Worked example

1.00 M ×10.0 mL → 100. mL gives 0.100 M.

Dilution Equation

Relate concentrations before and after dilution (moles conserved).

Equation

$c_1 V_1 = c_2 V_2$

Inline: $c_1 V_1 = c_2 V_2$$

Variables

Symbol	Quantity	Unit	Notes
$c_1$	initial molarity	M	—
$V_1$	initial volume	L	—
$c_2$	final molarity	M	—
$V_2$	final volume	L	—

Conditions and limitations

Only solvent added; solute does not react.

Rearrangements

$c_2 = c_1 V_1 / V_2$

Dimensional check: M·L = mol conserved ✓

Worked example

1.00 M ×10.0 mL → 100. mL gives 0.100 M.

Steps: write equation → substitute with units → check dimensional consistency → report with correct significant figures.

Common errors

• Using mass instead of moles
• Forgetting volume units must match

Related resources

• solutions-concentration topic
• Calculators — linked only when a real calculator implements this formula.
• Constants — sourced constants with version when values are required.

Sources

• NIST Physical Constants 2022 — CODATA.

Reviewed 2026-08-21 by Editorial Team; due 2027-08-21.