Three gases (8.00 g of methane, CH4, 18.0 g of ethane, C2H6, and an unknown amount of propane, C3H8) were added to the same 10.0-L container. At 23.0 ∘C, the total pressure in the container is 4.40 atm . Calculate the partial pressure of each gas in the container.
Express the pressure values numerically in atmospheres, separated by commas. Enter the partial pressure of methane first, then ethane, then propane.
pv = n r t
find total moles
convert grams to moles
partial pressure is proportional to molar fraction
To calculate the partial pressure of each gas in the container, we need to use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's find the number of moles of each gas using the given masses and molar masses:
Molar mass of methane (CH4):
1 carbon atom = 12.01 g/mol
4 hydrogen atoms = 4 * 1.01 g/mol = 4.04 g/mol
Total molar mass = 12.01 + 4.04 = 16.05 g/mol
Number of moles of methane:
8.00 g / 16.05 g/mol = 0.498 mol
Molar mass of ethane (C2H6):
2 carbon atoms = 2 * 12.01 g/mol = 24.02 g/mol
6 hydrogen atoms = 6 * 1.01 g/mol = 6.06 g/mol
Total molar mass = 24.02 + 6.06 = 30.08 g/mol
Number of moles of ethane:
18.0 g / 30.08 g/mol = 0.598 mol
Molar mass of propane (C3H8):
3 carbon atoms = 3 * 12.01 g/mol = 36.03 g/mol
8 hydrogen atoms = 8 * 1.01 g/mol = 8.08 g/mol
Total molar mass = 36.03 + 8.08 = 44.11 g/mol
Number of moles of propane (unknown amount):
Let's assume it is 'x' moles.
Now, let's use the ideal gas law to calculate the partial pressures of each gas:
For methane:
PV = nRT
P * V = n * R * T
P * 10.0 L = 0.498 mol * 0.0821 L.atm/mol.K * (23 + 273) K
P = (0.498 * 0.0821 * 296) / 10.0
P = 1.21 atm
For ethane:
P * 10.0 L = 0.598 mol * 0.0821 L.atm/mol.K * (23 + 273) K
P = (0.598 * 0.0821 * 296) / 10.0
P = 1.44 atm
For propane:
P * 10.0 L = x mol * 0.0821 L.atm/mol.K * (23 + 273) K
P = (x * 0.0821 * 296) / 10.0
Now, let's use the total pressure to find the partial pressure of propane:
4.40 atm = 1.21 atm + 1.44 atm + (x * 0.0821 * 296) / 10.0
2.75 atm = (x * 0.0821 * 296) / 10.0
275 = x * 0.0821 * 296
x = 275 / (0.0821 * 296)
x ≈ 11.21 mol
Using this value of x, we can find the partial pressure of propane:
P * 10.0 L = 11.21 mol * 0.0821 L.atm/mol.K * (23 + 273) K
P = (11.21 * 0.0821 * 296) / 10.0
P ≈ 2.20 atm
Therefore, the partial pressures of each gas in the container are approximately:
Methane: 1.21 atm
Ethane: 1.44 atm
Propane: 2.20 atm
To calculate the partial pressure of each gas in the container, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature
Let's start by calculating the number of moles of each gas.
For methane (CH4):
Molar mass of methane (CH4) = 12.01 g/mol (carbon) + 4 * 1.01 g/mol (hydrogen) = 16.05 g/mol
Number of moles of methane = (8.00 g) / (16.05 g/mol) = 0.498 mol
For ethane (C2H6):
Molar mass of ethane (C2H6) = 2 * 12.01 g/mol (carbon) + 6 * 1.01 g/mol (hydrogen) = 30.07 g/mol
Number of moles of ethane = (18.0 g) / (30.07 g/mol) = 0.598 mol
For propane (C3H8):
Since the amount of propane is unknown, we'll denote it as 'x'.
Molar mass of propane (C3H8) = 3 * 12.01 g/mol (carbon) + 8 * 1.01 g/mol (hydrogen) = 44.11 g/mol
Number of moles of propane = x mol
Now, let's calculate the total number of moles of gas in the container:
Total number of moles = number of moles of methane + number of moles of ethane + number of moles of propane
Using the given values, the total number of moles = 0.498 mol + 0.598 mol + x mol
Now, we can calculate the partial pressures of methane, ethane, and propane using the ideal gas law equation.
Since the total pressure is given as 4.40 atm, we can rearrange the equation as follows:
P = (n / V) * R * T
Let's substitute the values and calculate the partial pressures.
For methane:
Partial pressure of methane = (Number of moles of methane / Total number of moles) * Total pressure
Partial pressure of methane = (0.498 mol / (0.498 mol + 0.598 mol + x mol)) * 4.40 atm
For ethane:
Partial pressure of ethane = (Number of moles of ethane / Total number of moles) * Total pressure
Partial pressure of ethane = (0.598 mol / (0.498 mol + 0.598 mol + x mol)) * 4.40 atm
For propane:
Partial pressure of propane = (Number of moles of propane / Total number of moles) * Total pressure
Partial pressure of propane = (x mol / (0.498 mol + 0.598 mol + x mol)) * 4.40 atm
Now, you can plug in the values and calculate the partial pressures of each gas.