> 7	< 1.0 × 10-7 M	> 1.0 × 10-7 M

Practice Questions and Examples

• Practice: Which of the following statements about aqueous solutions is/are true?

  • a) For a basic solution the concentration of OH- is greater than the concentration of H+.

  • b) The pH of a neutral aqueous solution is 7.00 at all temperatures. (Incorrect; pH = 7 is only true at 25°C)

  • c) An acidic solution under normal conditions has a pH value less than 7.00.

  • d) If the concentration of OH- decreases then the concentration of H+ will also decrease. (Incorrect; they are inversely related)

  • e) The pH of aqueous solutions is less than 7. (Incorrect; only acidic solutions have pH < 7)

• Example: What is the hydroxide ion and hydronium ion concentration of an aqueous solution that has a pH equal to 6.12?

  • Find [H+]: $[\text{H}^+] = 10^{-6.12} = 7.59 \times 10^{-7}$ M

  • Find pOH: $\text{pOH} = 14 - 6.12 = 7.88$

  • Find [OH-]: $[\text{OH}^-] = 10^{-7.88} = 1.32 \times 10^{-8}$ M

• Example: A solution is prepared by dissolving 0.235 mol Sr(OH)2 in water to produce a solution with a volume of 750 mL.

  • a) What is the [OH-]? (Calculation steps shown in the notes; see above for method.)

  • b) What is the [H+]? (Use $K_w$ and calculated [OH-].)

• Practice: What is the $K_w$ of pure water at 20.0°C, if the pH is 7.083?

  • Correct answer: $6.82 \times 10^{-15}$

Additional info:

• The value of $K_w$ (the ion product constant for water) changes with temperature. At 25°C, $K_w = 1.0 \times 10^{-14}$, but at other temperatures, the value will differ.

• pH and pOH are always related through the equation $\text{pH} + \text{pOH} = 14$ at 25°C.