Re: nitrous in your car?

[Robert Myers <rmyers@inetone.net>]

Caution y'all - pedant alert!  Delete now unless you want to become
terminally bored.  :-)

At 04:44 AM 09/30/1999 -0500, you wrote:
>>Once all the liquid has been evaporated then the PV=nRT equation applies.
>
>
>I agree with everything you wrote except the above statement.  How can the
>Ideal gas law NOT apply?  Regardless of the state or amount of nitrous in
>the tank, if you increase the temperature of the tank (without releasing
>gas) the pressure is going to increase.  

True - the pressure will increase.  This pressure increase is due, however,
primarily to the increasing equilibrium vapor pressure of the liquid N2O
rather than some application of the ideal gas law (which is only a first
approximation at best).  Remember, we are dealing with a change of state
not just a gas in a close system.  This makes the system far more complex
than just a single phase gaseous system and the ideal gas law as typically
encountered in a freshman chemistry class is not capable of handling the
situation.  What happens when a sample of gas/liquid at equilibrium is
compressed (i.e, the volume available is reduced) at constant temperature?
Some more gas liquifies.  The pressure stays essentially constant and does
not increase as the ideal gas law would predict.  Similarly, what happens
when the volume of the container is increased?  More liquid vaporizes and
the pressure remains essentially constant.

One could argue that the "n" of the equation (PV = nRT) is changing since
the number of moles of gas is changing as liquid is either condensed or
evaporated but this is not the way the ideal gas law is commonly used.  In
this case then N(total) = n(liquid) + n(gas).  The n(gas) is the "n" you
would need to use in the ideal gas equation if you were trying to use it in
this situation.  It is usually regarded as a constant depending upon which
particular sample of a gas you were describing.  It will not be constant in
this case.

Remember the definition of an ideal gas?  Among other small details, the
individual molecules possess zero volume and they do not interact with each
other except by colliding with each other in perfectly elastic collisions.
There are no intermolecular attractive forces (because of this the
nonexistent "ideal gas" cannot be liquefied).  This situation is only a
decent approximation at very low pressures (where the molecules are very
far apart and their individual volumes are insignificant in comparison to
the total volume of the system and interactive forces, which decrease
markedly with distance, are insignificant) and/or very high temperatures
(where attractive forces are very small in comparison to the average
kinetic energies of the molecules).  We are dealing with neither of these
conditions inside this tank of N2O.  Here the temperature is well below the
critical temperature and the pressure is well above the critical pressure.

(Definition {just in case you might need it}: critical temperature - the
temperature above which a gas cannot be liquefied by pressure alone.
Critical pressure - the minimum pressure required to liquify a gas which is
at its critical temperature.)

>Remember, the tank exploded while
>the car was sitting in the garage...the nitrous system was not actively
>being used (other than the bottle heater, apparently).  Admittedly, there is
>only a small volume of gas in a full tank of nitrous oxide (mostly liquid),
>but even that small volume is subject to the Ideal gas law.

There must be some other explanation for the explosion.  A malfunctioning
heater which caused quite high temperature?  A defective or damaged tank?
Defective or damaged plumbing, etc?  A combination of more than one of
these things?  Something else?

>Bob W.
>
>
>
___
   Bob
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