Calculate the volume in L occupied by 0.842 mol of nitrogen gas at a pressure of 1.29 atm and a temperature of 312K. Note that R has a value of 0.0821 L atm/mol K. Report answer to 3 sig figs.
Answers
Explanation:
Your starting point here will be the ideal gas law equation, which looks like this
P
V
=
n
R
T
−−−−−−−−−−
Here
P
is the pressure of the gas
V
is the volume it occupies
n
is the number of moles of gas present in the sample
R
is the universal gas constant, equal to
0.0821
atm L
mol K
T
is the absolute temperature of the gas
Now, let's say that the given mass of gas is
m
. The number of moles of gas present in this given mass
m
depends on the molar mass of the gas, let's say
M
M
.
n
=
m
M
M
Plug this into the ideal gas law equation to get
P
V
=
m
M
M
⋅
R
T
Next, divide both sides of the equation by
T
to get
P
V
T
=
m
M
M
⋅
R
The molar mass of the gas, which tells you the mass of exactly
1
mole of the gas, is constant.
P
V
T
=
constant
R
M
M
⋅
m
P
V
T
=
constant
⋅
m
This means that for a given mass
m
, i.e. if you use a sample of gas of constant mass, you can say that
P
V
T
=
constant
This is the combined gas law equation and it tells you that for a given mass of gas
m
, you have
P
1
V
1
T
1
=
P
2
V
2
T
2
−−−−−−−−−−−−−
Here
P
1
,
V
1
,
T
1
are the pressure, volume, and absolute temperature of the gas at an initial state
P
2
,
V
2
,
T
2
are the pressure, volume, and absolute temperature of the gas at a final state