Question #bfdfb

For starters, you know that `1` molecule of pentane contains

• five atoms of carbon, `5 xx "C"`
• twelve atoms of hydrogen, `12 xx "C"`

This implies that carbon and hydrogen have a `5:12` atom ratio in pentane, i.e. for every `5` atoms of carbon present in your sample, you get `12` atoms of hydrogen.

You can use this atom ratio to figure out the number of atoms of carbon that are present in the sample.

`4.75 * 10^(23)color(red)(cancel(color(black)("atoms H"))) * "5 atoms C"/(12color(red)(cancel(color(black)("atoms H")))) = 1.979 * 10^(23)color(white)(.)"atoms C"`

Now, in order to convert the number of atoms of carbon to moles, use Avogadro's constant.

`1.979 * color(blue)(cancel(color(black)(10^(23)))) color(red)(cancel(color(black)("atoms C"))) * "1 mole C"/(6.022 * color(blue)(cancel(color(black)(10^(23))))color(red)(cancel(color(black)("atoms C")))) = "0.3286 moles C"`

Finally, to convert the number of moles to grams, use the molar mass of carbon.

`0.3286 color(red)(cancel(color(black)("moles C"))) * "12.011 g"/(1color(red)(cancel(color(black)("mole C")))) = color(darkgreen)(ul(color(black)("3.95 g")))`

The answer is rounded to three sig figs, the number of sig figs you have for the number of atoms of hydrogen present in the sample.