a mixture of gases contains 64g of methane, 64g of oxygen and 64g of sulphur dioxide. The pressure of the mixture is 210 kpa. what is the partial pressure (in kpa) of the methane expected to be?
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
To find the partial pressure of methane in the mixture, we need to know the mole fraction of methane and use it to calculate the partial pressure.
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.
To find the partial pressure of methane in the mixture, we first need to calculate the number of moles of each gas in the mixture.
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 · atm / (mol · 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 · atm / (mol · 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 · atm / (mol · K))
The value 0.08206 (L · atm / (mol · 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 · atm / (mol · 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 · atm / (mol · K)) = 209.94 kPa
Therefore, the expected partial pressure of methane in the mixture is approximately 209.94 kPa.