KINETIC THEORY OF GASES

6 )

A vessel contains 1 mole of O₂ gas (relative molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing 1 mole of He gas (relative molar mass 4) at a temperature 2T has pressure of..

8 P

(p/8)

2 P

View Solution

Answer :

PV = nRT

For both gases n = 1 mole

also vessels are same i.e. V is constant hence

P = {(nRT) / v}

P = constant × T

∴ P ∝ T

∴ (P₁ / P₂) = (T₁ / T₂)

given: P₁ = P

T₁ = T

T₂ = 2T

hence P₂ = {(P₁ T₂) / (T₁)} = {(P × 2T) / T} = 2P

7 )

The equation of state for 5 g of oxygen at a pressure P and temperature T. when occupying a volume V, will be

PV = [5 / (32)]RT

PV = [5 / (16)]RT

PV = [5/2]RT

PV = 5 RT

View Solution

Answer :

PV = nRT (1)

where n = no. of molecules.

& n = (M / M_o) = {(mass of gas) / (molar mass of gas)}.

for oxygen, M_o = 32 given is M = 5g. hence

n = (5 / 32)

hence from (1), PV = [5 / (32)] RT.

8 )

A gas at 1 atmosphere and having volume 100 ml is mixed with another gas of equal moles at 0.5 atm and having 50 ml in flask of one liter, what is the final pressure?

0.125 atm

0.75 atm

1 atm

0.5 atm

View Solution

Answer :

PV = nRT

hence n = (PV / RT)

given: P₁ = 1 atm, v₁ = 100 ml.

P₂ = 0.5 atm, V₂ = 50 ml

no. of moles of both gases is same.

Total number of moles are conserved.

n₁ + n₂ = n

{(P₁ V₁) / RT} + {(P₂ V₂) / (RT)} = (PV / RT)

∴ (1 × 100) + (0.5 × 50) = PV

∴ 100 + 25 = PV

PV = 125

given is volume of flask = V = 1 ∙ liter = 10³ m³

∴ P = {125 / V} = {125 / 10³}

∴ P = 0.125 atm

9 )

The quantity [(PV) / (k_BT)] represents

mass of gas

number of moles of gas

number of molecules of gas

K. E, of gas

View Solution

Answer :

PV = nRT ------ n = no. of moles

PV = (N / NA) RT

where N = no. of molecules

NA = Avogadro’s number

∴ PV = NT (R / NA)

as R/NA = K_B = Boltzmann's constant hence PV = NK_BT

(PV / KBT) = N = no. of molecules

10 )

Equation of gas in terms of pressure (P), absolute temperature (T) and density (ρ) is

[(P1T1) / Ï1] = [(P2T2) / Ï2]

[(P1Ï1) / T1] = [(P2Ï2) / T2]

[P1 / (T1Ï1)] = [P2 / (T2Ï2)]

[(P1Ï2) / T1] = [(P2Ï1) / T2]

View Solution

Answer :

PV = nRT

PV = (M / M_o) RT

∴ P = (M / V) (RT / M_o)

∴ P = ρ (RT / M_o) --- (M / V) = ρ = density

∴ (P / ρT) = (R / M_o) i.e. (P / ρT) = constant

hence

[P₁ / (T₁ρ₁)] = [P₂ / (T₂ρ₂)]

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