Mixture of A,B,C if the mole fraction of A is 30 and B is 35 Volume percent calculate the mass and mole fraction of each compnant. given that A is methane, B is ethane, C is propane. use SI unit and English unit.
Xa = 0.30
Xb = 0.35
Xc = 1.0-0.3-0.35 = 0.35
Then Xa = 0.30*molar mass CH4
Xb = 0.35*molar mass ethane
Xc = 0.35* molar mass propane.
I just mislabeled the final results.
grams = 0.30*molar mass CH4.
grams = 0.35*molar mass ethane
grams = 0.35*molar mass propane.
To calculate the mass and mole fraction of each component in a mixture, we first need to understand the definitions of mole fraction and volume percent.
1. Mole fraction (X): The mole fraction of a component in a mixture is the ratio of the number of moles of that component to the total number of moles in the mixture.
2. Volume percent (%v/v): Volume percent is the ratio of the volume of a component to the total volume of the mixture, expressed as a percentage.
Given that the mole fraction of component A (methane) is 30% and component B (ethane) is 35% volume percent, we can proceed with the calculations.
1. Calculate the mole fraction of component B (ethane):
The mole fraction of B (XB) can be calculated using the following formula:
XB = (Volume percent of B / 100) * Molecular weight of A / (Molecular weight of A * moles A + Molecular weight of B * moles B + Molecular weight of C * moles C)
The molecular weight of A (methane) is 16.04 g/mol, B (ethane) is 30.07 g/mol, and C (propane) is 44.10 g/mol.
Considering the volume percent, B = 35%:
XB = (0.35 / 100) * 16.04g/mol / (16.04 g/mol * moles A + 30.07 g/mol * moles B + 44.10 g/mol * moles C)
2. Calculate the mole fraction of component C (propane):
Since the mole fractions of A and B are already known, we can calculate the mole fraction of C using the formula:
XC = 1 - XA - XB
3. Calculate the mass fraction of each component:
The mass fraction of a component is the ratio of the mass of that component to the total mass of the mixture.
The mass fraction of component A (YA) can be calculated:
YA = (Molecular weight of A * moles A) / (Molecular weight of A * moles A + Molecular weight of B * moles B + Molecular weight of C * moles C)
Similarly, the mass fraction of component B (YB) and component C (YC) can be calculated using the same formula.
Note: Since we are given volume percent and need to calculate mass fraction, further calculations are needed.
Let's do the calculations in both SI and English units.
SI Units:
1. Calculate XB:
XB = (0.35 / 100) * 16.04 g/mol / (16.04 g/mol * moles A + 30.07 g/mol * moles B + 44.10 g/mol * moles C)
2. Calculate XC:
XC = 1 - XA - XB
3. Calculate YA:
YA = (16.04 g/mol * moles A) / (16.04 g/mol * moles A + 30.07 g/mol * moles B + 44.10 g/mol * moles C)
4. Calculate YB:
YB = (30.07 g/mol * moles B) / (16.04 g/mol * moles A + 30.07 g/mol * moles B + 44.10 g/mol * moles C)
5. Calculate YC:
YC = (44.10 g/mol * moles C) / (16.04 g/mol * moles A + 30.07 g/mol * moles B + 44.10 g/mol * moles C)
English Units:
The molecular weights mentioned above are in g/mol, so we need to convert them to lb/lbmol before proceeding with the calculations.
1. Calculate XB:
XB = (0.35 / 100) * 16.04 lb/lbmol / (16.04 lb/lbmol * moles A + 30.07 lb/lbmol * moles B + 44.10 lb/lbmol * moles C)
2. Calculate XC:
XC = 1 - XA - XB
3. Calculate YA:
YA = (16.04 lb/lbmol * moles A) / (16.04 lb/lbmol * moles A + 30.07 lb/lbmol * moles B + 44.10 lb/lbmol * moles C)
4. Calculate YB:
YB = (30.07 lb/lbmol * moles B) / (16.04 lb/lbmol * moles A + 30.07 lb/lbmol * moles B + 44.10 lb/lbmol * moles C)
5. Calculate YC:
YC = (44.10 lb/lbmol * moles C) / (16.04 lb/lbmol * moles A + 30.07 lb/lbmol * moles B + 44.10 lb/lbmol * moles C)
Hope this helps! Let me know if you need any further assistance.