CH 202 Problem 3.40

3.40 A sample of the male sex hormone testosterone, C19H28O2, contains 7.08 x 1020 hydrogen atoms.

(a) How many atoms of carbon does it contain?

This is just a dimensional analysis problem in disguise. Here, the conversion factor is the ratio of carbon to hydrogen in the molecular formula of testosterone. These units are defined below so that mathcad doesn't flip out:

now we convert:

(b) How many molecules of testosterone does it contain?

the conversion factor here is the following: one molecule of testosterone contains 28 H atoms.

(dummy unit)

(c) How many moles of testosterone does it contain?

In 1 mol of testosterone, there are 6.02 x 1023 testosterone molecules; this is our conversion factor between molecules and moles. In part (b), we found that the sample contained 2.53 x 1019 testosterone molecules. We have

(dummy unit here - don't worry about it)

(d) What is the mass of this samle in grams?

Here, we use the molar mass of testosterone to convert between grams and moles: this is the mass, in grams, of 1 mol of the substance. Numerically, the molar mass is the same thing as the formula weight; we just change the units from amu to units of grams / mole. First, we get the molar mass by adding up the atomic masses:

molar mass of testosterone

in part (c) we found that the sample contained 4.2 x 10-5 mol testosterone; we use the molar mass to convert to grams:

DAC 2/22/09