The pH Scale and Acid-Base Calculations

THE pH SCALE

Introduction to the pH Scale

The pH scale is a fundamental concept in general chemistry, used to classify the acidity or basicity of aqueous solutions. It provides a quantitative measure of the concentration of hydrogen ions (H+) in solution, ranging from 0 (most acidic) to 14 (most basic) under standard conditions (25°C, 1 M solution).

• Acidic solutions: pH < 7

• Neutral solutions: pH = 7

• Basic solutions: pH > 7

Stronger the acid, lower the pH; stronger the base, higher the pH.

Visual Representation of the pH Scale

The pH scale is typically represented as a color-coded bar, with red indicating strong acids (pH 0-3), green indicating neutral (pH 7), and purple/blue indicating strong bases (pH 11-14).

Key Definitions

• Acid: Substance that increases the concentration of hydrogen ions (H+) in solution.

• Base: Substance that increases the concentration of hydroxide ions (OH-) in solution.

• Neutral: Solution where concentrations of H+ and OH- are equal.

Examples: Identifying Acidity

• Example: Given the pH of several solutions, the one with the lowest pH is the most acidic. HNO3 (aq): pH = 1.2 NaOH (aq): pH = 12.7 CH3COOH (aq): pH = 3.01 Answer: HNO3 (aq) is the most acidic (lowest pH).

pH and pOH Calculations

Relationship Between pH and pOH

The pH and pOH of a solution are related by the following equation at 25°C:

$\mathrm{pH} + \mathrm{pOH} = 14$

This relationship allows calculation of one value if the other is known.

Formulas for pH and pOH

• $\mathrm{pH} = -\log[\mathrm{H}^+]$

• $\mathrm{pOH} = -\log[\mathrm{OH}^-]$

Where $[\mathrm{H}^+]$ is the molar concentration of hydrogen ions and $[\mathrm{OH}^-]$ is the molar concentration of hydroxide ions.

Example: Calculating pH from Concentration

• Example: A solution is prepared by dissolving HCN in 2 L of water. The pH is found to equal 0.34 moles. Calculate the pH of this HCN solution. Solution: Use $\mathrm{pH} = -\log[\mathrm{H}^+]$ with $[\mathrm{H}^+] = 0.34$ mol/L. $\mathrm{pH} = -\log(0.34) \approx 0.47$

Practice Problem: Calculating pOH

• Practice: A solution of NaOH was prepared in a chemistry lab and the pOH was determined to be 9.3. What is the concentration of OH- ions in the solution? Solution: $[\mathrm{OH}^-] = 10^{-9.3} \approx 5.0 \times 10^{-10}$ M

Additional pH and pOH Calculations

Calculating pOH from pH and Vice Versa

Recall that the pH scale goes up to 14 at 25°C. To calculate pOH from pH or vice versa, use:

$\mathrm{pH} + \mathrm{pOH} = 14$

Example: Calculating pOH and [H+]

• Example: You prepare a solution of HCl with a pH of 2.3 at 25°C. What would be the pOH and the concentration of hydrogen ions of this solution? Solution: $\mathrm{pOH} = 14 - 2.3 = 11.7$ $[\mathrm{H}^+] = 10^{-2.3} \approx 5.0 \times 10^{-3}$ M

Practice Problems

• Calculate [H+] of a lemon juice solution at 25°C with a pH of 2.5. $[\mathrm{H}^+] = 10^{-2.5} \approx 3.2 \times 10^{-3}$ M

• A 345 mL bottle of antacid (Mg(OH)2) contains 1.43 × 10-5 moles of hydroxide ions. Determine pH and pOH of the antacid. $[\mathrm{OH}^-] = \frac{1.43 \times 10^{-5}}{0.345} \approx 4.14 \times 10^{-5}$ M\mathrm{pOH} = -\log(4.14 \times 10^{-5}) \approx 4.38$ $\mathrm{pH} = 14 - 4.38 = 9.62$

Conceptual Practice: Properties of Aqueous Solutions

• When the concentration of hydrogen ions increases, concentration of hydroxide ions decreases.

• In a solution of weak acid, pH is usually higher than in a solution of strong acid of the same concentration.

• pH of pure water equals 7 at 25°C.

Summary Table: pH, pOH, and Ion Concentrations

Type of Solution	pH	pOH	[H+]	[OH-]
Strong Acid	0-3	11-14	High	Low
Neutral	7	7	$1.0 \times 10^{-7}$ M	$1.0 \times 10^{-7}$ M
Strong Base	11-14	0-3	Low	High

Additional info: These notes cover core concepts from General Chemistry Chapter 16: Acid-Base Equilibria, focusing on the pH scale, calculations, and properties of acids and bases in aqueous solution.