Standard Solutions and Working Standards

A standard solution (or stock solution) is one whose concentration is known accurately. It is prepared by weighing out a precisely known amount of solute and transferring it to a standard (volumetric) flask of a definite, calibrated volume. A small amount of solvent is first added and the flask is swirled/shaken to dissolve the solute completely; only then is more solvent added, carefully, up to the calibration mark etched on the flask's neck. The flask is stoppered and shaken thoroughly to make the concentration perfectly uniform throughout.

At the time of an actual experiment, a solution of the exact concentration needed is rarely the stock solution itself -- instead, it is prepared fresh by diluting the stock solution. This freshly diluted solution is called the working standard. A precisely known volume of stock solution is transferred (usually with a pipette) into a new container and made up to a calculated final volume with solvent.

The volumes involved can be calculated from the fact that the total amount of solute is unchanged by dilution -- concentration times volume before dilution equals concentration times volume after:

where $C_s, V_s$ are the concentration and volume of the stock solution, and $C_w, V_w$ are the concentration and volume of the working standard.

Worked example (Example Problem 1). What volumes of 4 M HCl and 2 M HCl should be mixed to get 500 mL of 2.5 M HCl? …