Which of the following gas samples has the same volume as 4.0 g of methane, CH4? (All volumes are measured at the same temperature and pressure.) A 1.0 g of helium B 1.0 g of hydrogen C 3.5 g of nitrogen D 35.5 g of chlorine - Scottish Highers Chemistry - Question 14 - 2019

To find the number of moles ( ( n )) of methane, use the formula: [ n = \frac{mass}{molar\ mass} = \frac{4.0 g}{16.042 g/mol} \approx 0.2496 mol ]

At standard temperature and pressure (STP), one mole of gas occupies 22.4 L. Thus, the volume occupied by 0.2496 moles of methane is:

[ Volume = n \times 22.4 L/mol \approx 0.2496 mol \times 22.4 L/mol \approx 5.596 L ]

Using the molar masses of each gas:

• Helium (He): 4.00 g/mol
• Hydrogen (H2): 2.02 g/mol
• Nitrogen (N2): 28.02 g/mol
• Chlorine (Cl2): 70.90 g/mol

Now calculate how many moles correspond to the offered masses:

• For 1.0 g of helium: [ n_{He} = \frac{1.0 g}{4.00 g/mol} = 0.25 mol;\ Volume = 0.25 \times 22.4 L/mol = 5.6 L]
• For 1.0 g of hydrogen: [ n_{H2} = \frac{1.0 g}{2.02 g/mol} \approx 0.495 mol;\ Volume = 0.495 \times 22.4 L/mol \approx 11.08 L]
• For 3.5 g of nitrogen: [ n_{N2} = \frac{3.5 g}{28.02 g/mol} \approx 0.125 mol;\ Volume = 0.125 \times 22.4 L/mol \approx 2.8 L]
• For 35.5 g of chlorine: [ n_{Cl2} = \frac{35.5 g}{70.90 g/mol} \approx 0.501 mol;\ Volume = 0.501 \times 22.4 L/mol \approx 11.22 L]

The only gas sample that has a volume close to 5.6 L is:

• A: 1.0 g of helium.

Thus, the answer is A.