Expressions of Concentration — Interactive Calculators

All-in-one toolkit for w/w%, w/v%, v/v%, Molarity, Molality, Normality, Mole Fraction, and ppm.

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Weight / Weight %
\( \%\frac{w}{w} = \dfrac{w_2}{W}\times 100 \)   (If \(W\) blank → uses \(w_1+w_2\))
Weight / Volume %
\( \%\frac{w}{v} = \dfrac{w_2}{V}\times 100 \)
Volume / Volume %
\( \%\frac{v}{v} = \dfrac{V_2}{V}\times 100 \)
Molarity (M)
\( M = \dfrac{n_2}{V} = \dfrac{w_2/M_2}{V} \ \text{(mol L}^{-1}\text{)} \)
Molality (m)
\( m = \dfrac{n_2}{w_1(\mathrm{kg})} = \dfrac{w_2/M_2}{w_1(\mathrm{kg})} \ \text{(mol kg}^{-1}\text{)} \)
Normality (N)
\( N = \dfrac{eq_2}{V} = \dfrac{w_2}{\text{GEW}_2\,V}, \ \text{GEW}_2=\dfrac{M_2}{e} \)
Mole Fraction (of solute, \(x_2\))
\( x_2=\dfrac{n_2}{n_1+n_2}, \ n_2=\dfrac{w_2}{M_2},\ n_1=\dfrac{w_1}{M_1} \)
Parts per million (ppm)
Mass fraction (general): \( \mathrm{ppm} = \dfrac{w_2}{W}\times 10^6 \)
Aqueous (approx.): \( 1~\mathrm{mg\,L^{-1}} \approx 1~\mathrm{ppm} \)

For the mg/L ≈ ppm approximation, assume density ≈ 1.00 g·mL⁻¹ and dilute aqueous solution.

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