Theory — The pH Scale, Acids, Bases, and Titration

Water itself splits very slightly into ions, and the product of the hydrogen ion and hydroxide ion concentrations is a fixed constant at a given temperature. At 25 degrees Celsius this ion product is 1.0 times ten to the minus fourteen.

Ion product of water[H⁺] × [OH⁻] = K_w = 1.0 × 10⁻¹⁴ (at 25 °C)
In pure water [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M, which is neutral

Defining pH and pOH

Because ion concentrations span many orders of magnitude, we use a logarithmic scale. The pH is the negative base-ten logarithm of the hydrogen ion concentration, and the pOH is the same for the hydroxide ion. They always add to 14 at 25 degrees Celsius.

pH and pOHpH = minus log₁₀[H⁺]  ·  pOH = minus log₁₀[OH⁻]
[H⁺] = 10^(minus pH)  ·  [OH⁻] = 10^(minus pOH)
pH + pOH = 14
pH below 7 is acidic, pH = 7 is neutral, pH above 7 is basic

The pH of Strong and Weak Acids and Bases

A strong acid or base dissociates completely, so the ion concentration equals the concentration of the solution. A weak acid or base only partly dissociates and reaches an equilibrium set by its dissociation constant, Ka for an acid or Kb for a base.

Strong acids and basesStrong acid: [H⁺] = C, so pH = minus log₁₀ C
Strong base: [OH⁻] = C, so pOH = minus log₁₀ C and pH = 14 minus pOH
Weak acid equilibriumFor a weak acid HA at concentration C: Ka = x² / (C minus x), where x = [H⁺]
Solving the quadratic gives [H⁺], and pH = minus log₁₀[H⁺]
A weak base is treated the same way using Kb to find [OH⁻]

Acid-Base Titration

A titration adds a solution of known concentration, the titrant, to a measured volume of an unknown, recording the pH after each addition. A graph of pH against the volume of titrant added is the titration curve. The equivalence point is where the moles of added titrant exactly equal the moles of the substance being titrated, marked by a steep jump in pH. Knowing the volume at equivalence lets you find the unknown concentration.

At the equivalence pointmoles of titrant = moles of analyte  →  C_b × V_b(eq) = C_a × V_a
so the unknown acid concentration is  C_a = C_b × V_b(eq) / V_a
Strong acid with strong base gives equivalence at pH 7; a weak acid with a strong base gives equivalence above pH 7

For a weak acid titrated with a strong base, the region before equivalence is a buffer, where the pH changes slowly and is described by the Henderson-Hasselbalch relation. At the half-equivalence point exactly half the acid is neutralized, the concentrations of the acid and its conjugate base are equal, and the pH equals the pKa.

Buffer region (weak acid)pH = pKa + log₁₀( [A⁻] / [HA] )
At half-equivalence, [A⁻] = [HA], so pH = pKa

Lower pH

More hydrogen ions, more acidic. Each drop of one pH unit means ten times more hydrogen ion.

Equivalence point

Where titrant moles equal analyte moles, seen as the steepest part of the titration curve.

Half-equivalence

For a weak acid, the pH there equals the pKa, a quick way to read off the acid strength.

QuantityRelationshipNotes
pHminus log₁₀[H⁺][H⁺] = 10^(minus pH)
pOHminus log₁₀[OH⁻]pH + pOH = 14
Strong acid pHminus log₁₀ Cfull dissociation
Weak acid pHfrom Ka = x²/(C minus x)x = [H⁺]
EquivalenceC_a V_a = C_b V_b(eq)find unknown concentration

Apparatus

The equipment a real pH and titration experiment uses. In the simulation these are modelled for you, but the readings correspond to what each instrument would measure.

7.00measures pH
pH meter
Measures pH directly for acids, bases, and buffers.
shows pH by colour
Indicator / litmus
Estimates pH from colour.
delivers titrant
Burette
Adds acid or base for the titration part.
holds solutions
Beaker
Holds the solutions whose pH is measured.
exact volume
Volumetric flask
Prepares buffer and standard solutions.
reagent solutions
Reagent bottles
Dispense the acid and base stock solutions.

Instructions — Running the Virtual Experiment

This is a record, calculate, and compare lab. In each part you set up a situation, calculate the answer by hand, enter your value, and only then does the simulation reveal its own result so you can compare. Record every value in your worksheet.

Part A — pH, pOH, and Ion Concentrations (Ion Concentrations tab)
1
Open Simulation → Ion Concentrations. Set a hydrogen ion concentration of the form a number times ten to a negative power, for example 4 × 10⁻⁵ M.
2
Calculate the pH from pH = minus log₁₀[H⁺], enter your value, and click Check. The simulation then reveals the pH, pOH, and [OH⁻] so you can compare. Record the set and confirm pH + pOH = 14.
Part B — pH of Acids and Bases (Acid & Base pH tab)
1
Open Acid & Base pH. Choose a type (strong acid, weak acid, strong base, or weak base) and a concentration. For a weak acid or base, also choose the substance, which sets Ka or Kb.
2
Calculate the pH by hand (directly for a strong acid or base, or by solving the equilibrium for a weak one), enter your value, and click Check to compare. Record several cases and note how a weak acid gives a higher pH than a strong acid of the same concentration.
Part C — Acid-Base Titration (Titration tab)
1
Open Titration. A 25.0 mL sample of acid is titrated with 0.100 M base. Choose a strong or a weak acid. Add the base in steps with the buttons, taking smaller steps near the jump, and the pH after each addition is recorded as a point on the curve.
2
From your curve, find the equivalence point, the volume where the pH rises most steeply. For a weak acid, also find the half-equivalence point and read the pKa there.
3
Calculate the acid concentration from C_a = C_b × V_b(eq) / V_a, enter your value, and click Calculate Cₐ & check to compare with the true concentration.
For your reportInclude your data tables, the titration curve, your worked calculations for at least one case in each part, screenshots, and a short discussion comparing your calculated values with the simulation.

Simulation — The pH Bench

pH Virtual LabCalculate first, then reveal and compare
024678101214
[H⁺] (M)pHpOH[OH⁻] (M)
No rows yet — set [H⁺], calculate pH, enter it, and check.

Set the hydrogen ion concentration

Reading
[H⁺]—
pH—
pOH—
[OH⁻]—
024678101214
TypeC (M)Ka or KbYour pHpH actual
No rows yet — choose a solution, calculate the pH, enter it, and check.

Choose the solution

Reading
Solutionstrong acid
Concentration0.10 M
Ka / Kb—
pH—
The acid sample is 25.0 mL and the base titrant is 0.100 M. Each addition records the pH as a point on the curve.
Base added V_b (mL)pH
No additions yet — add base to build the curve.

Acid being titrated

Add base titrant

Burette and flask
Acid volume V_a25.0 mL
Base conc. C_b0.100 M
Base added V_b0.0 mL
Current pH—
Acid conc. Cₐdetermine from curve

Team Questions

Question 1. A solution has [H⁺] = 1 × 10⁻³ M. What is its pH? (one number)
Question 2. If a solution has pH = 9, what is its pOH? (one number)
Question 3. Is a solution of pH 4 acidic, neutral, or basic? (one word)
Question 4. What is the pH of a 0.010 M solution of a strong acid? (one number)
Question 5. In a titration, what name is given to the point where moles of titrant equal moles of analyte? (two words)
Question 6. A strong acid is titrated with a strong base. What is the pH at the equivalence point? (one number)
Question 7 — Challenge. For a weak acid titrated with a strong base, the pH at the half-equivalence point equals what quantity? (one term)

Example Lab Report

A worked example showing the expected format and the record, calculate, and compare workflow.

pH, pOH, and Acid-Base Titration

Chemistry | Section: [Your Section] | Date: [Date]

Lab Members: [Names of all members present]

Objective

To define and calculate pH and pOH, to find the pH of strong and weak acids and bases, and to determine an unknown acid concentration by titration, comparing every calculated value with the simulation.

Part A — Ion Concentrations (worked example)

[H⁺] (M)pHpOH[OH⁻] (M)
4.0 × 10⁻⁵4.409.602.5 × 10⁻¹⁰

pH = minus log(4.0 × 10⁻⁵) = 5 minus log4 = 5 minus 0.60 = 4.40; pOH = 14 minus 4.40 = 9.60; [OH⁻] = 10^(minus 9.60) = 2.5 × 10⁻¹⁰ M. These matched the simulation.

Part B — Acid and Base pH (worked example)

For 0.100 M acetic acid, Ka = 1.8 × 10⁻⁵: solving Ka = x²/(0.100 minus x) gives [H⁺] = 1.34 × 10⁻³ M, so pH = 2.87. A strong acid at the same concentration gives pH = 1.00, confirming that the weak acid is less acidic.

Part C — Titration (worked example)

A 25.0 mL acid sample was titrated with 0.100 M base. The curve rose steeply at V_b = 25.0 mL, the equivalence point. The acid concentration was therefore C_a = (0.100 × 25.0) / 25.0 = 0.100 M, matching the simulation. For the weak acid, the half-equivalence point at 12.5 mL gave pH = 4.74, equal to the pKa.

Discussion and Conclusion

Every calculated value agreed with the simulation. The pH and pOH always summed to 14, a weak acid gave a higher pH than a strong acid of equal concentration, and the titration located the equivalence point and recovered the unknown concentration, with the weak-acid half-equivalence point reading off the pKa directly.

Practice Questions

Question 1
A solution has [H⁺] = 2.5 × 10⁻⁴ M. Find the pH, pOH, and [OH⁻].
Hint: pH = minus log(2.5 × 10⁻⁴) = 3.60; pOH = 10.40; [OH⁻] = 10⁻¹⁰·⁴⁰ = 4.0 × 10⁻¹¹ M.
Question 2
Calculate the pH of 0.050 M nitric acid (a strong acid) and of 0.050 M sodium hydroxide (a strong base).
Hint: acid pH = minus log(0.050) = 1.30; base pOH = 1.30, so pH = 12.70.
Question 3
For 0.20 M acetic acid (Ka = 1.8 × 10⁻⁵), calculate the pH.
Hint: x = √(Ka·C) ≈ √(3.6 × 10⁻⁶) = 1.9 × 10⁻³, so pH ≈ 2.72 (solving the quadratic gives nearly the same).
Question 4
A 20.0 mL acid sample reaches its equivalence point after 18.0 mL of 0.150 M base. Find the acid concentration.
Hint: C_a = C_b V_b / V_a = (0.150 × 18.0) / 20.0 = 0.135 M.
Question 5 — Challenge
Explain why the equivalence point of a weak acid with a strong base is above pH 7, while a strong acid with a strong base is exactly 7.
Hint: the weak acid produces a conjugate base at equivalence, which is itself weakly basic and raises the pH; a strong acid leaves only a neutral salt.