Compare Quantitatively

Question

Two containers of the same volume are evaluated. Container 1 is maintained at a temperature of 400 K and filled with oxygen gas to a pressure of 750 mm Hg. Container 2 is maintained at a temperature of 200 K and filled with hydrogen gas to a pressure of 750 mm Hg. Compare the two samples of gas quantitatively with regard to:
a. Number of molecules
b. Mass
c. Average molecular kinetic energy
d. Average molecular speed (rms)

Answer 1

a. PV = n₁kT₁  = n₂kT₂ where n₁ and n₂ are number of molecules of oxygen and hydrogen respectively.

    => n₁ / n₂ = T₂ / T₁ = 200 / 400 = 1 / 2

b. m₁ / m₂ = (n₁ * 32)/ (n₂ * 2) = 8, molecular weight of O₂ = M₁ = 32, molecular weight of H₂ = M₂ = 2

c. KE₁ / KE₂ = T_{1 /} T₂ = 400 / 200 = 2

d. V₁ / V₂ = √[(T₁ M₂) / (T₂ M₁)] = √[(400 * 2) / (200 * 32)] = 1/(2√2)