The partial pressure of NO₂ at equilibrium is 0.70 bar and the partial pressure of N₂O₄, at equilibrium is 0.23 bar.
Let x be the mole fraction of NO₂ and x' be the mole fraction of N₂O₄.
The total pressure according to Dalton's law of partial pressure is the sum of the partial pressures of each gas.
Let P be the total pressure of the gases, P' be the partial pressure of NO₂ = 1.4 bar and P" be the partial pressure of N₂O₄ = 0.46 bar.
So, P = P' + P"
= 1.4 bar + 0.46 bar
= 1.86 bar
Since P' = xP
x = P'/P
= 1.4 bar/1.86 bar
= 0.753
Also, P" = xP
x' = P"/P
= 0.46 bar/1.86 bar
= 0.247
Now, since the volume of the container is doubled at constant temperature, we use Boyle's law to determine the new pressure. P₁.
Boyle's law states that the pressure of a given mass of gas is inversely proportional to its volume provided the temperature remains constant. It is written mathematicaly as PV = constant
So, PV = P₁V₁
P₁ = (V/V₁)P
Since V/V₁ = 1/2
P₁ = (V/V₁)P
P₁ = P/2
P₁ = 1.86/2 bar
P₁ = 0.93 bar
So, the new partial pressure of NO₂, P₂ = xP₁
= 0.753 × 0.93 bar
= 0.70 bar
The new partial pressure of N₂O₄, P₃ = x'P₁
= 0.247 × 0.93 bar
= 0.23 bar
So, the partial pressure of NO₂ at equilibrium is 0.70 bar and the partial pressure of N₂O₄, at equilibrium is 0.23 bar.
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