You can use either millimoles per liter or parts per million (ppm) to describe the concentration of a chemical solution. Chemists commonly use both of these units to provide information about the quantity of a chemical dissolved in a unit amount of solution. In the case of millimoles, the concentration is given in terms of thousandths of a mole of the chemical per liter of solution, where a mole is a unit that stands for 6.02 x 10^23 atoms or molecules. On the other hand, ppm describes the concentration in terms of milligrams chemical per kg solution. You can convert between the two by first calculating the weight of one mole of the chemical compound.
Write down the formula for the chemical that is dissolved in your solution. For example, if the chemical was magnesium chloride, you would write down MgCl2, showing that each molecule of magnesium chloride is made of one atom of magnesium (Mg) and two of chlorine (Cl).
Look up the atomic weight of each element in the formula, using a periodic table. The atomic weight of magnesium (Mg) is 24.305 and that of chlorine (Cl) is 35.453.
Calculate the gram molecular weight of your chemical by adding together each element's atomic weight multiplied by the number of atoms of that element in the chemical formula. This is the weight, in grams, of one mole of your chemical. In the case of the MgCl2 example, the gram molecular weight would be (1)(24.305) + (2)(35.453) which gives 95.211 grams per mole.
Multiply the concentration of your solution, in millimoles per liter, by the gram molecular weight you just derived. The result is the number of milligrams of the chemical per liter of solution. If your chemical solution is dilute and is in water, which is very common when working with ppm measurements, the density of the solution at room temperature will be very close to 1 gram per milliliter. This means that the value you just calculated can also be considered as the milligrams of chemical per kilogram of solution, which is the definition of parts per million. So this calculation has converted the solution concentration from millimoles per liter to ppm.
The term "millimolar" (abbreviated mM) is sometimes used instead of millimoles per liter.