OpenSpecEngineering

Converts the concentration of a two-component solution between molarity, molality, mass percent, mole fraction, grams per liter and ppm by mass. You either describe the solution or pick a concentrated reagent at its typical assay and density. Lab staff, water treatment operators and process engineers use it to read a reagent label, make up a dilution or compare figures quoted on different bases.

Equations

Every basis goes through the solute mass fraction w:

c = 1000·w·ρ/M
b = 1000·w/((1 − w)·M)
x = (w/M)/(w/M + (1 − w)/M_s)

c is the molarity in mol/L and b the molality in mol per kg of solvent. x is the solute mole fraction. ρ is the solution density in g/mL, M the solute molar mass and M_s the solvent molar mass, both in g/mol [1]. Mass percent is 100·w, grams per liter is 1000·w·ρ and ppm (w/w) is 10⁶·w.

Inputs

• Solution: choose “Describe the solution below” to enter your own, or a concentrated reagent. A reagent uses its typical assay and density at about 20 °C [4], [5].
• Solute fills the molar mass from its formula and the IUPAC atomic weights [3]. Choose Custom to type it.
• Solution Density is the density of the solution itself, not of the solvent. Molality, mass percent and ppm don’t need it to convert among themselves, but molarity and grams per liter do. Take it from a density table for that solute and strength [2], [4].
• Input Basis and Input Value give the concentration you know.

Limits and common mistakes

• Using the density of water for a strong solution. A 1 mol/L salt solution is a few percent denser than water, and strong acids and caustic far more.
• Molarity and grams per liter change with temperature, because the volume does. Molality, mass percent and mole fraction don’t.
• The page treats the solute as one species. It doesn’t count ions separately, so the mole fraction of NaCl counts each formula unit once.
• Here ppm is by mass. In water work, mg/L is often called ppm too. It equals ppm (w/w) only when the density is close to 1 g/mL.
• A reagent’s assay varies by lot. Use the figure on the bottle for exact work.

Worked example

A water plant doses 50 % sodium hydroxide from a tote. The operator needs its molarity to work out a dilution.

1. Choose Solution Sodium hydroxide solution, 50 % NaOH, 1.53 g/mL.
2. Leave Solvent Molar Mass at 18.015 g/mol for water.
3. Press Solve. The Solution shows: Mass fraction w: 0.5
   Molarity: 19.1264 mol/L
   Molality: 25.0019 mol/kg
   Grams per litre: 765 g/L
   ppm (w/w): 500,000 ppm
   Mole fraction of solute: 0.310539
   Solute molar mass M (from formula): 39.997 g/mol

Check by hand: M = 22.99 + 15.999 + 1.008 = 39.997 g/mol, and c = 1000 × 0.5 × 1.53/39.997 = 19.13 mol/L. That matches the familiar figure of about 19 M for 50 % caustic.