Density of Gas and STP
Name: Anna C.
Date: Sunday, February 23, 2003
How are the density of gases at STP determined? It seems
that the density of a gas would depend on the size of the container that
the gas is placed in. The smaller the container the greater the density
of the gas. I am interested in this because I know the molar volume
(22.4 L) is calculated from the densities of gases at STP. But if a gas
takes the volume of whatever container the gas is placed in how can we
explain to students that 1 mole of a gas occupies 22.4 L? I would
appreciate any info.
Molar volume is not calculated from gas density.
Using the ideal gas equation ==> PV = nRT and standard (STP) conditions
P is the gas pressure in atmospheres (1 atm)
V is the (molar) volume in litres
n represents one mole of the gas
R is the gas constant (0.082 L.atm/K.mol)
T is the temperature in degrees Kelvin (273 K)
Solve for V to get: V = nRT/P
V = (1)(.082 L.atm/K.mol)(273 K) / (1 atm)
V = 22.4 L
Once we agree on standard conditions -- the conditions under which all ideal
gases can be compared to each other -- using the above relationship, we are
led to the conclusion that all such gases have a volume of 22.4 L.
Your question: "How are the density of gases at STP determined?"
Gas density is the mass of one mole of the gas divided by its volume (22.4
L) at STP
Put another way, density of gases is simply a measure of their molar mass
per (standard conditions) volume.
Indeed, if you compress the gas into a smaller volume, its density will
rise. However, in so doing, you would deviate from standard conditions.
Mass depends upon the quantity of matter present. Density (which is mass /
volume) is the same regardless of how large the volume is. You can think of
an analogy of identical coins, or marbles. How much a collection of coins or
marbles weighs depends upon how many coins or marbles there are, but the
weight per coin or per marble does not. That stays the same.
The ideal gas law states that P x V = n x R x T = (m/M) x R x T where P is
pressure in atm. V is volume in liters, n is number of moles, m is mass in
gm, M is molecular weight, R is the gas constant (= 0.08205) and T is
temperature in kelvins. The density is mass per volume, or m/V, so density =
P x M / R x T. None of the quantities on the left side of the equal sign
depends upon how much gas is present. It is better to think of a mole as
being 6.023x10^23 THINGS -- molecules, marbles, coins, whatever. It is a
number of objects. That number of gas molecules occupies 22.4 L. at P = 1
atm and T = 273.15 kelvins regardless of how heavy or light that each of the
molecules happens to be.
STP stands for "standard temperature and pressure", which means that the
temperature and pressure are defined at zero degrees Celsius and one
atmosphere pressure, respectively. If the temperature and number of moles
of a sample of a gas are held constant, then changing the volume will change
the pressure. For a given sample size (number of moles), pressure,
temperature, and pressure are inter-related so that fixing any two fixes the
third as well.
When a gas assumes the volume of its container, it does this by either
increasing or decreasing the average distance between molecules. This will
change the density, as you recognize, and it will also change the pressure.
So it works out that at STP, only a certain number of molecules of a gas
will fit into a container of a given volume.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Do not forget what STP means -- Standard Temperature & Pressure.
If you put the same quantity of gas into different size containers
its density will certainly change but so will the pressure it exerts on
its surroundings (the container). There will be only one volume
container that will hold it at STP.
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Update: June 2012