# Question 66091

Jul 12, 2017

Here's what I got.

#### Explanation:

Two things to keep in mind here

• the definition of a mole is given by Avogadro's constant
• we use subscripts to show how many atoms of a given element are present in one molecule or formula unit of a compound

So, you should know that in order to have exactly $1$ mole of propane molecules, your sample must contain $6.022 \cdot {10}^{23}$ molecules of propane.

This implies that in order to have $\textcolor{b l u e}{2}$ moles of propane, you need to have $\textcolor{b l u e}{2}$ times as many molecules of propane as you have in $1$ mole of this compound.

You can thus say that your sample contains

color(blue)(2) color(red)(cancel(color(black)("moles C"_3"H"_8))) * overbrace((6.022 * 10^(23)color(white)(.)"molecules C"_3"H"_8)/(1color(red)(cancel(color(black)("mole C"_3"H"_8)))))^(color(purple)("Avogadro's constant"))

$= \textcolor{\mathrm{da} r k \ge e e n}{\underline{\textcolor{b l a c k}{1.2 \cdot {10}^{24} \textcolor{w h i t e}{.} {\text{molecules C"_3"H}}_{8}}}}$

Now, a molecule of propane contains

• three atoms of carbon, $3 \times \text{C}$
• eight atoms of hydrogen, $8 \times \text{H}$

You know that this is the case because of the two subscripts used in the chemical formula of propane.

"C"_3"H"_8 implies {(3 xx "C"), (8 xx "H") :}

You can thus say that your sample contains

1.2 * 10^(24) color(red)(cancel(color(black)("molecules C"_3"H"_8))) * "3 atoms C"/(1color(red)(cancel(color(black)("molecule C"_3"H"_8))) )

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{3.6 \cdot {10}^{24} \textcolor{w h i t e}{.} \text{atoms C}}}}$

and

1.2 * 10^(24) color(red)(cancel(color(black)("molecules C"_3"H"_8))) * "8 atoms H"/(1color(red)(cancel(color(black)("molecule C"_3"H"_8))) )#

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{9.6 \cdot {10}^{24} \textcolor{w h i t e}{.} \text{atoms H}}}}$

I'll leave the answers rounded to two sig figs, but don't forget that you only have one significant figure for the number of moles of propane.