A 0.500 L of gases is at 307 K and contains N2 at a pressure of 1.40 atm and O2 at a pressure of 0.24 atm. What is the mole fraction of each of the two gases? (Molar mass: N=14 g/mol, O=16 g/mol)
First, we need to calculate the total pressure of the mixture:
Ptotal = PN2 + PO2 = 1.40 atm + 0.24 atm = 1.64 atm
Next, we can use the ideal gas law to calculate the number of moles of each gas:
nN2 = (PN2 * V) / (R * T) = (1.40 atm * 0.500 L) / (0.0821 L·atm/mol·K * 307 K) = 0.0273 mol
nO2 = (PO2 * V) / (R * T) = (0.24 atm * 0.500 L) / (0.0821 L·atm/mol·K * 307 K) = 0.00413 mol
The total number of moles is then:
ntotal = nN2 + nO2 = 0.0273 mol + 0.00413 mol = 0.0314 mol
Finally, we can calculate the mole fraction of each gas:
XN2 = nN2 / ntotal = 0.0273 mol / 0.0314 mol = 0.869
XO2 = nO2 / ntotal = 0.00413 mol / 0.0314 mol = 0.131
Therefore, the mole fraction of N2 is 0.869 and the mole fraction of O2 is 0.131.
To find the mole fraction of each gas, we first need to calculate the moles of each gas present.
Step 1: Calculate the moles of N2 gas.
We can use the ideal gas law equation, PV = nRT, to calculate the moles of N2 gas.
R = ideal gas constant = 0.0821 L·atm/mol·K
V = volume = 0.500 L
P = pressure of N2 gas = 1.40 atm
T = temperature = 307 K
n(N2) = (P * V) / (R * T)
n(N2) = (1.40 atm * 0.500 L) / (0.0821 L·atm/mol·K * 307 K)
n(N2) ≈ 0.0357 mol
Step 2: Calculate the moles of O2 gas.
Using the same equation as before:
P = pressure of O2 gas = 0.24 atm
n(O2) = (P * V) / (R * T)
n(O2) = (0.24 atm * 0.500 L) / (0.0821 L·atm/mol·K * 307 K)
n(O2) ≈ 0.0073 mol
Step 3: Calculate the total moles of gas.
To calculate the total moles of gas, we sum the moles of N2 and O2.
Total moles of gas = n(N2) + n(O2)
Total moles of gas = 0.0357 mol + 0.0073 mol
Total moles of gas ≈ 0.043 mol
Step 4: Calculate the mole fraction of each gas.
The mole fraction of a gas is calculated by dividing the moles of that gas by the total moles of gas.
mole fraction of N2 = n(N2) / Total moles of gas
mole fraction of N2 ≈ 0.0357 mol / 0.043 mol
mole fraction of N2 ≈ 0.831
mole fraction of O2 = n(O2) / Total moles of gas
mole fraction of O2 ≈ 0.0073 mol / 0.043 mol
mole fraction of O2 ≈ 0.169
Therefore, the mole fraction of N2 is approximately 0.831 and the mole fraction of O2 is approximately 0.169.