# Question 60fe9

May 25, 2016

Element $\text{A}$ is carbon.

#### Explanation:

The idea here is that you can determine the identity of element $\text{A}$ by calculating its molar mass.

To do that, you basically need to know two things

• how many grams of element $\text{A}$ you have in a given sample of $\text{A"_2"O}$
• how many moles of $\text{A}$ you have in the aforementioned sample

So, your compound is said to be 60% $\text{A}$ and 40% $\text{O}$ by mass. If you were to pick a $\text{100-g}$ sample of this compound, you could say that it contains

• $\text{60 g A}$

• $\text{40 g O}$

Use the molar mass of oxygen to determine how many moles you have in this sample

40 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16color(red)(cancel(color(black)("g")))) = "2.5 moles O"

Now, take a look at the compound's chemical formula. One mole of $\text{A"_color(red)(2)"O}$ contains

• $\textcolor{red}{2} \textcolor{w h i t e}{a} \text{moles of A}$

• $\text{1 mole of O}$

So, if this $\text{100 g}$ sample contains $2.5$ moles of oxygen, it follows that it must contain

2.5 color(red)(cancel(color(black)("moles O"))) * (color(red)(2)color(white)(a)"moles A")/(1color(red)(cancel(color(black)("mole O")))) = "5 moles A"

Since the sample contains $\text{60 g}$ of $\text{A}$, it follows that one mole of $\text{A}$ will have a mass of

1 color(red)(cancel(color(black)("mole A"))) * "60 g"/(5color(red)(cancel(color(black)("moles A")))) = "12 g"#

This means that the molar mass of $\text{A}$ is equal to

${\text{molar mass of A" = "12 g mol}}^{- 1}$

A quick look in the periodic table will reveal that the unknown element is carbon, $\text{C}$. Your unknown compound is dicarbon monoxide, $\text{C"_2"O}$.

https://en.wikipedia.org/wiki/Dicarbon_monoxide