In the histology laboratory, concentrated solutions can be diluted to prepare less concentrated solutions. For example, working solutions of a particular chemical may be prepared from an existing stock or stronger solution of that chemical very easily.
The following formula, derived from the ratio and proportion formula, will allow changes in concentrations between two solutions:
C_{1 }x V_{1 }= C_{2 }x V_{2 }
where
C_{1} = stock concentration (beginning concentration)
V_{1} = volume of stock required to prepare new solution
C_{2}= concentration of new or working solution (desired concentration)
V_{2}= volume of new solution desired
AND
if you know 3 of the 4 values (and the units are the same on both sides of the equation), the fourth can be calculated.
Example:
A histology student performing a Prussian blue stain for ferric iron needs 2% potassium ferrocyanide solution to complete the process but only finds 5% stock solution on the stock room shelf. How milliliters of the stock will he need to prepare 400 mL of 2% potassium ferrocyanide solution?
2% x 400 mL = 5% x (X) mL
2 x 400 = 5(X)
800/5 = X
X = 160 mL of 5% stock solution diluted to 400 mL