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Grade 10-11 (age 15-17)

high school Molar Concentration

A spoonful of sugar tastes sweeter in a cup of water than in a whole bucket, so the strength of a solution depends on more than how much is dissolved. Molar concentration is the number of moles of solute in 1 L of solution: the moles of solute n divided by the volume of solution V. Adding water to dilute a solution leaves the moles of solute unchanged, so M V = M′ V′ holds before and after, and that equation gives the new concentration directly. The beaker in the diagram holds 0.5 mol of solute, so changing only the volume with the slider keeps the number of dots fixed while the color and the molarity change.

Same Amount, Different Volume, Different Strength

2.0 L
👀 What the Beaker Shows
①The 18 gold dots are the 0.5 mol of dissolved solute; changing the volume does not change their number
②At 2 L, each liter holds 0.25 mol of solute, so the molarity is 0.25 mol/L
③Halve the volume to 1 L and the molarity doubles to 0.5 mol/L: for a fixed number of moles, molarity is inversely proportional to volume
④V is the volume of the whole solution, not of the water added. That is why a solution is made by dissolving the solute first and then filling with water up to the mark

Definition of Molar Concentration

Molar concentration
M = nV
Moles of solute n (mol) divided by the volume of solution V (L); the unit is mol/L, also written M
Moles, Concentration and Volume
n = M V
Knowing the concentration and the volume gives the moles of solute dissolved in it right away

Dilution: Adding Water

Dilution formula
M V = M′ V′
concentration × volume before = concentration × volume after (both are the moles of solute)
💧 The Moles of Solute Stay the Same
①Dilution only adds water to increase the volume; no solute is added or removed
②So the moles before dilution, M V, equal the moles after, M′ V′
③In the beaker, doubling the volume halves the molarity; that is this same relationship
④As long as both sides use the same volume unit, mL can be used as is

Work It Out

Example 1
0.5 mol of NaOH is dissolved in water to make 2 L of solution. Find the molarity.
1
Put n = 0.5 mol and V = 2 L into M = n / V.
M = 0.52
2
Divide.
M = 0.25 mol/L
▸ 0.25 mol/L
This matches the diagram with the volume set to 2.0 L. If the volume is given in mL, divide by 1000 to convert to L first.
Example 2
Water is added to 100 mL of a 2 M solution until the total volume is 500 mL. What is the new molarity?
1
Only water was added, so the moles of solute are unchanged. Use M V = M′ V′.
2 × 100 = M′ × 500
2
Solve for M′.
M′ = 200500 = 0.4 M
▸ 0.4 M
The volume became 5 times larger, so the concentration dropped to 1/5. Both sides are in mL, so there is no need to convert to L.

Summary

Key result
M = nV, n = M V, M V = M′ V′
molarity = moles ÷ volume, moles = molarity × volume, and dilution keeps the product of concentration and volume unchanged
2021 CSAT Science (Chemistry I) type, adapted
How many moles of sulfuric acid are dissolved in 200 mL of a 1.5 M sulfuric acid solution?
①0.1 mol
②0.2 mol
③0.3 mol
④0.45 mol
⑤3 mol
▸ ③ 0.3 mol
1
Use n = M V and convert the volume to liters (200 mL = 0.2 L).
n = 1.5 × 0.2
2
Multiply.
n = 0.3 mol
🎯 Exam Points
①Molarity M = n / V, where V is the volume of solution in liters
②Find moles with n = M V
③In a dilution, M V = M′ V′
④Divide mL by 1000 to get L
⑤V is the volume of the whole solution, not of the solvent (water)
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Language of Chemistry — The Mole
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Evolution of Atomic Models

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