Molar Concentration

Same Amount, Different Volume, Different Strength

Solution volume V (L) · solute fixed at 0.5 mol2 L

👀 See It

①Even with the same amount of solute (moles), a larger solution volume is more dilute

②Molar concentration is the moles of solute per 1 L of solution

③Dissolving the same moles in a larger volume lowers the concentration

Definition of Molar Concentration

Molar concentration

M = nV

Moles of solute n (mol) divided by solution volume V (L) — units mol/L

Moles–concentration–volume

n = M V

Knowing concentration and volume gives the dissolved moles at once

Dilution — Making It Weaker

Dilution formula

M V = M′ V′

Concentration × volume before = concentration × volume after

💧 The Moles of Solute Stay the Same

①Dilution adds water, increasing only the volume

②The moles of solute do not change

③Hence M V = M′ V′ (equal moles before and after)

Compute It Directly

Example 1

Dissolve 0.5 mol of NaOH in water to a total volume of 2 L. Find the molar concentration.

Put n=0.5, V=2 into M = n/V.

M = 0.52

Compute.

M = 0.25 mol/L

▸ 0.25 mol/L

Volume must be in L — for mL, divide by 1000 to get L.

Example 2

Adding water to 100 mL of a 2 M solution to make 500 mL total — what is the concentration?

It is dilution, so use M V = M′ V′.

2 × 100 = M′ × 500

Solve for M′.

M′ = 200500 = 0.4 M

▸ 0.4 M

In dilution, if the volume unit is the same on both sides, mL works directly.

Wrap-up

Key result

M = nV, n = M V, M V = M′ V′

Concentration = moles/volume, moles = conc × volume, dilution preserves the product

2021 CSAT Science (Chemistry Ⅰ) type, adapted

How many moles of sulfuric acid are in 200 mL of a 1.5 M solution?

①0.1 mol

②0.2 mol

③0.3 mol

④0.45 mol

⑤3 mol

▸ ③ 0.3 mol

n = M V; convert volume to L (200 mL = 0.2 L).

n = 1.5 × 0.2

Compute.

n = 0.3 mol

🎯 Exam Points

①molar concentration M = n/V (V in L)

②n = MV converts to moles

③dilution is M V = M′ V′

④convert mL to L by dividing by 1000

⑤it is the solution (total) volume, not the solvent (water) volume

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