Ideal Gas Laws - Gaseous Video Lecture | Chemistry for GRE Paper II

hey it's professor Dave let's talk about
ideal gases
let's recall our
definition of a gas as the phase of
matter where atoms of a substance are in
motion and fill their container
if we make a couple simplifying
assumptions about gases
we can make some easy predictions those are that one
particles in the gas are dimensionless
points in random motion
and the identity of the gas is irrelevant, could be anything, and two
that the particles don't interact apart
from elastic collisions
bouncing off one another like balls on a
pool table. these things aren't
completely true
but they make the math easy and
surprisingly accurate
so these kinds of samples are called
ideal gases
when examining an ideal gas we want to
be able to discuss four variables
one: pressure, this is the force the gas
is exerting on its container
or rather how much the particles are
hitting the sites. two:
temperature, this is the amount of heat
energy available to be transferred into
kinetic energy of motion
the higher the temperature the faster
the particles move
3: volume, how big is the container
and four: moles, how many particles are
there
in the container. so how many particles
how big is the container, how fast are the
particles moving
and how often do they hit the sides. as
it turns out these variables depend on
one another in interesting ways
that have been formulated into laws. let's
look at a piston
while keeping the moles and temperature
the same, in other words the same number
of particles moving at the same speed
if we compress the volume the pressure
must go up
the particles will be hitting the sides
more often because there is less
distance to travel to hit a side
that means that pressure and volume are
inversely proportional
if one goes down the other goes up. this
is expressed
in Boyle's law. P1V1 equals P2V2
if we double one variable we have to cut
the other one in half
in order to keep this equation valid.
volume and temperature are also related
if we have gas in a balloon and we
heat it up, the particles will move more
quickly
in order to keep pressure constant
or hit the sides with the same frequency,
the volume will have to expand
this means that volume and temperature
are directly proportional
if one doubles the other must double.
this is expressed
in Charles's law. when we do calculations
with temperature
we must always use an absolute
temperature scale called the Kelvin
scale
one degree kelvin is the same magnitude
as one degree Celsius
but zero kelvin is absolute zero
the lowest temperature possible, a
complete absence of heat energy
this helps us avoid weird mathematical
issues that would arise
if we were doing a calculation involving
a negative or zero temperature
to get Kelvin from celsius just add 273
to go the other way, subtract. the
combined gas law
is like a combination of Boyle's and Charles's,
avogadro's law says that equal volumes of
gas at the same temperature and
pressure
contain the same number of molecules,
specifically
that one mole of ideal gas occupies 22.4 liters
at standard temperature and pressure,
regardless of the identity of the gas
lastly all the variables correlate in one
equation
called the ideal gas law. this also
contains the gas constant
R, which makes these calculations
intelligible in our manmade units
there are a number of values for R
depending on the units
we will predominately use this one. this
equation is useful when we aren't
looking at a change
but just to know the value of all four
variables at once
like in this case we could know the
pressure
temperature and volume for a gas and
quickly calculate how many moles of
particles
must be in the sample. so if you're
looking at a sample of gas
and you have three of the four variables
you can solve for the fourth
using the ideal gas law. if you are given
some initial conditions as well as some
final conditions
you can use one of the other laws to
find the other information
just plug in what you know and solve for
what you don't. let's check comprehension
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and as always feel free to email me