To calculate the partial pressure of each gas in the container, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of the gas
R = Ideal gas constant
T = Temperature
First, we need to calculate the number of moles for each gas.
For methane, CH4:
Given mass of methane = 8.00 g
Molar mass of methane (CH4) = 16.04 g/mol
Number of moles of methane (n1) = mass / molar mass = 8.00 g / 16.04 g/mol
For ethane, C2H6:
Given mass of ethane = 18.0 g
Molar mass of ethane (C2H6) = 30.07 g/mol
Number of moles of ethane (n2) = mass / molar mass = 18.0 g / 30.07 g/mol
For propane, C3H8:
The mass of propane is unknown, let's call it 'm'.
Molar mass of propane (C3H8) = 44.10 g/mol
Number of moles of propane (n3) = mass / molar mass = m / 44.10 g/mol
Next, we need to calculate the total number of moles, which is the sum of the moles of each gas:
Total number of moles (ntotal) = n1 + n2 + n3
Now, we can calculate the partial pressure of each gas using Dalton's Law of Partial Pressures:
P1 = (n1 / ntotal) * Ptotal
P2 = (n2 / ntotal) * Ptotal
P3 = (n3 / ntotal) * Ptotal
Given:
Total pressure (Ptotal) = 5.20 atm
Volume (V) = 10.0 L
Temperature (T) = 23.0 °C = 23.0 + 273.15 K (convert to Kelvin)
Convert temperature from °C to Kelvin:
T = 23.0 + 273.15 K = 296.15 K
Now, we can substitute the values into the equations and calculate the partial pressures:
P1 = (n1 / ntotal) * Ptotal = (8.00 g / 16.04 g/mol) / (8.00 g / 16.04 g/mol + 18.0 g / 30.07 g/mol + m / 44.10 g/mol) * 5.20 atm
P2 = (n2 / ntotal) * Ptotal = (18.0 g / 30.07 g/mol) / (8.00 g / 16.04 g/mol + 18.0 g / 30.07 g/mol + m / 44.10 g/mol) * 5.20 atm
P3 = (n3 / ntotal) * Ptotal = (m / 44.10 g/mol) / (8.00 g / 16.04 g/mol + 18.0 g / 30.07 g/mol + m / 44.10 g/mol) * 5.20 atm
Now, you can calculate the partial pressure of each gas by substituting the values of moles into the above equations and perform the calculations.