Question

the pressure of 5 moles of a mixture of a nitrogen gas oxygen gas and hydrogen gas is measured to be 12 pa .if the partial pressure of nitrohen gas is 2 pa and oxygen gas is 4 pa .how many moles of hydrogen are in the mixture

Answer 1

Answer:-

Given:-

Total no.of moles of a mixture of nitrogen, oxygen & hydrogen = 5 moles.

Total pressure of the mixture (Pₜₒₜₐₗ) = 12 pa.

Partial pressure of Nitrogen = 2 pa

Partial pressure of oxygen = 4 pa.

We know that,

Dalton's law of Partial pressure states that;

Total pressure exerted by two or more gases in a mixture is the sum of the partial pressures of individual gases.

⟹ Pₜₒₜₐₗ = P₁ + P₂ + P₃ +...+ Pₙ

So, Partial pressure of Hydrogen = Total pressure - Partial pressure of Nitrogen - Partial pressure of Oxygen

⟹ Partial pressure of Hydrogen = 12 - 2 - 4 = 6 pa.

Now,

We know,

Partial pressure of a component = Mole fraction of the component × Total pressure of the mixture

⟹ Partial pressure of Hydrogen = Mole fraction of Hydrogen × Total pressure of the mixture

Putting the respective values we get,

⟹ 6 = Mole fraction of Hydrogen × 12

⟹ 6/12 = Mole fraction of Hydrogen

⟹ 1/2 = Mole fraction of Hydrogen

Now,

Mole fraction of a substance = Total number of moles of the substance (n)/ Total number of moles in the mixture (nₜₒₜₐₗ)

⟹ 1/2 = no. of moles of H/5

⟹ (1/2)(5) = no. of moles of H

⟹ 2.5 moles. = no. of moles of H

∴ There are 2.5 moles of Hydrogen in the mixture.