How do you use gravimetric analysis to find the mass composition of a solid sample?

In gravimetric analysis, you usually add a reagent to a solution of your unknown and determine the mass of the precipitate that forms.

Since you know the formula of the precipitate, you can work backwards to calculate the mass of the unknown.

EXAMPLE

You dissolve 0.4500 g of impure potassium chloride in water and add an excess of silver nitrate. You get 0.8402 g of insoluble silver chloride. Calculate the percent by mass of #"KCl"# in the original sample.

Solution:

The chemical equation is

#"KCl(aq)" + "AgNO"_3"(aq)" → "KNO"_3"(aq)" + "AgCl(s)"#

You work backwards from the mass of #"AgCl"# through the following conversions:

#"grams of AgCl" → "moles of AgCl" → "moles of KCl" → "grams of KCl" → "% KCl"#

a. #0.8402 color(red)(cancel(color(black)("g AgCl"))) ×"1 mol AgCl"/(143.32 color(red)(cancel(color(black)("g AgCl")))) = 5.862 × 10^-3 "mol AgCl"#

b. #5.862 × 10^-3 color(red)(cancel(color(black)("mol AgCl"))) × "1 mol KCl"/(1 color(red)(cancel(color(black)("mol AgCl")))) = 5.862 × 10^-3 "mol KCl"#

c. #5.862 × 10^-3 color(red)(cancel(color(black)("mol KCl"))) ×"74.55 g KCl"/(1 color(red)(cancel(color(black)("mol KCl")))) = "0.4370 g KCl"#

d. #"% KCl" = (0.4370 color(red)(cancel(color(black)("g"))))/(0.4500 color(red)(cancel(color(black)("g")))) × 100 % = "97.12 % by mass"#