Mole Fraction Calculator

The fractions of every component must sum to exactly one, which is the useful check.

Mole fraction of solute0.0176961 ÷ (1 + 55.51)

Molarity1 mol/L (M)1 mol ÷ 1 L of SOLUTION — the total volume, not the solvent

Molality1 mol/kg (m)1 mol ÷ 1 kg of SOLVENT — the water alone, not the solution

THE DIFFERENCE MATTERSmolarity moves with temperature; molality does nota solution expands when warmed, so the moles per litre falls while the moles per kilogram is unchanged. Freezing point and boiling point work MUST use molality

Moles of solute1 mol58.44 g ÷ 58.44 g/mol

Normality1 Nmolarity × 1 equivalents. Normality depends on the REACTION, so the same bottle can be 1 M and 2 N

Parts per million58,440 ppmmg per litre, which equals ppm in dilute water because a litre of water is a million milligrams

Mole fraction of solvent0.982304the two must sum to exactly one

Percent by mass5.5213%

The formula

molarity = mol ÷ L of solution; molality = mol ÷ kg of solvent

Per litre of solution, or per kilogram of solvent

Molarity divides by the volume of the finished solution. Molality divides by the mass of the solvent alone.

For dilute aqueous solutions the two are nearly equal, because a litre of dilute solution is close to a kilogram of water. For concentrated ones they diverge sharply, and using the wrong one is a real error.

Only one of them survives a temperature change

Warm a solution and it expands, so the moles per litre falls. Nothing has left the flask — the litre simply holds less material.

Molality is defined by mass, which does not change. This is why colligative properties — freezing point depression, boiling point elevation — are always expressed in molality, and why using molarity for them gives answers that drift with the room.

Normality depends on the reaction

A one molar solution of sulfuric acid is two normal when both protons react and one normal when only the first does.

Molarity is a property of the bottle; normality is a property of what you are doing with it. That ambiguity is why IUPAC discourages normality and why it survives in titration work anyway.

Standard atomic weights are averages

The masses used here are weighted means over the isotopes found naturally on Earth, which is why chlorine is 35.45 rather than a whole number.

For work with a specific isotope, or with material from an unusual source, the isotopic mass is the right figure and it is not this one.