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.
[10]​

Answer 1

Given : oxygen gas of mass 35g is available at 27° and 72cm Hg pressure.

later, if we keep this pressure constant, the RMS velocity of this oxygen molecules becomes double at a certain temperature.

To find : The volume of oxygen gas and later we have to find the value of temperature.

solution : no of moles of oxygen gas, n = 35g/32g/mol = 1.09375

temperature, T = 27° = 300K

pressure , P = 72 cm Hg = 72/76 = 0.9437 atm

now using formula, PV = nRT

V = nRT/P

= (1.09375 ×0.082 × 300)/(0.9437)

= 28.51 L

the volume of oxygen gas is 28.51 L (approx)

RMS velocity, v ∝ √T

so, v₁/v₂ = √{T₁/T₂}

⇒1/2 = √{300K/T₂}

⇒1/4 = 300/T₂

⇒T₂ = 1200 K

Therefore the temperature at which rms velocity of oxygen gas will become double is 1200 K.