Concentration

Solutions vary in concentration. You might want one or two lumps of sugar in your coffee. Vodka has more alcohol than wine. In chemistry the concentrations of solutions are expressed in various units. A common method is to give the grams of solute dissolved in 100 grams or 1 liter of solvent. These units are typical of descriptions of solubility. Reactants are often described in terms of moles of solute per liter of solution (molarity, M). These are typically prepared by weighing a sample of solid, putting it in a volumetric flask and adding enough solvent to dissolve the solid. More solvent is added to bring the solution to the marked volume of the flask. The volume of a solution may be quite different than the total volume of the separate components.

Environmental concentrations are frequently given in parts per million (ppm) or parts per billion (ppb). The ppm of solute is calculated by dividing the mass of solute by the mass of solution and multiplying by 1 million (10⁶). For ppb the ratio is multiplied by 1 billion (10⁹).

In physical chemistry it is common to use mole fractions to express concentration. The mole fraction of component A is written as X_A and is the ratio of moles of A to the sum of the moles of all components.

Sometimes the units of concentration are given in molality (m). Here the moles of solute are divided by kilograms of solvent.

Mass percent is another method of expressing concentration. Concentrated acids usually give an assay in mass percent and the density (or specific gravity) at some temperature. If you want to prepare a dilute solution of a concentrated acid you have to do a bit of calculating. Lets take 70.8% nitric acid with a density of 1.424 g/ml as an example. Since we want to prepare a solution of a certain molarity (M) we need to calculate the molarity of the concentrated solution. We know that 100g of the acid will contain 70.8g of HNO₃. We calculate the formula weight of HNO₃ by adding up the atomic weights of the components to get 63.0 g/mol. To get the moles of HNO₃ in 100g of acid we divide the 70.8 grams of HNO₃ by 63.0 g/mol to get 1.12 moles. Next we need to know the volume of the 100g of acid. We divide 100g by the density (1.424 g/ml) to get the volume in milliliters and divide by 1000 ml/liter to get the volume in liters (0.0702 L). We next divide the moles of solute (1.12 mol) by the volume in liters (0.0702 liter) to get 16.0 mol/liter.