# A sample of sulfur having a mass of 1.28 g combines with oxygen to form a compound with a mass of 3.20g. What is the empirical formula of the compound?

Dec 29, 2015

${\text{SO}}_{3}$

#### Explanation:

Since your compound will only contain sulfur and oxygen, you can conclude that the difference between the mass of sulfur and the mass of the final compound will represent the mass of oxygen.

${m}_{\text{compound" = m_"oxygen" + m_"sulfur}}$

In your case, the mass of oxygen will be equal to

${m}_{\text{oxygen" = "3.20 g" - "1.28 g" = "1.92 g}}$

• $\text{1.28 g}$ of sulfur
• $\text{1.92 g}$ of oxygen

Your next step will be to use the molar masses of the two elements to determine how many moles of each you have in this $\text{3.-20 g}$ sample of compound.

$\text{For O: " 1.92 color(red)(cancel(color(black)("g"))) * "1 mole O"/(15.9994color(red)(cancel(color(black)("g")))) = "0.1200 moles O}$

$\text{For S: " 1.28 color(red)(cancel(color(black)("g"))) * "1 mole S"/(32.065color(red)(cancel(color(black)("g")))) = "0.03992 moles S}$

In order to determine the empirical formula of the compound, you need to find the smallest whole number ratio that exists between these two elements in the compound.

In order to do that, divide both values by the smallest one to get

"For O: " (0.1200 color(red)(cancel(color(black)("moles"))))/(0.03992color(red)(cancel(color(black)("moles")))) = 3.01 ~~ 3

"For S: " (0.03992color(red)(cancel(color(black)("moles"))))/(0.03992 color(red)(cancel(color(black)("moles")))) = 1

Since a $1 : 3$ mole ratio is the smallest possible while using whole numbers, the empirical formula of the compound will be

"S"_1"O"_3 implies color(green)("SO"_3)