mols CH4 = grams/molar mass = ?
mols O2 = g/molar mass = ?
mols SO2 = g/molar mass = ?
total mols = mols CH4 + mols O2 + mols SO2
XCH4 = mols CH4/total mols
pCH4 = XCH4*Ptotal
mols O2 = g/molar mass = ?
mols SO2 = g/molar mass = ?
total mols = mols CH4 + mols O2 + mols SO2
XCH4 = mols CH4/total mols
pCH4 = XCH4*Ptotal
1. Calculate the moles of each gas:
- Moles of methane (CH4) = mass of methane / molar mass of CH4
Moles of methane = 64 g / (12.01 g/mol + 4 * 1.01 g/mol) = 4 g/mol
- Moles of oxygen (O2) = mass of oxygen / molar mass of O2
Moles of oxygen = 64 g / (2 * 16.00 g/mol) = 2 g/mol
- Moles of sulphur dioxide (SO2) = mass of sulphur dioxide / molar mass of SO2
Moles of sulphur dioxide = 64 g / (32.07 g/mol + 2 * 16.00 g/mol) = 1 g/mol
2. Calculate the total moles in the mixture:
Total moles = moles of methane + moles of oxygen + moles of sulphur dioxide
Total moles = 4 g/mol + 2 g/mol + 1 g/mol = 7 g/mol
3. Calculate the mole fraction of methane:
Mole fraction of methane = moles of methane / total moles
Mole fraction of methane = 4 g/mol / 7 g/mol = 4/7
4. Calculate the partial pressure of methane:
Partial pressure of methane = mole fraction of methane * total pressure
Partial pressure of methane = (4/7) * 210 kPa
Therefore, the partial pressure of methane is approximately 120 kPa.
The number of moles of a substance can be calculated using the formula:
Number of moles = Mass (in grams) / Molar mass
The molar mass of methane (CH4) is:
1 carbon atom (12.01 g/mol) + 4 hydrogen atoms (4 * 1.01 g/mol) = 16.05 g/mol
Number of moles of methane = 64g / 16.05 g/mol
Next, we can use the ideal gas law to calculate the partial pressure:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.08206 L 路 atm / (mol 路 K))
T = temperature (in Kelvin)
In this case, we are given the pressure (210 kPa) and we assume that the volume and temperature are constant. Therefore, we can re-arrange the equation to solve for the number of moles:
n = PV / RT
Now, we can substitute the values into the equation:
n = (210 kPa) / [(0.08206 L 路 atm / (mol 路 K)) * T]
Since the volume and temperature are constant, their values cancel out. So we can simplify the equation further:
n = 210 kPa / 0.08206 (L 路 atm / (mol 路 K))
The value 0.08206 (L 路 atm / (mol 路 K)) is the value of the ideal gas constant or R.
Now, substitute the value of R into the equation and calculate the number of moles of methane:
n = 210 kPa / 0.08206 (L 路 atm / (mol 路 K)) = 2559.4168 mol
Finally, we can calculate the partial pressure of methane by multiplying the number of moles by the ideal gas constant:
Partial pressure of methane = n * R
Partial pressure of methane = 2559.4168 mol * 0.08206 (L 路 atm / (mol 路 K)) = 209.94 kPa
Therefore, the expected partial pressure of methane in the mixture is approximately 209.94 kPa.