Respuesta :
Answer:
The number of moles neon in the mixture is 0.148 moles
The number of fluorine in the mixture is 0.200 moles
Explanation:
Step 1: Data given
Volume = 2.6 L
Total pressure = 3.0 atm at 0.0 °C
When the mixture is heated to 14.0 °C, the entropy of the mixture increases by 0.30 J/K
Step 2: Calculate total moles
Neon is a monoatomic gas, composed of Ne atoms.
Fluorine is a diatomic gas, composed of F₂ molecules.
The heat capacities are different because F₂ has rotational degrees of freedom and for that reason, Cv(F₂) ≅ (5/2)R while Cv(Ne) ≅ (3/2)R.
n(total) = PV/RT = (3.00 atm)(2.6 L)/(0.08206 L-atm/mol*K)(273.15) = 0.348 mol
For one mole heated at constant volume,
Step 3: Define ∆S
∆S = Cv*ln(287.15/273.15) = 0.04998*Cv
So, for 0.348 mol,
∆S = (0.348 mol)(0.04998)Cv = 0.30 J/K
⇒ Cv = 17.25 J/mol*K for the Ne/F₂ mixture.
Step 4: Calculate Cv
For pure Neon (Ne), Cv = (3/2)R = 1.5 * 8.314 J/mol*K = 12.471 J/mol*K
For pure F₂, Cv = (5/2)R = 2.5 * 8.314 J/mol*K = 20.785 J/mol*K
Step 5: Calculate moles of Ne and F2
if X is the mole fraction of Ne, we can find X by setting the observed ∆S to the weighted average of the ∆S's expected for the two different gases in the mixture:
17.25 J/mol*K = X * 12.471 J/mol*K + (1 – X) * 20.785 J/mol•K
17.25 = x12.471 + 20.785 - 20.785x
-3.535 = -8.314x
x = 0.425
1 - x = 0.575
moles Ne = (0.425)(0.348 mol) = 0.148 mol
moles F₂ = (0.575)(0.348 mol) = 0.200 mol
The number of moles neon in the mixture is 0.148 moles
The number of fluorine in the mixture is 0.200 moles
