Among the assumptions made in the kinetic theory of gases, is the one stating th

Question

Among the assumptions made in the kinetic theory of gases, is the one stating that atoms and molecules are very small and thus occupy only a negligible portion of the volume, under normal conditions of temperature and pressure. This can be illustrated by calculating the volume physically occupied by the air molecules in our classroom. In order to do this, we can take all individual air molecules (both nitrogen and oxygen) as being the equivalent of spheres with a diameter of 0.71 nm.

Calculate the volume physically occupied by air molecules in our classroom, under the same conditions as stated in question 1 above.

(Reminder : Avogadro’s number is : 6.022 x 1023 molecules/mol)

Explanation / Answer

Suppose the volume of the class in 1 m3

P = 10^5 N/m2

V = 1 m3

n = no of moles of air molecules

R = 8.314

T = 298 K

PV = nRT

=> n = PV / RT

=> n = 10^5 x 1 / 8.314 x 298 = 40.36 moles of air molecules

Therefore total no. of molecules = 6.022 x 10^23 x 40.36 = 2.43 x 10^25 molecules

Radius of each molecule = 0.71 / 2 = 0.355 nm = 3.55 x 10^-10 m

Volume of each molecule = (4/3) x pi x (r)^3 = (4/3) x 3.14 x (3.55 x 10^-10)^3 = 1.873 x 10^-28 m3

Volume of all the molecules combined = 1.873 x 10^-28 x 2.43 x 10^25 = 4.55 x 10^-3 m3 = 0.00455 m3

Therefore in a 1 m3 room air molecules occupy a mere volume of 0.00455 m3 (0.455 %)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.