SME
Principles of Biology I · Problem type
Diluting a stock solution
Use this for “How much 1 M stock makes 250 mL of 40 mM buffer?”
Diagram
Water spreads the same solute out: M₁V₁ = M₂V₂ = 0.01 mol of solute.
The paler tint is the weaker solution.
Each dot is 0.001 mol of solute: 10 dots.
This is an example. Type your own values to start a new problem.
C₁ (M)
×
V₁ (mL)
=
C₂ (M)
×
V₂ (mL)
W
Water added
calculated
Formulas
C₁
×
V₁
=
C₂
×
V₂
1 × 10 = 0.04 × 250
W
=
V₂
−
V₁
240 = 250 − 10
Assumptions
•
Water adds volume but no solute, so the moles stay the same: C₁V₁ = C₂V₂.
•
V₂ is the final volume; the water added is V₂ − V₁.
•
1 M = 1000 mM, so 40 mM is 0.040 M; either unit works for both molarities.
Step-by-step
WE KNOW
C₁ = 1 M, C₂ = 0.04 M, V₂ = 250 mL
FIND
stock volume (V₁), water added (W)
Step 1 · Find stock volume (V₁)
Use C₁ × V₁ = C₂ × V₂
The
stock
must
carry
the
moles
the
dilution
needs,
C₂
V₂
;
divide
by
the
stock’s
molarity.
V₁
=
C₂
×
V₂
C₁
V₁
=
0.04
×
250
1
V₁
=
10
mL
Step 2 · Find water added (W)
Use W = V₂ − V₁
The water makes up the rest of the final volume.
W
=
250
−
10
W
=
240
mL
Check
Put the numbers back in. Both sides should match.
1 × 10 = 0.04 × 250 ✓
240 = 250 − 10 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.