# Question 383ec

Apr 8, 2017

${\text{43.3 g mol}}^{- 1}$

#### Explanation:

For starters, you can use the mass of the compound and the mass of oxygen to determine how many grams of element $\text{A}$ you have in your sample

$\text{mass of compound = mass of A + mass of O}$

In your case, you will have

$\text{mass of A" = "0.359 g" - "0.128 g" = "0.231 g}$

Now, the problem wants you to determine the molar mass of substance $\text{A}$, which implies that you must figure out the mass of exactly $1$ mole of $\text{A}$.

Use the molar mass of oxygen to calculate the number of moles of oxygen present in the sample

0.128 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16.0 color(red)(cancel(color(black)("g")))) = "0.00800 moles O"

According to its chemical formula, the oxide contains $2$ moles of $\text{A}$ for every $3$ moles of oxygen. This means that the sample must contain

0.00800 color(red)(cancel(color(black)("moles O"))) * "2 moles A"/(3color(red)(cancel(color(black)("moles O")))) = "0.00533 moles A"

Since you know that $0.00533$ moles of $\text{A}$ have a mass of $\text{0.231 g}$, you can say that $1$ mole of $\text{A}$ will have a mass of

1 color(red)(cancel(color(black)("mole A"))) * "0.231 g"/(0.005333color(red)(cancel(color(black)("moles A")))) = "43.3 g"#

Therefore, you can say that element $\text{A}$ has a molar mass of

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{molar mass A = 43.3 g mol}}^{- 1}}}}$

The answer is rounded to three sig figs.