Answer:
moles Ne = 0.154 mol
moles F₂ = 0.217 mol
Explanation:
Step 1: Data given
Volume of the vessel system = 2.5 L
Total pressure = 3.32 atm at 0.0 °C
The mixture is heated to 15.0 °C
The entropy of the mixture increases by 0.345 J/K
The heat capacity of monoatomic gas = 3/2R and that for a diatomic gas = 5/2R
Step 2: Define the gas
Neon is a monoatomic gas, composed of Ne atoms
⇒ Cv(Ne) ≅ (3/2)R
Fluorine is a diatomic gas, composed of F₂ molecules.
⇒ Cv(F₂) ≅ (5/2)R
Step 3: Calculate moles of gas
p*V = n*R*T
⇒ with p = the total pressure = 3.32 atm
⇒ with V = the total volume = 2.5 L
⇒ with n = the number of moles of gas
⇒ with R = the gas constant = 0.08206 L*atm/K*mol
⇒ with T = the temperature = 273.15 Kelvin
n(total) = p*V/RT = (3.32 atm*2.5 L)/(0.08206 L*atm/mol•K*273.15) = 0.3703 mol
Step 4: Calculate moles of Ne and F2
For one mole heated at constant volume,
∆S = Cv*ln(288.15/273.15) = 0.05346*Cv
⇒ ∆S for 0.3703 mol,
∆S = (0.3703 mol)(0.05346)Cv = 0.345 J/K
⇒ Cv = 17.43 J/mol*K for the Ne/F₂ mixture.
For pure 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
if X is the mole fraction of Ne, we can find X by:
17.43 J/mol*K = X* 12.471 J/mol*K + (1 – X) * 20.785 J/mol*K
⇒ 20.875 – 8.314 * X = 17.43
X = 0.415 , 1 – X = 0.585
moles Ne = (0.415)(0.3703 mol) = 0.154 mol
moles F₂ = (0.585)(0.3703 mol) = 0.217 mol
