Chemistry Reference
In-Depth Information
The Ideal Gas Law can be used when any one of the four variables is
missing, provided the other information is known. R, which is a constant, is
the same for every calculation. The units that come with the constant, R,
dictate the units that we must have for the other quantities for the calcula-
tion. For example, we must work in Kelvin for temperature and kilopascals
for pressure. If we were asked to do a problem with atmospheres of pres-
sure or Celsius degrees for temperature, we would need to make a conver-
sion before we performed our Ideal Gas Law calculation.
For our first example using the Ideal Gas Law, let's calculate the molar
volume of a gas at STP, which we assumed to be true in previous chapters.
Example 1
What volume in dm
3
would 1.00 mole of hydrogen gas occupy at
standard temperature and pressure (STP)?
Given: P = 101.3 kPa; n = 1.00 mole;
R = 8.31 dm
3
× kPa/mol × K; T = 273 K
Find:
V
V
=
nRT
(1.00 mol)(8.31 dm
3
× kPa/mol × K)(273 K)
(101.3 kPa)
Formula:
=
P
= 22.4 dm
3
So, the Ideal Gas Law can be used to verify our value for the volume
occupied by one mole of any gas (molar volume) at STP. Remember that
one dm
3
is equivalent to one liter, so these units are interchangeable.
For our next example, let's pretend that the value of the constant was
unknown. How could we use the known and accepted value for the molar
volume of a gas at STP to calculate the value of the constant, R?
Example 2
Assuming that the molar volume of a gas (22.4 dm
3
/mole) at STP
has been experimentally verified, use this information and the Ideal
Gas equation to mathematically determine the value of R.
Given: P = 101.3 kPa; V = 22.4 dm
3
; n = 1.00 mole; T = 273 K
Find: R
Formula:
PV
nT
(101.3 kPa)(22.4 dm
3
)
(1.00 mol)(273 K)
R
=
=
= 8.31 kPa × dm
3
/mol × K
