A 100 L flask contains a mixture of methane and argon gasses at 25 degree C . The mass of argon present is 228 g and the mole fraction of methane in the mixture is 0.650 . calculate the total kinetic energy of gaseous mixture
Well, isn't this a gas-tly situation! Let's first calculate the number of moles of methane present in the mixture.
To do this, we need to find the mass of methane. Since we know the mass of argon (228 g) and the total mass of the mixture, we can subtract the mass of argon from the total to get the mass of methane.
The total mass of the mixture is the sum of the mass of methane and the mass of argon, which is 228 g + mass of methane.
Now, let's find the mass of methane. Since we have the mole fraction of methane (0.650), we can multiply it by the total mass of the mixture to get the mass of methane.
Mass of methane = 0.650 * (total mass of the mixture - 228 g)
Once we have the mass of methane, we can calculate the number of moles using the molar mass of methane (16.04 g/mol).
Now that we know the number of moles of methane and argon, we can calculate the total kinetic energy.
The total kinetic energy of a gas is given by the equation:
Total kinetic energy = (3/2) * R * T * n
Where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin (25°C = 298 K), and n is the total number of moles of gas.
Now, let's calculate the total kinetic energy of this gas combo, shall we?
Or should I say, let's turn up the heat on this calculation and make it gas-tacular! *wink*
To calculate the total kinetic energy of a gaseous mixture, we need to know the individual kinetic energies of each gas component.
The kinetic energy of a gas can be calculated using the formula:
KE = (3/2) * n * R * T
Where:
KE is the kinetic energy of the gas
n is the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
First, let's calculate the number of moles of methane in the mixture. We can use the mole fraction of methane to do this.
The mole fraction (X) is the ratio of the number of moles of a particular gas to the total number of moles in the mixture. The mole fraction can be calculated using the following formula:
X = (moles of component) / (total moles of mixture)
Given that the mole fraction of methane (X) is 0.650 and the mass of methane is unknown, we can calculate the moles of methane as follows:
moles of methane = X * (mass of argon) / (molar mass of methane)
The molar mass of methane (CH4) is the sum of the atomic masses of carbon (C) and hydrogen (H). The atomic masses are: carbon (12.01 g/mol) and hydrogen (1.01 g/mol).
molar mass of methane = (12.01 g/mol) + 4 * (1.01 g/mol) = 16.05 g/mol
Now we can calculate the moles of methane:
moles of methane = 0.650 * (228 g) / (16.05 g/mol)
Next, we can calculate the number of moles of argon in the mixture by subtracting the moles of methane from the total moles of the mixture:
moles of argon = (mass of argon) / (molar mass of argon)
The molar mass of argon (Ar) is 39.95 g/mol.
moles of argon = (228 g) / (39.95 g/mol)
Now that we have the moles of each gas, we can calculate the total moles of the mixture by summing the moles of methane and argon.
total moles of mixture = moles of methane + moles of argon
Now, let's convert the temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
Finally, we can calculate the kinetic energy of each gas using the formula mentioned earlier and sum them up to get the total kinetic energy of the gaseous mixture.
total kinetic energy = KE(methane) + KE(argon)
You know g Ar = 228. Convert to mols, then calculate mols CH4 from mol fraction Ar.
XAr = 1.00-0.65 = [mols Ar/(mols Ar + mols CH4)].
Then total KE/mol = 3/2(RT) which allows you to calculate KE for n mols CH4 followed by KE for n mols Ar. Then add those together. (Alternatively you can add moles to find total mols and do all at once.)