Answer:
The answer to the question is
The ratio of the two gas pressures [tex]\frac{P_{x} }{P_{y} }[/tex] , that is Px to Py = 1/6
Step-by-step explanation:
Let the gases Volumes be V₁ and V₂
Where volume of X = V₁ and
volume of Y = V₂
The volume of Y is half the volume of X
∴ V₂ = [tex]\frac{1}{2}[/tex] × V₁
Let the number of moles be n₁ and n₂ in X and Y respectively
therefore n₂ = 3 × n₁
The pressure of the gas in X is Pₓ and the pressure of the gas in Y is [tex]P_{y}[/tex] then we have
P₁ × V₁ = n₁ × R × T₁ , and P₂ × V₂ = n₂ × R × T₂
(P₁ × V₁)/(n₁ × T₁) = (P₂ × V₂)/(n₂ × T₂)
but T₁ = T₂
Therefore
(P₁ × V₁)/n₁ = (P₂ × V₂)/n₂. However n₂ = 3 × n₁ and V₂ = [tex]\frac{1}{2}[/tex] × V₁ therefore substituting in the equation we have
(P₁ × V₁)/n₁ = (P₂ × [tex]\frac{1}{2}[/tex] × V₁ )/(3 × n₁) from where
P₁ /P₂ = ([tex]\frac{1}{2}[/tex] × V₁ × n₁)/(V₁×3 × n₁) =0.5/3 = 1/6
The ratio of [tex]\frac{P_{x} }{P_{y} }[/tex] = 1/6
