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 5.20 atm . Calculate the partial pressure of each gas in the container.

Question

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 5.20 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.

Answer 1

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.