Calculating the molar concentration of a solution is a relatively straightforward process: Determine how many moles of a substance you have and then divide it by the liters of solution. The first part is tricky because you have to work out the details of the chemical formula for the solute. The math, however, is simple arithmetic.
TL;DR (Too Long; Didn't Read)
To find the molar concentration of a solution, divide the moles of solute by liters of solution.
Defining Molar Concentration
The molar concentration of a solution is the number of moles of solute divided by the liters of water of the solution. You measure molar concentration in moles per liter. One mole of solute in one liter of water gives a concentration of 1 M.
Find Mass of Solute
An early step in determining molar concentration is finding the mass of the solute – the grams of the dissolved substance. Written problems usually state the mass, although you may have to convert to grams from some other unit. In a lab setting, you measure the mass of the solute on a balance or scale before you dissolve it. As with all lab work, exercise care to be as accurate as the equipment allows because your measurements affect the accuracy of your calculations and results.
Determine Molar Mass
To find the number of moles of solute, you first need to calculate the molar mass of the substance. For the chemical formula for your solute, look up each element on the periodic table and write down the average atomic mass in atomic mass units (AMUs). For any element that appears in multiples, multiply the mass by the number of atoms per molecule of that element. Take care to include groups that also appear in multiple amounts. Add up the total AMUs to get the molar mass. For example, the formula for acetic acid is CH3COOH. Note that the molecule has a total of two carbon atoms, two oxygen atoms and four hydrogen atoms. You multiply the atomic mass of carbon by 2, oxygen by 2 and hydrogen by 4 and then add the results to get the total molar mass in grams per mole. The atomic masses of carbon, oxygen and hydrogen are 12.01, 16.00 and 1.008, respectively. Multiplying the masses and quantities gives you (12.01 x 2) + (16.00 x 2) + (1.008 x 4) = 60.05 grams per mole.
Calculate Moles of Solute
Calculate the moles of your solute by dividing the mass in grams by grams per mole. For example, you have 10g of acetic acid. Dividing 10g by 60.05 g/mole gives 0.1665 moles of solute.
Calculating Molar Concentration
Find the molar concentration by dividing the moles you calculated by liters of water used to make the solution. For example, the acetic acid in the above example is completely dissolved in 1.25 L of water. Divide 0.1665 moles by 1.25 L to get the molar concentration, 0.1332 M.
Measuring Acids and Bases
For acids and bases, you can determine the molar concentration of unknown solutions by measuring the pH or pOH of the solution. The math is slightly more complicated, involving the common antilogarithm or exponents of 10. To find the molar concentration of an acid, measure the pH, then multiply it by -1 and take the common antilog of the result. For example, you measure a sample of hydrochloric acid, and the pH reading is 2. Multiply 2 by -1 and get -2. The common antilog of -2 (10 to the -2 power) gives the concentration 0.01 M.