Question

A gas sample contains 4.00g of CH4 and 2.00g of He. What is the volume of the sample at STP?

Answer 1

To calculate the volume of the gas sample at standard temperature and pressure (STP), we find the moles of each gas (CH4 and He) using their molar masses and then multiply by the molar volume (22.4 L/mol) to get their individual volumes at STP. Adding these volumes together gives us the total volume of the gas sample, which is 16.8 L.

Step-by-step explanation:

To calculate the volume of a gas sample at standard temperature and pressure (STP), we can use the molar volume concept where one mole of any gas occupies 22.4 liters at STP. Methane (CH4) has a molar mass of 16.00 g/mol, and helium (He) has a molar mass of 4.00 g/mol.

To find the moles of CH4, we divide 4.00 g by its molar mass, 16.00 g/mol, which gives us 0.250 moles. Similarly, for He, we divide 2.00 g by its molar mass, 4.00 g/mol, which gives us 0.500 moles. To find the total volume, we sum the volumes of CH4 and He after multiplying their mole quantities by the molar volume (22.4 L/mol).

Total volume of CH4 = 0.250 moles × 22.4 L/mol = 5.60 L

Total volume of He = 0.500 moles × 22.4 L/mol = 11.2 L

Therefore, the total volume of the gas sample at STP is 5.60 L + 11.2 L = 16.8 L.

Answer 2

As we know that 1 mole of any gas when acting perfectly / ideally occupies 22.4 L of volume.

It means that in order to calculate volume occupied both by CH₄ and He, we must calculate their moles.

Hence,
Moles are given as,
Moles = Mass / Mass

Moles of CH₄;
Mole-CH₄ = 4 g / 16 g.mol⁻¹

Mole-CH₄ = 0.25 mol

Moles of He;
Mole-He = 2 g / 4 g.mol⁻¹

Mole-He = 0.5 mol

Now adding moles of both gases,

= 0.25 + 0.5

= 0.75 mol

Therefore, when,

1 mole of gas occupy = 22.4 L of Volume

Then,

0.75 mol will occupy = X L of Volume

Solving for X,
X = (0.75 mol × 22.4 L) ÷ 1 mole

X = 16.8 L