A mixture of three gases O2, N2 and CO2 is
Answers
Answer:
To make this problem a little interesting, let's assume that you're not familiar with Dalton's Law of partial pressures, which tells you that the partial pressure of a gas that's part of a gaseous mixture is proportional to that gas' mole fraction.
Here's how you can think about what's going on, Let's assume that the mixture is at a pressure
P
total
, a temperature
T
, and occupies a volume
V
.
If you were to isolate the nitrogen gas in the same volume, you could write, using the ideal gas law equation
P
N
2
⋅
V
=
n
N
2
⋅
R
T
⇒
P
N
2
=
n
N
2
⋅
R
T
V
Here
P
N
2
is the pressure exerted by the nitrogen gas when alone in the same volume as the mixture.
Now do the same for oxygen and carbon dioxide.
P
O
2
⋅
V
=
n
O
2
⋅
R
T
⇒
P
O
2
=
n
O
2
⋅
R
T
V
P
C
O
2
⋅
V
=
n
C
O
2
⋅
R
T
⇒
P
C
O
2
=
n
C
O
2
⋅
R
T
V
Now, what would happen if you were to have the nitrogen gas, the oxygen gas, and the carbon dioxide in the same volume? The pressure would change to
P
total
, and the total number of moles in the mixture would be
n
total
=
n
N
2
+
n
O
2
+
n
C
O
2
This means that you could write
P
total
⋅
V
=
n
total
⋅
R
T
P
total
=
n
total
⋅
R
T
V
This is equivalent to
P
total
=
[
n
N
2
+
n
O
2
+
n
C
O
2
]
⋅
R
T
V
(
1
)
P
total
=
P
N
2
n
N
2
⋅
R
T
V
+
P
O
2
n
O
2
⋅
R
T
V
+
P
C
O
2
n
C
O
2
⋅
R
T
V
Therefore,
P
total
=
P
N
2
+
P
O
2
+
P
C
O
2