Chemists live in a fantasy world.
Okay, maybe that’s not fair.
But I can’t help but point out that this gas law is called the IDEAL GAS LAW.
Not the REAL GAS LAW.
The Ideal Gas Law is for an IDEALIZED, theoretical conception of gases that doesn’t match reality
except under certain conditions.
It’s a MODEL of gas behavior that helps make the math simpler.
Real quick here - let me tell you the differences between ideal gases and real gases.
An ideal gas is composed of particles that are like the tiniest perfect spheres,
vanishingly small,
like when you talk about points in math.
So the individual particles aren’t taking up any space.
That’s weird, and not based in reality, but again,
it makes the math much simpler.
And most of the time it’s basically true -
the particles of gas take up a NEGLIGIBLE amount of space
compared to the entire volume a gas is occupying.
Picture a helium balloon - It’s mostly empty space,
not solid helium.
So we can get away with this assumption,
except at very high pressure when you squeeze particles of gas
close to each other and all of a sudden whoops!
the volume of gas particles matters very much,
thank you,
excuse me,
stop pushing me!
When IDEAL gas particles run into each other,
they bounce off each other without losing any energy.
Hmm, must be nice, never needing any energy,
just bouncing around forever.
Again, that’s not reality,
but we can get away with this assumption much of the time, because the amount of energy
lost when
real gas particles collide is so small it’s a rounding error.
We also say that Ideal gases aren’t attracted to each other.
This is another unreal assumption -
remember intermolecular forces are a thing -
there are gases that ARE attracted to each other.
This is especially significant at low temperatures,
when gas particles slow down -
now the intermolecular forces become more comparable to
the kinetic energy of the particles.
What’s more, if you cool a real gas down far enough,
eventually there will be a phase change into liquid -
and that’s DEFINITELY no longer an ideal “gas.”
We never consider phase changes when we talk about ideal gases.
So by now you should have the idea that
the ideal gas model breaks down when you look at
very low temperatures and very high pressure.
But lucky for us, most of the time those aren’t the conditions we live in.
Most of the time in the real world, or in the lab,
when we’re studying gases, these conditions work just fine
for the mathematical predictions of the ideal gas law to come out right.
Now let’s talk about this ideal gas law,
just keeping this idea in the back of our mind that it especially works well at
higher temperature and lower pressure.
The Ideal Gas Law equation is PV = nRT.
P stands for Pressure.
V stands for Volume
n is the number of moles of the gas.
T is the temperature.
And R is the Ideal Gas Constant, which makes the math work.
Pressure is directly proportional to the number of molecules and temperature.
In other words, if you add more molecules of a gas,
they will bang around more on the container and exert more pressure.
Similarly, if you increase the temperature of a gas,
that increases its kinetic energy.
It will have more collisions per second against the container,
which means the gas is exerting more pressure.
So pressure and temperature are also directly proportional to each other.
Pressure is inversely proportional to volume.
If you increase the size of the container,
now there will be fewer collisions per second.
But if you compress the container and make the volume smaller,
now the particles will hit the sides more often per second. Lower Volume, Higher pressure.
Higher volume, lower pressure.
If you find the directly proportional or inversely proportional concepts confusing,
I recommend you spend some time thinking about the graphs of these variables,
graphing just two variables at a time.
The relationship between Pressure and Volume is Boyle’s Law.
PV= a constant.
So as pressure goes up, volume goes down.
As volume goes up, pressure goes down.
That’s an inverse relationship.
Now keep in mind this only holds if
Temperature and the number of particles of gas stays constant.
Here’s Charles’s Law, which is the relationship between volume and temperature.
V over T is a constant.
These two variables are Directly proportional.
The volume of a gas decreases when the temperature falls.
If you raise the temperature, the gas expands -
the volume increases.
These two variables move in the same direction,
so it’s a direct relationship.
Notice that Pressure and the number of gas particles aren’t part of this equation.
You can also say that Pressure and number of gas particles are constant.
Avogadro’s Law relates the Volume with the Quantity of gas.
V over n is a constant.
These are also directly related.
The more gas particles you have, the more room they will take up.
Again, notice that Pressure and Temperature are not part of Avogadro’s law.
Avogadro’s Law works if Pressure and Temperature are held constant.
If you put Boyle’s Law, Charles’s Law, and Avogadro’s Law together,
you get the Ideal Gas Law equation.
PV=nRT.
Here we have one constant, R, the Ideal Gas Constant,
which is a combination of the constants from the other gas laws.
Keep in mind, the same relationships exist between the variables
as in the simpler laws.
Pressure and Volume are still inversely related.
Volume and Temperature are still directly related.
In the meantime, until it clicks,
remember that values on the SAME side of the Ideal Gas Law equation are
INVERSELY proportional to each other (holding the other variables constant).
By the same token, values on OPPOSITE sides of the equation
are DIRECTLY proportional to each other when the other variables are held constant.
Now let’s work some example problems
to see the Ideal Gas Law in action.
We’re going to do 5 complete example problems.
If you need more help, especially if you’re studying for a test,
we have a Gas Laws practice test with a complete answer key.
This is available for purchase on our website - socratica.com.
We’ll add a link in the description.
Before we get started,
I want to remind you to keep your eye on units.
Pay close attention to the units of things like pressure and temperature,
and make sure they match the units you use for R,
the ideal gas constant.
You might have to stop and do a conversion before you plug things in.
Here’s what we’re using for R,
and so in our practice problems, we’ll convert units as needed
so everything matches.
My other piece of advice is to always work the problem as far as you can
using the general equation with variables before you plug in values for P,V, n, and
T.
This lets your instructor know that YOU know which is the right equation to use
and how it works.
Don’t just write down the numbers from the problem -
because if you’re wrong, you won’t get any partial credit.
Example 1: You feed your dog a new kind of kibble that
doesn’t agree with him.
You think fast and save your family by capturing the 10 moles of smelly gas he produces in
a tank.
The tank is 3m by 3m by 4.5m.
What is the pressure produced by the gas if you keep the temperature at 15 degrees Celsius?
The Ideal Gas Law is PV=nRT.
Write that down first, and solve for the variable you need.
So we solve for P, pressure, by dividing both sides by V, volume.
P=nRT/V R = 8.31 L kPa/K mol
Now substitute in the values from the problem.
We’ll have to do a little converting to make sure the units match the units we have
in the gas constant.
We need the volume to be in Liters, and we need temperature to be in Kelvin.
Volume of the tank is 3m times 3m times 4.5m, which is 40.5 cubic meters.
1 Liter = 0.001 cubic meters.
V = (40.5 m^3)(1L/0.001 m^3)
= 40,500 L.
That’s a lot of gas.
The other conversion we need to do is the temperature -
It's in Celsius, and we need it in Kelvin.
Temp in Kelvin = temp in C + 273.15
This equals 15 + 273.15 = 288.15 K
Now let’s substitute everything in .
P= nRT/V
= (10)(8.31 L kPa/K mol) (288.15 K) / 40,500 L
= 0.59 kPa
So you just need to make sure your tank can withstand
0.59 kPa of pressure so it doesn’t escape and poison your family.
Speaking of poisoning your family, let’s see example 2.
Your grandmother insists on using an antique coal stove.
It produces toxic carbon monoxide at a rate of 5 moles per hour.
How long will it take to generate 10L of gas
if the temperature is 20 degrees celsius and the pressure is .8 atm?
PV=nRT
R= 8.31 L kPa/ K mol so we’ll have to convert
atm to kPa and temp from C to K.
1 atm = 101.3 kPa
0.8 atm ( 101.3 kPa/1 atm) = 81.04 kPa
20C + 273.15 = 293.15 K
The problem asks How long will it take?
we have a conversion factor here, 5 moles are produced per hour.
So we’ll use the Ideal Gas law and solve for n, number of moles,
and then use that conversion factor to get the number of hours.
n = PV/RT
=(81.04 kPa) (10L)/(8.31 L kPa/ K mol) (293.15)
= 8104/2436.08 = 3.33 mol
We’re not finished, hang on.
That’s the number of moles, and the question, remember, is
how long does it take to generate that much gas.
Let’s use the conversion factor from the problem - 5 moles per hour.
3.33 moles (1 hour/5 moles) = 0.67 hours,
or ⅔ of an hour, about 40 minutes.
Let’s look at a happier example. It’s your birthday!
Your family takes you to the beach and you get a new bicycle.
It’s perfect, except it has two flat tires.
If the volume of each tire needs to be 0.45 L, how many moles of gas will you need
to pump on a hot 28 degree celsius day?
Here’s a little trick - the pressure at sea level is 1 atm.
I doubt your instructor would make you know that by heart, but it doesn’t hurt.
We’ll use the Ideal Gas Law, PV = nRT,
and solve for n, number of moles.
n= PV/RT.
R= 8.31 L kPa/ K mol
so we’ll have to convert atm to kPa
and temp from C to K.
1 atm = 101.3 kPa
28C + 273.15 = 301.15K
n= (101.3 kPa) (2x.45L remember there are two tires)/(8.31 L kPa/ K mol)(301.15K)
= 0.04 moles of gas.
You really want to take a hot air balloon ride,
but you can’t afford a ticket.
Instead, you tie 100 big helium balloons to your lawn chair and hope for the best.
Each balloon has 40 moles of helium.
You take off from a hill next to your house where the air pressure is 50 kPa.
Your departure time is 6AM, when the temperature is 12 degrees Celsius.
At noon, the temperature has risen to 18 degrees Celsius.
You look up and you see the balloons have gotten much bigger.
What is the difference in volume?
First, what’s the volume at 6 AM?
PV=nRT solve for V
V1=nRT1/P
= (40)(8.31)(285.15)/(50 kPa)
= 1895.68L about 19 L per balloon.
What’s the new volume at noon?
V2 = nRT2/P
= (40)(8.31)(291.15)/(50kPa)
= 1935.57L.
Difference = V2-V1 = 1935.57 - 1895.68 = 39.89 L
Challenge for you - think about if you HAD to use the Ideal Gas
Law here.
Could this problem have been simplified,
given that the number of moles and pressure were unchanged.
Elon Musk heard about your sad balloon trip,
and he felt sorry for you, so he offers to send you to space for a week.
The catch is, you’re going to be all on your own in the capsule.
A solo astronaut produces about 1 kilogram of CO2 every day.
What volume of CO2 will you produce during your 7 day trip?
You’ll be at 2.7 Kelvin and 101.3 kPa.
Now in this problem, we have a mass of CO2,
not the number of moles.
To use the Ideal Gas Law, PV = nRT,
we’re going to have to convert from mass to number of moles.
We can do that using the molar mass of CO2,
that is the mass of one mole of that compound.
This is also sometimes called the Gram molecular mass.
If you need some review, we have a video on how to do this!
We’ll share a link to that video.
Find the molar masses for each element from the Periodic Table:
The mass of one mole of Carbon atoms is = 12.01 g
The mass of one mole of Oxygen atoms = 16.00 g
1 mole of CO2 = 12.01 + 2(16.00) = 44.01 g/mol
n= 1000g CO2 (1 mol/44.01 g) = 22.72 moles.
PV =nRT solve for V
V=nRT/P
= (22.72 moles)(8.31 L kPa/ K mol)(2.7K)/101.3 kPa
= 5.03 L CO2 gas PER DAY x 7 days = 35.2 L
One of my big secrets for successful studying is
to only study what you DON’T know.
This only works if you have a good practice test.
Your instructor may have a practice test for you, or there might be one at the end of the
chapter of your textbook.
If you want to get your hands on a good-quality practice test with the answers worked out
in full,
we have one for sale on our website, socratica.com.
Your purchase means we’ll be able to make more videos like this one,
completely free for you.
Thanks for watching!