THE pH OF SOLUTIONS

pH is a measure of the acidity or alkalinity of a solution. It's calculated using the negative logarithm of the hydronium ion concentration: pH = -log₁₀[H₃O⁺]. To calculate pH, you need the concentration of hydronium ions (H₃O⁺) in moles per liter (molarity). For example, if a solution has a hydronium ion concentration of 1 x 10⁻⁷ M, the pH would be 7 (10⁻⁷ to the base 10 is 7).

H

Hydronium Ions (H₃O⁺):

Acids donate H⁺ ions, which combine with water molecules to form H₃O⁺. 

Logarithm:

The logarithm (log) tells you the power to which a base (usually 10) must be raised to produce a given number.

 

pH Scale:

The pH scale ranges from 0 to 14. A pH of 7 is neutral. Values below 7 are acidic, and values above 7 are basic (alkaline). 

pOH:

pOH is a related scale that measures the alkalinity of a solution. pOH + pH = 14. 

Strong vs. Weak Acids/Bases:

Strong acids and bases completely dissociate in water, while weak acids and bases only partially dissociate. This affects how their concentrations are used in pH calculations. 

EXAMPLES:

Strong Acid:

If you have a solution of 0.055 M HBr (a strong acid), the pH is -log(0.055) = 1.26. 

Strong Base:

If you have a solution of 0.0035 M LiOH (a strong base), you would first calculate the pOH ( -log(0.0035) = 2.46) and then subtract it from 14 to get the pH (14 - 2.46 = 11.54). 

Weak Acid:

For weak acids, you often need to use an ICE table and the acid dissociation constant (Ka) to determine the [H₃O⁺] before calculating the pH.

 

Calculating [H₃O⁺] from pH:

If you know the pH, you can calculate the hydronium ion concentration using the reverse of the pH equation: [H₃O⁺] = 10⁻pH.

pH calculations often require a calculator, especially for more complex solutions. 

pH measurements can be done using pH meters or indicators. 

WORKED EXAMPLES:

1. Calculating pH from Hydrogen Ion Concentration:

Problem: What is the pH of a solution with a hydrogen ion concentration of 0.001 M?

 

Solution ⭐:

pH = -log[H+] = -log(0.001) 

pH = 3.000 

This solution is acidic. 

2. Calculating pH of a Strong Acid Solution:

Problem: What is the pH of a 0.0235 M HCl solution? 

Solution ⭐:

HCl is a strong acid, so [H+] = 0.0235 M. 

pH = -log(0.0235) = 1.629. 

This solution is acidic. 

3. Calculating pH of a Strong Base Solution:

• Problem: What is the pH of a 0.0035 M KOH solution? 

Solution ⭐:

• KOH is a strong base, so [OH-] = 0.0035 M. 

• pOH = -log(0.0035) = 2.46. 

• pH = 14 - 2.46 = 11.54. 

This solution is basic. 

4. Calculating pH of a Weak Acid Solution (using Ka):

Problem:

• What is the pH of a 0.1 M solution of formic acid (HCOOH), given Ka = 1.77 x 10^-4? 

Solution ⭐:

• Formic acid (HCOOH) dissociates into H+ and HCOO-. 

• Set up an ICE table (Initial, Change, Equilibrium). 

• Ka = [H+][HCOO-] / [HCOOH] = x^2 / (0.1 - x). 

• Since Ka is small, we can simplify to x^2 / 0.1. 

x = [H+] = √(Ka * 0.1) = √(1.77 x 10^-4 * 0.1) = 0.0042 M. 

• pH = -log(0.0042) = 2.38. 

This solution is acidic. 

5. Calculating pH of a Weak Base Solution (using Kb):

Problem: Calculate the pH of a 5 mol/L aqueous ammonia solution (Kb = 1.8 x 10^-5).