Question

Considering the value of ideal gas constant in S.I. unit, find the volume of 35g O2 at 27°C and 72
cm Hg pressure. Later, if we keep this pressure constant, the r.m.s velocity of this oxygen molecules
become double at a certain temperature. Calculate the value of this temperature.

Answer 1

Given:

Quantity = 35g

Temperature = 27°C

Pressure = 72cm Hg pressure

To Find:

Value of the temperature.

Solution:

Quantifying the basic values -

Temperature of Gas = T = 27°C + 273 = 300k

Molar mass = n = number of moles = (35 g)/(32 g/mol) = 1.09 mol

General Gas Constant = R = 8.314 J/mol.k

Kinetic Energy of gas molecule = 3/2KT

and K.E = 1/2mv²

Comparing both equations, -

3/2KT = 1/2mv²

v² = 3KT/m

v = √(3KT/m)

v₁ = √(3K × 300/m)  ( Being the value of T)

v₁ = √(900 K/m)

Similarly v2 = 2v1 = √(3KT2/m)

 2√(900 K/m) = √(3KT2/m)

4(900) = 3T2

T2 = 1200 K

Answer: The value of temperature is 1200K.