in this video I want to go over one of the gas laws called Boyle's law
Boyle's law states that the pressure of a gas
is inversely related to the volume
when temperature and the amount of gas
are held constant alright the important term here
is this inverse relationship between pressure and volume
what does it mean to have an inverse relationship what that means is that
when pressure of the gas is
increased volume will decrease
if we increase the volume of the gas on the other hand
then we would expect for pressure to decrease
graphically we can show this
relationship to look something like this:
as we increase the pressure
here along the x-axis the volume
decreases the formula
for Boyle's law is p1 times v1
is equal to p2 times v2 this is pressure
and volume at condition number one when they are multiplied
they're equal to the pressure and volume
of the gas under condition number two
so how can we use this formula
in a problem look right here at this problem we have a sample of nitrogen gas
this nitrogen gas has a volume of 4.2
liters and it's at a pressure of 1 atmosphere
if we decrease the pressure
to 0.75 atmospheres we have no change in temperature
and no change in the amount of gas what will be the new
volume before we solve it we can use Boyle's law
to predict what we expect to happen if we
decrease the pressure of the gas from one atmosphere to 0.75 atmospheres
then this inverse relationship indicates that the pressure the volume
of the gas should increase let's see if that holds true
so let's determine what variables the problem gives us
it tells us that this gas under condition one has a
volume of 4.2 liters it also tells us
that the pressure of this gas at condition one is 1 atmosphere
and it tells us that we're going to decrease the pressure
to 0.75 atmospheres so that's going be our p2
and it is asking us
to solve for the volume when we decrease the pressure
so we are going to solve for
v2, in order to solve for v2 we just input
the values given to us in the problem into our formula
we've got p1 and we're going to multiply that by v1which is 4.2
liters and that's going to be equal to
0.75 atmospheres
multiplied by
v2 in order to solve for v2
we need to get this pressure value
on the left side of the equal sign in order to do that we use
algebra and we just multiply by the inverse
the inverse of 0.75 atmospheres in the numerator
is going to be 1 over 0.75 atmospheres
what that allows us to do is to cancel those values out
what we do to one side of the equal sign we always have to do to the other side
so we're going to multiply this side by
one over 0.75 atmospheres
so when we clean this equation up
we find that v2 is equal to
one multiplied by one multiplied by 4.2
liters and all that is going to be divided by 0.75 atmospheres
make sure units cancel out correctly
to ensure that we set up the problem correctly here we have atmospheres in
the numerator
atmospheres in the denominator those will cancel out
the only value or the only unit that we're left with is liters
we're solving for volume which is measured in liters when
this is solved we find that v2 is equal to 5.6 liters
so in fact what we see happening
is when we decrease the pressure of our gas we see that
inverse relationship of our volume
increasing when pressure decreases