Which of the following gas samples would have the largest volume, if all samples are at the same temperature and pressure? a 8x10^23 molecules of N2
b 0.107 moles CO2
c They would all have the same volume

a) 8×10²³ molecules of N2

Explanation:

Let us consider the same temperature and pressure of both sample are standard temperature and pressure.

Standard temperature = 273.15 K

Standard pressure = 1 atm

Number of moles of CO₂ = 0.107  mol

Volume of CO₂ = ?

Solution:

PV = nRT

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

1 atm × V = 0.107 mol × 0.0821 atm.L /mol.K × 273.15 K

1 atm × V = 2.4 atm.L

V = 2.4 atm.L/1 atm

V = 2.4 L

Volume of N₂:

Number of moles of N₂:

1 mole =  6.022 ×10²³ molecules

8×10²³ molecules × 1 mol /  6.022 ×10²³ molecules

1.33 mol

PV = nRT

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

1 atm × V = 1.33 mol × 0.0821 atm.L /mol.K × 273.15 K

1 atm × V = 29.83  atm.L

V = 29.83  atm.L/1 atm

V = 29.83 L

answer : (a) volume of the gas = 8.67 ×   l

                (b) second virial coefficient b = -1.21226 l/mole

solution :   given,     t = 300k

                                p = 20atm

                                z = 0.86

                                n = 8.2 mmoles = 8.2 × moles

                                r =   0.082 l atm/k/mol

        find,     (a) volume of gas   and (b) second virial coefficient b at 300k.

formula used :            

                          and            

(a)            

                    = \times 0.082\times 300}{20}[/tex]

                    = 8.67 ×   l

(b)      

                    = (0.00867-1) × 8.659

                    = - 8.5839 l/mole