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 3.90 . Calculate the partial pressure of each gas in the container.
Do you use units in your chem class?
To find the partial pressure of each gas in the container, we can use Dalton's Law of Partial Pressures. According to this law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of individual gases.
1. First, let's convert the quantities of each gas to moles. We'll use the ideal gas law equation: PV = nRT.
For methane (CH4):
PCH4 * V = nCH4 * R * T
nCH4 = (PCH4 * V) / (R * T)
nCH4 = (3.90 atm * 10.0 L) / (0.0821 L*atm/(mol*K) * 296 K) = 1.68 mol
For ethane (C2H6):
PC2H6 * V = nC2H6 * R * T
nC2H6 = (PC2H6 * V) / (R * T)
nC2H6 = (3.90 atm * 10.0 L) / (0.0821 L*atm/(mol*K) * 296 K) = 3.71 mol
(Note: We do not know the amount of propane, so let's denote it as nC3H8 mol.)
2. Next, we need to find the mole fraction of each gas in the mixture.
Mole fraction = moles of gas / total moles of all gases
For methane:
Mole fraction of CH4 (XCH4) = nCH4 / (nCH4 + nC2H6 + nC3H8)
XCH4 = 1.68 mol / (1.68 mol + 3.71 mol + nC3H8 mol)
For ethane:
Mole fraction of C2H6 (XC2H6) = nC2H6 / (nCH4 + nC2H6 + nC3H8)
XC2H6 = 3.71 mol / (1.68 mol + 3.71 mol + nC3H8 mol)
For propane:
Mole fraction of C3H8 (XC3H8) = nC3H8 / (nCH4 + nC2H6 + nC3H8)
XC3H8 = nC3H8 / (1.68 mol + 3.71 mol + nC3H8 mol)
3. Now, we can calculate the partial pressure of each gas using the mole fractions and the total pressure of the mixture.
For methane:
PCH4 = XCH4 * PT
PCH4 = XCH4 * 3.90 atm
For ethane:
PC2H6 = XC2H6 * PT
PC2H6 = XC2H6 * 3.90 atm
For propane:
PC3H8 = XC3H8 * PT
PC3H8 = XC3H8 * 3.90 atm
Remember, we still do not know the amount of propane (nC3H8), so we cannot calculate its partial pressure. However, we have successfully set up the equations to calculate the partial pressure of each gas once the amount of propane is known.