A mixture of argon and hydrogen gases contains argon at a partial pressure of 241 mm Hg and hydrogen at a partial pressure of 534 mm Hg. What is the mole fraction of each gas in the mixture?
A mixture of argon and hydrogen gases contains argon at a partial pressure of 241 mm Hg and hydrogen at a partial pressure of 534 mm Hg. What is the mole fraction of each gas in the mixture?
pAr = 241 mm
pH2 = 534 mm
ptotal = 241 + 534 = ?
XAr = pAr/ptotal
XH2 = pH2/ptotal
p total is 775
775 is correct for Ptotal. That will let you calculate X for Ar and X for H2.
XAr = 241/775 = ?
XH2 = 534/775 = ?
To find the mole fraction of each gas in the mixture, we need to first calculate the total pressure of the mixture.
The total pressure of a gas mixture is given by the sum of the partial pressures of each gas.
In this case, the total pressure of the mixture is the sum of the partial pressures of argon and hydrogen:
Total pressure = argon partial pressure + hydrogen partial pressure
Total pressure = 241 mmHg + 534 mmHg
Total pressure = 775 mmHg
Now, we can calculate the mole fraction of each gas.
The mole fraction of a gas is defined as the ratio of the number of moles of that gas to the total number of moles in the mixture.
The number of moles of a gas can be calculated using the ideal gas law:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
Since the volume and temperature are constant, the equation can be simplified to:
P = nRT
To find the number of moles of each gas, we rearrange the equation:
n = P / RT
Now, let's calculate the number of moles of argon and hydrogen:
Number of moles of argon = Argon partial pressure / Total pressure * Total number of moles
Number of moles of argon = 241 mmHg / 775 mmHg * Total number of moles
Number of moles of hydrogen = Hydrogen partial pressure / Total pressure * Total number of moles
Number of moles of hydrogen = 534 mmHg / 775 mmHg * Total number of moles
Finally, we can calculate the mole fraction of each gas:
Mole fraction of argon = Number of moles of argon / Total number of moles
Mole fraction of hydrogen = Number of moles of hydrogen / Total number of moles