Question

$C_3{H}_{7}OH$ is propanol. Suppose you have $85.9$ g sample of propanol. How many carbon atoms are in the sample?

Answer 1

$2.58\cdot {10}^{24}$ carbon atoms.

Explanation:

The molecular formula of propanol is $C_3{H}_{8}O$.
First, we should calculate its molecular mass. I prefer to work with rounded numbers because that's how I was taught and frankly it makes life much easier. You should have memorized that the molar masses of carbon, hydrogen, and oxygen are, respectively, $12\frac{g}{mol}$, $1\frac{g}{mol}$ and $16\frac{g}{mol}$

So let's add all that up:

$M=(3\cdot 12)+(8\cdot 1)+(1\cdot 16)$

$M=60\frac{g}{mol}$

Okay, but that doesn't tell us much by itself. Elements make up substances in different proportions, because they have different masses, so how much of propanol is actually carbon, in terms of percentage? Remember, $36$ g of that is carbon:

$\begin{array}{c}60g\to 100\%\\ 36g\to x\%\end{array}\}\Rightarrow x=60\%$

So now we know that any given sample of propanol is sixty percent carbon. Now we can use the information that we were given: $85.9g$. If that's the total mass of propanol, sixty percent of that must be carbon:

$\begin{array}{c}85.9g\to 100\%\\ yxg\to 60\%\end{array}\}\Rightarrow y=51.54g$

Now, let us return to the concept of a mole. A mole is a quantity of $6\cdot {10}^{23}$ of something. You might be used to using a more accurate value, but for now let us use that simplified number. Molar mass is the mass of a mole of something; so $6\cdot {10}^{23}$ atoms of carbon have a total mass of $12g$. With that in mind, we can now work out how many atoms of carbon have a total mass of $51.54g$:

$\begin{array}{c}6\cdot {10}^{23}\text{atoms}\to 12g\\ zx\text{atoms}\to 51.54g\end{array}\}\Rightarrow z=2.58\cdot {10}^{24}\text{atoms}$