If a certain lead-based paint contains 18.5% PbCr2O7 and 73.6% of the paint evaporates , what mass of lead will be in a paint chip that weighs 0.75 g?

Question

Lead compounds are often highly colored and are toxic to mold, mildew, and bacteria, properties that in the past were useful for paints used before 1960. Today we know lead is very hazardous and it is not used in paint, however, old paint is still a problem. If a certain lead-based paint contains 18.5% PbCr2O7 and 73.6% of the paint evaporates as it dries, what mass of lead (in grams) will be in a paint chip that weighs 0.75 g?

Answer 1

Since we working with percentages, let's assume that we start out with 100 grams of paint.

Then, we have 18.5 grams of PbCr₂O₇, lead (II) dichromate, and 73.6 grams of the paint evaporates,

leaving us with 26.4 grams of dried paint, from which we extract our 0.75-gram chip.

The molecular mass of PbCr₂O₇ is 423.2 grams, and the atomic mass of lead is 207.2 grams, so

18.5 grams of PbCr₂O₇ contains 207.2 * 18.5 / 423.2  =  9.06 grams of lead.

If a 26.4-gram "chip" of paint contains 9.06 grams of lead, then a 0.75-gram chip should contain

0.75 * 9.06 / 26.4  =  0.257 grams of lead.