Three gases (8.00 of methane, , 18.0 of ethane, , and an unknown amount of propane, ) were added to the same 10.0- container. At 23.0 , the total pressure in the container is 3.50 . Calculate the partial pressure of each gas in the container.
Partial pressure is divided according to mole ratio.
Figure out the moles of each, than add to get total moles.
pressuremethane= molesmethane/totalmoles * total pressure
pressurethane= moleethane/totalmoles * total pressure
and so on. until you get the ones you know.
then pressure propane= total pressure-sum of partial pressures ethane, methane, ...
To calculate the partial pressure of each gas in the container, we can use the ideal gas law equation:
PV = nRT
Where:
P = Total pressure in the container
V = Volume of the container
n = Number of moles of gas
R = Ideal gas constant
T = Temperature
First, let's calculate the total number of moles in the container by dividing the mass of each gas by its molar mass.
The molar mass of methane (CH4) is 16.04 g/mol.
The molar mass of ethane (C2H6) is 30.07 g/mol.
The molar mass of propane (C3H8) is 44.10 g/mol.
For methane:
n1 = 8.00 g / 16.04 g/mol = 0.499 mol
For ethane:
n2 = 18.0 g / 30.07 g/mol = 0.598 mol
We don't know the amount of propane, so let's call it x mol.
Now we can substitute the values into the equation to solve for x:
(0.499 + 0.598 + x) * 3.50 atm = 10.0 L * R * 23.0 °C
We need to convert the temperature to Kelvin by adding 273.15:
(0.499 + 0.598 + x) * 3.50 atm = 10.0 L * R * (23.0 + 273.15) K
Next, we need to convert the pressure from atm to Pa (Pascal) because the ideal gas constant (R) is usually expressed in J/(mol*K) which requires pressure in Pa. 1 atm = 101325 Pa.
(0.499 + 0.598 + x) * 101325 Pa = 10.0 L * R * 296.15 K
We can simplify the equation by dividing both sides by 101325:
(0.499 + 0.598 + x) = (10.0 L * R * 296.15 K) / 101325 Pa
Now we can use the ideal gas constant, R = 0.0821 L*atm/(mol*K), to substitute the value:
(0.499 + 0.598 + x) = (10.0 L * 0.0821 L*atm/(mol*K) * 296.15 K) / 101325 Pa
Simplifying the equation will give us the value of x, the number of moles of propane.
Once we know the number of moles of each gas, we can calculate the partial pressure of each gas using the equation:
Partial Pressure of a gas = (Number of moles of the gas / Total moles of the mixture) * Total pressure in the container
For methane:
Partial Pressure of methane = (0.499 mol / (0.499 + 0.598 + x) mol) * 3.50 atm
For ethane:
Partial Pressure of ethane = (0.598 mol / (0.499 + 0.598 + x) mol) * 3.50 atm
For propane:
Partial Pressure of propane = (x mol / (0.499 + 0.598 + x) mol) * 3.50 atm
By calculating the value of x and substituting it into the partial pressure equations, we can determine the partial pressure of each gas in the container.