At STP, 50.0 mL of a gas weighs 0.301g and is found to be 47.4% sulfur and 52.6% chlorine. What is the molecular formula of the gas?

Answer 1

Let's begin by determining the empirical formal of the unknown compound. We do this by finding the moles of each element in the compound.

moles S = 47.4% x 0.301 g = 0.1427 g S x 1 mol S / 32.1 g = 4.44x10^-3 moles S

moles Cl = 52.6% x 0.301 g = 0.158 g Cl x 1 mol Cl / 35.5 g = 4.46x10^-3 moles Cl

Since they are in a 1:1 mole ratio, the empirical formula is SCl

To find the molecular formula, we need to know how many moles of gas. We can determine this from the fact that at STP 1 mole of any ideal gas = 22.4 L

50.0 ml x 1 L / 1000 ml = 0.0500 L

0.0500 L x 1 mol / 22.4 L = 2.23x10^-3 moles of gas

molar mass of gas = g / mol = 0.301 g / 2.23x10^-3 moles = 135 g / mol

Molar mass of the empirical formula (SCl) = 32.1 + 35.5 = 67.6

How many of these does it take to make the molar mass of the gas?

135 g / mole ÷ 67.6 g / mole = 2

Thus, molecular formula of the gas = S₂Cl₂

Answer 2

Question: At STP, 50.0 mL of a gas weighs 0.301g and is found to be 47.4% sulfur and 52.6% chlorine. What is the molecular formula of the gas?

Explanation: Avogadro’s law states that any two gases under the same temperature and pressure that occupy the same volume will have the same number of individual atoms or molecules.

 

Relevant Constant: At STP, 1 mole (6.023x10²³ particles) of gas will occupy approximately 22.4 liters of volume. 

50.0mL gas x 1L/1000mL = 0.05 L (volume of gas in liters)

0.05L x 1 mole gas/22.4L = 2.2321x10^-3 moles of gas

0.301g of gas/ 2.2321x10^-3 moles of gas = 134.85g/mol gas (molar mass of the gas)

Given:

47.4% sulfur by mass

0.301g x 0.474 = 0.142674g S

52.6% Chlorine by mass

0.301g x 0.526 = 0.158326 g Cl

Convert mass to moles:

0.142674g S x 1 mol S/32 g S = 4.46x10^-3 mol S

0.158326g Cl₂ x 1 mol Cl₂/ 70.906 g Cl₂ = 2.23x10^-3 mol Cl₂

Find mole-to-mole ratio:

4.46x10^-3 mol S/2.23x10^-3 mol Cl₂ = 2 mol S/1 mol Cl₂  

Therefore, the empirical formula is SCl

Calculate the molecular formula from the empirical formula:

Sulfur molar mass = 32.00 g S

Chlorine molar mass = 35.453 g Cl

SCl = 67.453g/mol SCl

Molecular formula = Empirical formula × n

N= 134.85 / 67.453 =1.999=2

(SCl)x2= S₂Cl₂

Therefore, the molecular formula of the gas is S₂Cl₂

The molecular formula of the gas that is 47.4% sulfur and 52.6% chlorine is S₂Cl₂.