pH Calculations
Master pH calculations for strong acids and bases, understand the pH scale, dilution effects, and work with the acid dissociation constant Ka.
The pH Scale
The pH scale measures how acidic or basic a solution is. It is defined as the negative logarithm (base 10) of the hydrogen ion concentration.
pH = -log10[H+]
Key Relationships
- • pH < 7: acidic solution
- • pH = 7: neutral (pure water at 25 degrees C)
- • pH > 7: basic (alkaline) solution
- • Each pH unit = 10-fold change in [H+]
Reverse Calculation
To find [H+] from pH:
[H+] = 10-pH
For bases: pOH = -log[OH-] and pH + pOH = 14 (at 25 degrees C)
Strong Acids and Bases
Strong acids fully dissociate in water -- every molecule produces H+ ions. Strong bases fully dissociate to produce OH- ions. This makes pH calculations straightforward.
Complete Dissociation
Strong Acid (HCl)
HCl → H+ + Cl-
0.01 M HCl gives [H+] = 0.01 M
pH = -log(0.01) = 2.0
Strong Base (NaOH)
NaOH → Na+ + OH-
0.01 M NaOH gives [OH-] = 0.01 M
pOH = 2.0, so pH = 12.0
Dilution: When a strong acid is diluted, [H+] decreases and pH increases (becomes less acidic). Use C1V1 = C2V2 to find the new concentration, then recalculate pH.
Weak Acids and the Dissociation Constant Ka
Weak acids only partially dissociate in water. The extent of dissociation is described by the acid dissociation constant Ka.
For a weak acid HA:
HA ⇌ H+ + A-
Ka = [H+][A-] / [HA]
A larger Ka means a stronger weak acid
Simplifying Assumption
For a weak acid with initial concentration C and small Ka:
• If x = [H+] at equilibrium, then Ka = x2 / (C - x)
• If x is small compared to C (less than 5%), we approximate: Ka ≈ x2 / C
• Therefore: [H+] = √(Ka × C) and then pH = -log[H+]
Key Vocabulary
pH
The negative base-10 logarithm of the hydrogen ion concentration: pH = -log10[H+].
Strong Acid
An acid that fully dissociates in water (e.g. HCl, HNO3, H2SO4). [H+] equals the acid concentration.
Ka (Acid Dissociation Constant)
A measure of the strength of a weak acid. Ka = [H+][A-] / [HA].
Dissociation
The process by which a compound breaks apart into ions in solution. Can be complete (strong) or partial (weak).
Worked Examples
Calculate the pH of a 0.0025 M HCl solution.
Step 1: HCl is a strong acid, so [H+] = 0.0025 M = 2.5 × 10-3 M
Step 2: pH = -log(2.5 × 10-3)
Step 3: pH = 2.60
Calculate the pH of 0.05 M NaOH at 25 degrees C.
Step 1: NaOH is a strong base. [OH-] = 0.05 M
Step 2: pOH = -log(0.05) = 1.30
Step 3: pH = 14 - pOH = 14 - 1.30 = 12.70
A weak acid HA has Ka = 1.8 × 10-5 and concentration 0.10 M. Find the pH.
Step 1: Use the approximation: [H+] = √(Ka × C) = √(1.8 × 10-5 × 0.10)
Step 2: [H+] = √(1.8 × 10-6) = 1.34 × 10-3 M
Step 3: pH = -log(1.34 × 10-3) = 2.87
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the pH of a 0.001 M HCl solution?
Question 2
A solution has a pH of 5. What is the hydrogen ion concentration [H+]?
Question 3
When a strong acid solution is diluted by a factor of 10, the pH:
Question 4
The pH of 0.1 M NaOH at 25 degrees C is:
Question 5
A weak acid with a larger Ka value compared to another weak acid is:
Key Concepts Summary
- ●pH = -log10[H+] and [H+] = 10-pH.
- ●Strong acids/bases fully dissociate: [H+] equals the acid concentration directly.
- ●For bases: pH + pOH = 14 at 25 degrees C.
- ●Diluting by a factor of 10 changes pH by 1 unit.
- ●For weak acids: [H+] = √(Ka × C) when the approximation is valid.