Question

A sample of a gas at STP contains $3.01\times {10}^{23}$ molecules and has a mass of 20.0 grams. This gas would :

• A. have a molar mass of 20.0 g/mol and occupy 11.2 liters
• B. occupy 22.4 liters and have a molar mass of 30.0 g/mol
• C. occupy 22.4 liters and have a molar mass of 20.0 g/mol
• D. have a molar mass of 40.0 g/mol and occupy 33.6 liters
• E. have a molar mass of 40.0 g/mol and occupy 11.2 liters

Answer 1

The correct option is E have a molar mass of 40.0 g/mol and occupy 11.2 liters

1 mol = $6.022\times {10}^{23}$
$3.01\times {10}^{23}=\frac{3.01\times {10}^{23}}{6.022\times {10}^{23}}=0.5moles$
Hence, as per given, 0.5 moles of gas has mass = 20 grams.
So, 1 mol of gas has mass =$2\times 20=40$ grams.
Hence, we can say that this gas has molar mass = 40 gram/mole.
1 mole gas has 22.4 L volume at STP, hence, 0.5 moles of this gas 11.2 L volume.