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.
Here you change solution volume to watch molarity drop and practice the dilution relation.
Same Amount, Different Volume, Different Strength
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With the amount of solute (moles) fixed, increasing only the solution volume dilutes the molar concentration
2 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.
1
Put n=0.5, V=2 into M = n/V.
M = 0.52
2
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?
1
It is dilution, so use M V = M′ V′.
2 × 100 = M′ × 500
2
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.