Question

Which of the following gas samples would have the largest volume, if all samples are at the same temperature and pressure?
a 0.498 moles CO2
b 19.91 grams of Ar
c They would all have the same volume

Answer 1

Answer:

They would all have the same volume.

Explanation:

Let us consider the same temperature and pressure of both Ar and CO₂ is standard temperature and pressure.

Standard temperature = 273.15 K

Standard pressure = 1 atm

Number of moles of CO₂ = 0.498 mol

Volume of CO₂ = ?

Solution:

PV = nRT

R = general gas constant = 0.0821 atm.L /mol.K

1 atm × V = 0.498 mol × 0.0821 atm.L /mol.K × 273.15 K

1 atm × V = 11.17 atm.L

V = 11.17 atm.L/1 atm

V = 11.17 L

Volume calculation for Ar:

Number of moles of Ar:

Number of moles = mass/molar mass

Number of moles = 19.91 g /39.95 g/mol

Number of moles = 0.498 mol

Number of moles are same thus it will occupy same volume. We can prove it through calculation given below,

PV = nRT

R = general gas constant = 0.0821 atm.L /mol.K

1 atm × V = 0.498 mol × 0.0821 atm.L /mol.K × 273.15 K

1 atm × V = 11.17 atm.L

V = 11.17 atm.L/1 atm

V = 11.17 L