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A 0.500 g sample of He at STP has a volume that is one-half that of an unknown pure gas also at STP. The unknown pure gas sample has a mass of 36.5 g. What is the molar mass of the unknown gas?

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Eduard22sly

The molar mass of the unknown gas which has a mass of 36.5 g is 146 g/mol

  • We'll begin by calculating the number of mole in 0.5 g of He.

Mass of He = 0.5 g

Molar mass of He = 4 g/mol

Mole of He =.?

[tex]Mole = \frac{mass}{molar mass} \\\\= \frac{0.5}{4}\\\\[/tex]

Mole of He = 0.125 mole

  • Next, we shall determine the volume occupied by 0.125 mole of He at stp

At standard temperature and pressure (stp),

1 mole of He = 22.4 L

Therefore,

0.125 mole of He = 0.125 × 22.4

0.125 mole of He = 2.8 L

  • Next, we shall determine the volume of the unknown gas.

Volume of He = 2.8 L

Volume of unknown gas =?

Volume of He = ½ × Volume of unknown gas

2.8 = ½ × Volume of unknown gas

Cross multiply

Volume of unknown gas = 2.8 × 2

Volume of unknown gas = 5.6 L

  • Next, we shall determine the mole of the unknown gas that occupied 5.6 L at stp.

22.4 L = 1 mole of unknown gas

Therefore,

5.6 L = [tex]\frac{5.6}{22.4}\\\\[/tex]

5.6 L = 0.25 mole of unknown gas.

  • Finally, we shall determine the molar mass of the unknown gas.

Mole of unknown gas = 0.25 mole

Mass of unknown gas = 36.5 g

Molar mass of unknown gas =?

[tex]Molar mass = \frac{mass}{mole} \\\\ = \frac{36.5}{0.25}\\\\[/tex]

= 146 g/mol

Therefore, the molar mass of the unknown gas is 146 g/mol

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