high school Molar Concentration

Molar Concentration

Molarity is moles of solute per liter of solution, so the same amount of solute is more dilute in a larger volume. Moles, concentration, and volume link by M = n/V and n = MV, and on dilution the solute moles stay fixed so MV = M′V′. Volume must be in liters when you use these formulas. Change the solution volume and watch molarity drop, then practice the dilution relation.

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

exam-style

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

← Previous

Language of Chemistry — The Mole

Evolution of Atomic Models

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