Determine the mole fraction of helium in a gaseous mixture consisting of 0.524 g He,
(a)
0.0069
(b)
0.0259
(c)
0.481
(d)
0.493
(e)
0.131
Interpretation:
The mole fraction of helium in a gaseous mixture is to be calculated.
Concept introduction:
The mole fraction of an individual gas, for a combination of gases, is the ratio of the moles of the individual gas to the total number of moles of the mixture.
Here,
Also, the mole fraction of an individual gas, for a combination of gases, can be calculated from the ratio of the partial pressure of the individual gas to the total pressure of the combination.
Here,
The number of moles can be calculated as
Here, m represents the mass of the molecule, M represents the molar mass of the molecule, and
Answer to Problem 1KSP
Solution: Option (d).
Explanation of Solution
Given information:
Mass of helium
Mass of argon
Mass of methane
Reason for the correct option:
The molar mass of helium is
Calculate the number of moles of helium as follows:
Substitute
The molar mass of argon is
Calculate the number of moles of argon as follows:
Substitute
The molar mass of methane is
Calculate the number of moles of methane as follows:
Substitute
From Dalton’s law for the combination of gases, the total number of moles can be calculated as
Substitute
Calculate the mole fraction for
Substitute
Thus, for
Hence, option (d) is correct.
Reason for the incorrect options:
Option (a) is incorrect because the calculated value of mole fraction of heliumfor the given gaseous mixturedoes not match the given value in option (a).
Option (b) is incorrect because the calculated value of mole fraction of helium for the given gaseous mixturedoes not match the given value in option (b).
Option (c) is incorrect because the calculated value of mole fraction of helium for the given gaseous mixturedoes not match the given value in option (c).
Option (e) is incorrect because the calculated value of mole fraction of helium for the given gaseous mixturedoes not match the given value in option (e).
Hence, options(a), (b), (c), and (e) are incorrect.
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