How to Convert g/L to mol/L

A concentration in g/L tells you the mass of a substance in each liter of solution. A concentration in mol/L tells you the amount of that substance, in moles, per liter. To convert between them, you need the substance’s molar mass; there is no single conversion factor that works for every chemical.

The conversion formula

Let the mass concentration be in g/L and the molar mass be in g/mol. The molar concentration is

$$c = \frac{\text{mass concentration}}{\text{molar mass}}$$

The units show why this works:

$$\frac{\mathrm{g/L}}{\mathrm{g/mol}} = \mathrm{mol/L}$$

For example, a substance with a molar mass of 50 g/mol has 0.02 mol in every liter for each 1 g/L of mass concentration. A heavier substance gives fewer moles per liter for the same mass concentration.

How to convert g/L to mol/L

1. Identify the substance whose concentration is being reported. You need its chemical formula to determine its molar mass.
2. Find the molar mass in g/mol. Add the atomic masses of all atoms in the formula, accounting for subscripts.
3. Divide the value in g/L by the molar mass in g/mol.
4. Report the answer in mol/L and round it to a sensible number of significant figures.

The g/L value should refer to grams of the specified solute per liter of final solution. It is not generally grams per liter of solvent. If the solution contains several solutes, convert each one separately using its own molar mass.

Worked example: sodium chloride

Suppose a solution contains 5.85 g of sodium chloride per liter. Sodium chloride has the formula NaCl. Using atomic masses of about 22.99 g/mol for sodium and 35.45 g/mol for chlorine, its molar mass is

$$M(\mathrm{NaCl}) = 22.99 + 35.45 = 58.44\ \mathrm{g/mol}$$

Now divide the mass concentration by that molar mass:

$$\begin{aligned} c &= \frac{5.85\ \mathrm{g/L}}{58.44\ \mathrm{g/mol}} \\ &= 0.1001\ \mathrm{mol/L} \end{aligned}$$

To three significant figures, the concentration is 0.100 mol/L. The units cancel because the grams in the numerator and denominator cancel, while dividing by g/mol changes the remaining liters into moles per liter.

Converting the result to mmol/L

Sometimes you may want the answer in millimoles per liter. Since 1 mol equals 1000 mmol, multiply the mol/L result by 1000. For the sodium chloride example, 0.100 mol/L is 100 mmol/L. Conversely, divide a value in mmol/L by 1000 to express it in mol/L.

Choosing the correct molar mass

Use the molar mass of the substance represented by the grams in the original concentration. For a hydrate such as copper(II) sulfate pentahydrate, CuSO4·5H2O, include the five water molecules when calculating the molar mass if the stated grams are grams of that hydrate. Using the molar mass of anhydrous CuSO4 instead would give the wrong amount of the weighed material.

If you need the concentration of an ion produced by a dissolved compound, first calculate the compound’s mol/L concentration, then use the formula’s stoichiometric ratio. For example, one mole of CaCl2 produces two moles of chloride ions, so its chloride-ion concentration is twice its CaCl2 concentration, assuming complete dissociation.

Common mistakes

• Trying to convert without knowing the substance: g/L cannot be changed to mol/L without a molar mass.
• Multiplying instead of dividing: grams per liter divided by grams per mole gives moles per liter. Multiplying does not give the required units.
• Using the wrong formula mass: distinguish a hydrate, a salt, and an ion, and use the molar mass matching the stated mass.
• Confusing solution volume with solvent volume: mol/L is moles per liter of solution. The volume is measured after the solute is dissolved and the solution is made up to its final volume.
• Rounding too early: keep extra digits during the calculation, then round the final result based on the precision of the given data.