Question

A sample of C3H8 has 3.20 × 1024 H atoms. How many carbon atoms does the sample contain? What is the total mass of the sample in grams?

Answer 1

A sample of C3H8 has 3.20 × 10^24 H atoms.

We will use Avogadro's number for this problem. Avogadro's number states that there are 6.022x 10^23 atoms per mole of a substance. We will use dimensional analysis, notice how the units cancel in the computation below:

3.20 × 10^24 atoms H * (1 mole H/6.022x 10^23 atoms H) * (3 moles C/8 moles H) * (6.022x 10^23 atoms C/1 mole C) = 1.2 x 10^24 atoms C

To get the total mass of the sample in grams, let us note that there are 3 moles of carbon and 8 moles of hydrogen per mole of C3H8, and using the molecular weights of C (12 g/mol) and H  (1 g/mol), we get (12*3)+(1*8)= 44 g/mol as the molar mass.

3.20 × 10^24 atoms H * (1 mole H/6.022x 10^23 atoms H) * (1 mole C3H8/8 moles H) * (44 g C3H8 / 1 mole C3H8) = 29.23 g C3H8