Molarity & Titration

the idea

Molarity is moles per liter of solution, so it converts volume into moles.

M = mol solute ÷ L solution. A 0.100 M NaOH solution means every liter carries 0.100 mol of NaOH. Measure out a volume and you've measured out moles. That's why burettes and volumetric flasks are the chemist's scales.

Plant version: ppm and molarity answer the same question in different units: how much solute is riding along in each liter. 200 ppm chlorine is 200 mg/L. Molarity just counts the solute in moles instead of milligrams, which is what you need once a reaction's mole ratio is involved.

Molarity

M = mol ÷ L

Moles from a solution

mol = M × L

Dilution

M₁V₁ = M₂V₂

calculate

Make a solution

Solute Solve for

Mass (g) Volume (mL) Molarity (M)

dilution

Adding water changes the volume, not the moles.

Before and after dilution, the moles of solute are identical: M₁V₁ = moles = M₂V₂. Solve for whichever piece is missing.

M₁ stock (M) V₁ stock (mL) M₂ final (M) V₂ final (mL)

Leave exactly one box blank and it gets solved.

simulate

Titration curve

Add NaOH from the burette and watch the pH. At the equivalence point, moles of base added = moles of acid present. Phenolphthalein turns pink just past it, around pH 8.2.

Acid concentration (M) Acid volume (mL) NaOH concentration (M)

NaOH added:

engineering version

The chemistry under the TA test

You know the procedure. Here's why the formula works: %TA = mL NaOH × N × 0.090 ÷ sample g × 100.

mL × N = mmol of NaOH. (Molarity in mol/L is the same number as mmol/mL. For NaOH, N = M.)
Lactic acid has one acidic H, so 1 mmol NaOH neutralizes 1 mmol lactic acid. That's the mole ratio.
0.090 is lactic acid's molar mass in g/mmol (90.08 g/mol ÷ 1000). It converts mmol of acid to grams.
Divide by sample grams and × 100 to get mass percent. With a 9 g sample and 0.1 N NaOH, everything cancels to %TA = mL ÷ 10. That's why the 9 g sample size is standard.

NaOH used (mL) NaOH normality (N) Sample (g)

Phenolphthalein's endpoint (~pH 8.2–8.3) sits right on lactic acid's equivalence point, around pH 8. That's why it's the indicator for this test. Try "Lactic acid" in the simulator and look at where the jump lands.

practice

Molarity, dilution, titration

exam traps

Common mistakes

Using mL in M = mol ÷ L. Convert to liters first, or use mmol with mL.
Adding 1.00 L of water to the solute. The final solution is 1.00 L. Fill to the line.
Assuming the equivalence point is always pH 7. That's only true for strong acid + strong base. A weak acid's equivalence point is basic.
Ignoring the mole ratio in a titration. H₂SO₄ needs 2 NaOH per acid molecule.
Mixing up endpoint and equivalence point. The endpoint is where the indicator changes, and a good indicator puts it close to equivalence.