Solution Dilution

General Chemistry • Chemical Reactions

Written by STEM Calculators Team Published October 17, 2025 Updated February 24, 2026

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Initial solution

M₁ (mol·L⁻¹)

V₁

Final solution

M₂ (mol·L⁻¹)

V₂

Sig figs

How to enter:
• Provide M₁, V₁, and exactly one of M₂ or V₂. The missing value is solved from \(M_1V_1=M_2V_2\).
• Convert volumes to liters before using the equation (the tool does this automatically).
• If both M₂ and V₂ are entered, the tool runs a quick consistency check.

Paste / import values (optional)

Paste one line as: M1,V1,V1unit,M2,V2,V2unit,sig (units: L or mL). Example: 1.00,50,mL,0.10,,mL,4

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Solution Dilution

In a dilution, solvent is added but the amount of solute remains the same. Therefore the moles \(n\) are conserved: \[ n_1 = n_2 \quad\Longrightarrow\quad M_1V_1 = M_2V_2, \] where \(M\) is molarity (mol·L⁻¹) and \(V\) is solution volume (in liters).

What you can solve

Given \(M_1\), \(V_1\) and target \(M_2\), find the required \(V_2\): \(V_2=\dfrac{M_1V_1}{M_2}\).
Given \(M_1\), \(V_1\) and target \(V_2\), find the resulting \(M_2\): \(M_2=\dfrac{M_1V_1}{V_2}\).
Solvent to add after dilution: \(V_{\text{add}} = V_2 - V_1\).
(Optional) If the solute formula is known, the solute mass is \(m = n\,M_m = (M_1V_1)\,M_m = (M_2V_2)\,M_m\) and is constant through dilution.

Worked Examples

Example A (solve for final volume). How much water is needed to prepare 0.100 M NaCl from 50.0 mL of 1.00 M NaCl?

\[ \begin{aligned} V_2 &= \frac{M_1V_1}{M_2} = \frac{1.00\ \mathrm{mol\,L^{-1}} \times 0.0500\ \mathrm{L}}{0.100\ \mathrm{mol\,L^{-1}}} = 0.500\ \mathrm{L} \\ V_{\text{add}} &= 0.500\ \mathrm{L} - 0.0500\ \mathrm{L} = 0.450\ \mathrm{L} \end{aligned} \]

Example B (solve for final molarity). What is the molarity after diluting 125 mL of 0.500 M H₂SO₄ to 500 mL?

\[ \begin{aligned} M_2 &= \frac{M_1V_1}{V_2} = \frac{0.500\ \mathrm{mol\,L^{-1}} \times 0.125\ \mathrm{L}}{0.500\ \mathrm{L}} = 0.125\ \mathrm{mol\,L^{-1}} \end{aligned} \]

Tips & Guardrails

Always convert volumes to liters before applying \(M_1V_1=M_2V_2\).
For a proper dilution (decreasing concentration), \(M_2 < M_1\) and usually \(V_2 > V_1\).
State symbols (s, l, g, aq) are ignored; write neutral formulas only (no charges).
Report a reasonable number of significant figures; your calculator lets you choose 3–6 s.f.

Frequently Asked Questions

What equation does the Solution Dilution calculator use?

It uses the dilution relationship M1V1 = M2V2, which comes from conserving moles of solute during dilution when only solvent is added.

How do I know whether to solve for M2 or V2?

If you have a target concentration, enter M2 and solve for the required final volume V2. If you know the final volume after dilution, enter V2 and solve for the resulting molarity M2.

Why does the calculator convert mL to liters before solving?

Molarity is defined in mol/L, so volumes must be in liters for units to be consistent. The conversion is V(L) = V(mL) / 1000.

How is the amount of solvent to add calculated?

After finding the final volume V2, the calculator computes solvent to add as Vadd = V2 - V1. For a dilution that lowers concentration, V2 is typically larger than V1.

Initial solution

Final solution

Calculation steps

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