Page 20 - Basic physical chemistry for the atmospheric sciences

6 Basic physical chemistry
where 1000 m is the number of grams of the gas and M the molecular
weight of the gas. Also,

R
R = (I.Se)
*
MlOOO

where R is divided by 1 0 00 to obtain the gas constant for l g of gas. It
can be seen from Eq. l . Sd) that at constant temperature and pressure
(
the volume occupied by any gas is proportional to the number of
moles (and therefore the number of molecules) in the gas. The gas
constant for l molecule of any gas is also a universal constant, called
the Boltzmann constant k. Since the gas constant for NA molecules
i s R *
R* S . 3 143 1 0 . 3 1 0 6
1
2
k = = l S 1 x - 3 J deg- 1 molecule - ( l. S f)
NA 6_ 022 x 2 3
For a gas containing n0 molecules per cubic meter, the gas equation
can be written

p = nokT ( l . 8 g)
In chemistry, it is common because it is convenient, to depart
from SI units in the gas equation and, instead, to express pressure in
atmospheres and volume in liters ( T is still in K). In this case, for nA
moles of gas A with pressure p A and volume VA we can write the ideal
gas equation as

.
(l 8 h)
where R� is the universal gas constant in "chemical units" (indicated
by the subscript c); the value of R� is 0.0821 L atm deg-1 mo1 - 1• Since
nA V A is the number of moles of the gas per liter, that s , the molarity
i
/
[A) of the gas
( 1 .Si)

Exercise 1.3. Carbon dioxide occupies about 354 parts per mil l ion
by volume (ppmv) of air. How many C02 molecules are there in I m 3
of air at 1 atm and 0°C?
Solution. Let us calculate first the number of molecules in I m3 of
any gas at 1 atm and 0°C (which is called the Loschmidt number). This