
I'm trying to understand how I could determine
the molecular weight of a liquid from its vapor
density? I missed this lecture in class and the
book doesn't seem to be helping much, can you
please help?

Question Date: 20041103   Answer 1:
The molecular weight of an unknown material can be
determined when this material is in a dilute
"ideal gas" state. An ideal gas is defined as one
in which there are no intermolecular forces
between the atoms or molecules. In such a gas, all
the internal energy is in the form of kinetic
energy and any change in internal energy is
accompanied by a change in temperature. An
ideal gas (like any other thermodynamic system)
can be characterized by three state variables:
pressure (P), volume (V), and absolute temperature
(T). For ideal gas the relation between them is
expressed by the formula: P V = N k T, where
N is the number of molecules in the gas, and k is
a physical constant, known as Boltzmann constant.
From this formula it follows that equal volumes of
gases at the same temperature and pressure contain
the same number of molecules regardless of their
chemical nature and physical properties  a
principle first stated in 1811 by the Italian
chemist Amedeo Avogadro. The ideal gas law
works extremely well at high temperature and low
pressure. It offers a way to extract the number of
gas molecules N confined inside a given volume V.
If we now measure the total mass of the sample M
(by, for instance, condensing it from gas to
liquid), we can extract the molecular mass
M/N. The vapor will be at equilibrium with the
liquid state (what physicists call "coexistence")
only at low temperature and/or high pressure which
are outside the ideal gas regime. In other words,
gasliquid coexistence can be understood only if
the molecular interactions are taken into account.
Therefore, the attempt to use the ideal gas law
to the vapor above a liquid would yield a somewhat
inaccurate estimate for the molecular weight.
  Answer 2:
If you know the vapor density, then you know the
mass per volume of the vapor.Now, this isn't quite
enough to determine the molecular weight yet. (I
am assuming that the overall exercise you are
being asked to do is to determine the molecular
weight of a liquid by using data from its gas
phase  a "classic" chemistry lab experiment.)
The vapor density can change depending on the
pressure and temperature of the gas. If we assume
that the gas can be treated as an ideal gas, then
we can use the ideal gas law of: PV = nRT, where
P is the pressure, V is the volume of gas, n is
the number of moles of gas, R is a constant, and T
is the temperature. If we rearrange that
equation, we get: n / V = RT / P. Once you know
the temperature and pressure, then everything on
the right side of the equation is known. Now,
since the number of moles can be determined by: n
= mass / molecular weight,and we know that mass
over volume is the density, then we can substitute
all that back into the rearranged ideal gas
equation to give:(Vapor density) / M.W. = RT / P
,or, rearranging again:MW = (Vapor density * P) /
(RT)Now, if the gas can not be considered ideal,
then the problem gets considerably more difficult
as the nonidealities of the gas would need to be
considered.
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