A tank contains 20.0 liters of air at 30°C and 5.01*10^5 N/m^2 pressure. What is the mass of air and what volume will it occupy at 1 atmospheric pressure at 0°C? The average Molecular mass of air is 28.8g/mole.
Answers
Answer: The ideal gas law can be used to find the density of a gas at conditions that are not standard. For example, we will determine the density of ammonia gas (NH3)
(
NH
3
)
at 0.913atm
0.913
atm
and 20oC
20
o
C
, assuming the ammonia is ideal. First, the molar mass of ammonia is calculated to be 17.04g/mol
17.04
g/mol
. Next, assume exactly 1mol
1
mol
of ammonia (n=1)
(
n
=
1
)
and calculate the volume that such an amount would occupy at the given temperature and pressure.
V=nRTP=1.00mol×0.08206L⋅atm/K⋅mol×293K0.913atm=26.3L(14.9.3)
(14.9.3) V=
n
R
T
P
=
1.00
mol
×
0.08206
L
⋅
atm/K
⋅
mol
×
293
K
0.913
atm
=26.3L
Now the density can be calculated by dividing the mass of one mole of ammonia by the volume above.
Density=17.04g26.3L=0.647g/L(14.9.4)
(14.9.4) Density=
17.04
g
26.3
L
=0.647g/L
As a point of comparison, this density is slightly less than the density of ammonia at STP, which is equal to (170.4g/mol)(22.4L/mol)=0.761g/L
(
170.4
g/mol
)
(
22.4
L/mol
)
=
0.761
g/L
. It makes sense that the density should be lower compared to that at STP since both the increase in temperature (from 0oC
0
o
C
to 20oC
20
o
C
) and the decrease in pressure (from 1atm
1
atm
to 0.913atm
0.913
atm
) would cause the NH3
NH
3
molecules to spread out a bit further from one another.
Summary
Calculations of molar mass and density of an ideal gas are described.
Contributors and Attributions
CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.
Explanation: