What is the mole fraction of H2 in a gaseous mixture containing 1.0g H2, 8.0g O2, and 16g CH4. Express in 2 decimal places
Answers
Explanation:
Explanation:
In order to be able to calculate the mole fraction of each component in the mixture, you will have to convert the masses given to you to moles.
To do that, use the molar mass of oxygen gas, nitrogen gas, and hydrogen gas, respectively
15.08
g
⋅
1 mole O
2
31.9988
g
=
0.47127 moles O
2
8.17
g
⋅
1 mole N
2
28.0134
g
=
0.29165 moles N
2
2.64
g
⋅
1 mole H
2
2.0159
g
=
1.3096 moles H
2
The total number of moles present in the mixture will be
n
total
=
n
O
2
+
n
N
2
+
n
H
2
n
total
=
0.47127
+
0.29165
+
1.3096
=
2.0725 moles
So, to get the mole fraction of a component
i
of the mixture, all you have to do is divide the number of moles of that component by the total number of moles present.
χ
i
=
n
i
n
total
You will have
χ
O
2
=
0.47127
moles
2.0725
moles
=
0.227
χ
N
2
=
0.29165
moles
2.0725
moles
=
0.141
χ
H
2
=
1.3096
moles
2.0725
moles
=
0.632
Now, you could calculate the partial pressure of each gas by using the ideal gas law equation three times, once for every gas.
P
V
=
n
R
T
However, a simpler approach would be to use the ideal gas law equation once to find the total pressure exerted by the mixture, then use the mole fractions of the gases to find their respective partial pressure - think Raoult's Law.
So, the pressure exerted by the mixture will be
P
total
=
n
total
⋅
R
T
V
P
total
=
2.0725
moles
⋅
0.0821
atm
⋅
L
mol
⋅
K
⋅
(
273.15
+
15
)
K
15.50
L
P
total
=
3.163 atm
The partial pressure of each gas
i
will depend on its mole fraction and on the total pressure of the gas
P
i
=
χ
i
×
P
total
Plug in your values to get
P
O
2
=
0.227
⋅
3.163 atm
=
0.718 atm
P
N
2
=
0.141
⋅
3.163 atm
=
0.446 atm
P
H
2
=
0.632
⋅
3.163 atm
≈
2.00 atm
All the answers are rounded to three sig figs.