Commercial Solutions & Reagents

Calculate molarity, molality, normality and mass concentration from the reagent formula, purity and density · M = (% p/p · ρ · 10) / MW

Presets

Parameters

Chemical formula

Molecular formula of the solute (e.g. H2SO4, NaOH, Ca(OH)2)

Purity

Weight percentage of solute in the commercial solution (% w/w)

0100

Density

Density of the commercial solution in g/mL

0.0125

Equivalents

Number of equivalents per mole (H⁺ donated, OH⁻ donated, or electrons transferred)

110

Formula breakdown

Molar mass (MW)

Element	Count	Atomic mass	Subtotal
H	×2	1.008	2.016
S	×1	32.06	32.06
O	×4	15.999	63.996
MW =			98.07 g/mol

Mass concentration

\boldsymbol{C_{\text{g/L}} = 98 \times 1.84 \times 10}

=1803 g/L

≡ 180.3 % p/v

Molarity (M)

\displaystyle \boldsymbol{M = \frac{1803}{98.07}}

=18.39 mol/L

Mole fraction (x): 0.9

Molality (m)

\displaystyle \boldsymbol{m = \frac{98 \times 1000}{98.07 \times (100 - 98)}}

=499.6 mol/kg

Normality (N)

\boldsymbol{N = 18.39 \times 2}

=36.77 eq/L

Prepare working solution

Work out how much concentrated reagent to measure and how much solvent to add to reach a target concentration and volume, using the molarity (M) computed above (C₁·V₁ = C₂·V₂).

Target concentration (Cf)

mol/L

Final volume (Vf)

Concentrated reagent to measure

54.39 mL

Solvent to add

945.6 mL

Fundamentals & Explanation

From the label to the concentration

A commercial reagent is characterized by its formula (which gives the molar mass $\text{MW}$ ), its mass purity ( $\%\,\text{w/w}$ ) and its density ( $\rho$ ). If you don't have a simple formula —hydrates, organics, mixtures— you can enter $\text{MW}$ directly. From those three figures every concentration unit follows:

1. Mass concentration (g/L)

C_{\text{g/L}} = \%\,\text{w/w} \times \rho\;(\text{g/mL}) \times 10

2. Molarity (M)

M = \frac{C_{\text{g/L}}}{\text{MW}}

3. Molality (m)

m = \frac{\%\,\text{w/w} \times 1000}{\text{MW}\,(100 - \%\,\text{w/w})}

4. Normality (N)

N = M \times n_{eq}

5. Mass/volume (% w/v)

\%\,\text{w/v} = \frac{C_{\text{g/L}}}{10}

6. Mole fraction (x)

x = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}}

Map of concentration units

Unit	Definition	Changes with T?
Molarity (M)	mol solute / L solution	Yes
Normality (N)	equivalents / L solution	Yes
Mass conc. (g/L)	g solute / L solution	Yes
% w/v	g solute / 100 mL solution	Yes
Molality (m)	mol solute / kg solvent	No
% w/w	g solute / 100 g solution	No
Mole fraction (x)	mol solute / total mol	No

Units «per liter of solution» depend on temperature (volume expands); those based on mass or total moles do not.

1. Mass doesn't change with temperature; volume does

Reagents are labeled in $\%\,\text{w/w}$ because mass is an invariant: 98 g of solute per 100 g of solution stays that way at 5 °C or 35 °C. Volume, on the other hand, expands with heat. That is why molality (mol/kg solvent) and mole fraction are the preferred units in cryoscopy, ebullioscopy and work with strong thermal swings, while molarity drifts slightly. The analyst measures the density ( $\rho$ ) at the working temperature to convert mass to volume accurately.

2. Equivalents: why normality depends on the reaction

Normality is molarity times the number of equivalents per mole ( $n_{eq}$ ), but that number is not a fixed property of the substance: it depends on the reaction. In acid–base, $n_{eq}$ = protons exchanged (H₂SO₄ → 2); in redox, = electrons transferred (H₂O₂ as an oxidant → 2). H₃PO₄ can be 1, 2 or 3 N depending on the titration endpoint. That is why the equivalents field is editable: set it to match your reaction context.

3. From the concentrated bottle to your working solution

Once the reagent's molarity is known, preparing a diluted solution is just the dilution law $\;C_1 V_1 = C_2 V_2$ : the volume to measure is $V_1 = (C_2 V_2)/C_1$ . The «Prepare working solution» block does exactly this. Remember the safety rule: concentrated acid or base always goes into the water, never the reverse. For chained dilutions or the general case, see the Dilution calculator.

4. 100% purity and the edge of validity

At 100% purity there is no solvent: molality becomes undefined (division by zero) and the computed molarity represents the molar density of the pure substance — useful for liquids such as glacial acetic acid, but meaningless as a «prepared solution» for a crystalline solid (e.g. NaOH pellets). The mole fraction, by contrast, stays well defined ( $x = 1$ ) and underlies colligative properties and Raoult's law; see the Colligative Properties calculator.

References

[1] IUPAC. Compendium of Chemical Terminology (Gold Book), entries amount concentration, molality, mole fraction and equivalent.
[2] Skoog, D. A., West, D. M., Holler, F. J. & Crouch, S. R. (2014). Fundamentals of Analytical Chemistry (9th ed.). Cengage Learning.
[3] CIAAW / IUPAC. Standard Atomic Weights — atomic weights used for the molar-mass calculation.

Commercial Solutions & Reagents

Parameters

Formula breakdown

Fundamentals & Explanation

Map of concentration units

1. Mass doesn't change with temperature; volume does

2. Equivalents: why normality depends on the reaction

3. From the concentrated bottle to your working solution

4. 100% purity and the edge of validity

References

You may also like:

Map of concentration units

1. Mass doesn't change with temperature; volume does

2. Equivalents: why normality depends on the reaction

3. From the concentrated bottle to your working solution

4. 100% purity and the edge of validity

References