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In analytical chemistry, accurately describing how much of a substance is present in a solution is essential. Concentrations are most commonly expressed as molarity (M), defined as moles of solute per liter of solution (mol/L). However, when dealing with very low concentrations, molarity can become unwieldy. For example, a 0.001 M solution of NaOH is more conveniently expressed as 1 mmol/L (mmol/L), or millimolar (mM), by shifting the decimal point three places to the right.

For laboratory preparation, mass‑based units such as grams per liter (g/L) or milligrams per liter (mg/L) are often preferred because they directly inform how much solid to weigh. To switch between these systems, you need the molar mass of the compound, expressed in grams per mole (g/mol). Below, we walk through the conversion process with clear, step‑by‑step examples.

Converting from mg/L to mmol/L

Start with the known mass concentration and the molar mass of the solute. For a 259 mg/L NaOH solution:

1. Convert milligrams to grams: 259 mg ÷ 1000 = 0.259 g.
2. Divide by the molar mass of NaOH (39.997 g/mol): 0.259 g ÷ 39.997 g/mol ≈ 0.00648 mol/L.
3. Multiply by 1000 to express in millimoles: 0.00648 mol/L × 1000 = 6.48 mmol/L.

Thus, a 259 mg/L NaOH solution is equivalent to a 6.48 mM solution.

Converting from mmol/L to mg/L

Take a 10 mM MgCl₂ solution and determine its mass concentration:

1. Convert millimoles to moles: 10 mmol ÷ 1000 = 0.010 mol.
2. Multiply by the molar mass of MgCl₂ (96.211 g/mol): 0.010 mol × 96.211 g/mol = 0.962 g.
3. Convert grams to milligrams: 0.962 g × 1000 = 962 mg.

Therefore, a 10 mM MgCl₂ solution contains 962 mg/L of the salt. Knowing both representations allows chemists to choose the most convenient unit for calculation or laboratory preparation.