SME
Grade 10 Science · Problem type
Diluting a stock solution
Use this for “How much 2.00 M stock makes 200 mL of 0.500 M, and how much water is added?”
Diagram
Water spreads the same solute out: M₁V₁ = M₂V₂ = 0.1 mol of CuSO₄.
The paler tint is the weaker solution.
Each dot is 0.005 mol of CuSO₄: 20 dots.
This is an example. Type your own values to start a new problem.
M₁ (mol/L)
×
V₁ (mL)
=
M₂ (mol/L)
×
V₂ (mL)
w
Water added
worked out (not typed)
Formulas
M₁
×
V₁
=
M₂
×
V₂
2 × 50 = 0.5 × 200
w
=
V₂
−
V₁
150 = 200 − 50
Assumptions
•
Water adds volume but no solute: the moles, M × V, stay the same.
•
Both volumes are in the same unit, so the units cancel.
Step-by-step
WE KNOW
M₁ = 2 mol/L, V₁ = 50 mL, M₂ = 0.5 mol/L
FIND
diluted volume (V₂), water added (w)
Step 1 · Find diluted volume (V₂)
Use M₁ × V₁ = M₂ × V₂
The
moles
of
solute,
M₁
V₁
,
stay
the
same.
Divide
them
by
the
new
molarity.
V₂
=
(
M₁
×
V₁
)/
M₂
V₂
=
(2
×
50)/0.5
V₂
=
100/0.5
V₂
=
200
mL
Step 2 · Find water added (w)
Use w = V₂ − V₁
The water makes up the difference between the volumes.
w
=
200
−
50
w
=
150
mL
Check
Put the numbers back in. Both sides should match.
2 × 50 = 0.5 × 200 ✓
150 = 200 − 50 ✓
Topic check
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