It might take some time to become confident of your understanding of solutions and concentration. Being able to measure and calculate concentration using different systems such as molarity, parts per million and milligrams per liter is one thing, but being able to convert between these measurements is another thing altogether. Once you become familiar with how conversion equations work, you'll start to find converting between concentration measurements much easier, and maybe even have some fun.
Things You'll Need
 Molecular weight calculator
 Periodic table

Calculate the molecular weight of the solute in the solution. For example, assume the solute is sodium chloride, which has the molecular formula NaCl. To find the molecular weight of sodium chloride, add the weight of Na (22.99) to Cl (35.45), which equals 58.44 grams per mole.

To convert milligrams per liter to molarity, use this formula: Molarity = mg/L / (molecular weight of solute) x 1,000. If we assume that the solute in the solution is sodium chloride and the concentration is 0.5 mg/L, the equation would be Molarity = 0.5 mg/L / (58.44) x 1,000. The answer is 8.556 micromoles (μM).

Convert from micromoles to moles or millimoles if necessary. To calculate moles, use the equation Moles = micromoles / 1,000,000. To calculate millimoles, use the equation Millimoles = micromoles / 1,000.
Tips & Warnings
 Use an online conversion calculator to doublecheck your answers.
References
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