vodcast 9 2 gas laws pt1 rough ios
Summary
TLDRThis educational video script covers gas laws, focusing on Boyle's, Charles', and Gay-Lussac's laws. It explains how pressure, volume, and temperature relate in gas behavior, emphasizing the importance of using Kelvin for temperature. The script guides viewers through algebraic problem-solving, illustrating each law with examples. It concludes with the combined gas law, a comprehensive formula for scenarios where multiple variables change.
Takeaways
- đ Boyle's Law explains the inverse relationship between pressure and volume at constant temperature.
- đ Algebra is crucial when solving gas law problems, and all temperatures must be in Kelvin.
- đĄ Temperature always needs to be converted to Kelvin by adding 273 to the Celsius value.
- đ Boyle's Law formula: P1 * V1 = P2 * V2, showing how pressure and volume change inversely.
- đ Charles's Law demonstrates the direct relationship between volume and temperature at constant pressure.
- đ Charles's Law formula: V1 / T1 = V2 / T2, where temperature and volume rise and fall together.
- đ Gay-Lussac's Law illustrates the direct relationship between pressure and temperature at constant volume.
- 𧟠The Combined Gas Law merges Boyle's, Charles's, and Gay-Lussac's laws into one formula: P1 * V1 / T1 = P2 * V2 / T2.
- đ When using the Combined Gas Law, if a variable is constant, it can be canceled out to simplify the equation.
- đ§ Solving gas law problems requires methodically plugging values into the appropriate formula and applying algebra to isolate the unknown variable.
Q & A
What are the three key variables in gas laws?
-The three key variables in gas laws are pressure (P), temperature (T), and volume (V).
What does Boyle's Law state?
-Boyle's Law states that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature.
How do you convert Celsius to Kelvin?
-To convert Celsius to Kelvin, you add 273 to the temperature in degrees Celsius.
What is the mathematical formula for Boyle's Law?
-The mathematical formula for Boyle's Law is P1V1 = P2V2.
What does Charles's Law state?
-Charles's Law states that the volume of a fixed mass of gas varies directly with the Kelvin temperature at constant pressure.
What is the mathematical formula for Charles's Law?
-The mathematical formula for Charles's Law is V1/T1 = V2/T2.
What is the combined gas law and when is it used?
-The combined gas law is an equation that combines Boyle's, Charles's, and Gay-Lussac's laws into one formula. It is used when none of the variables (pressure, volume, or temperature) are held constant.
What is the combined gas law formula?
-The combined gas law formula is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
Why is it important to keep track of the units when solving gas law problems?
-It is important to keep track of the units when solving gas law problems because they must be consistent throughout the calculations, and the final answer should reflect the correct unit for the variable being solved for.
What is the significance of the 'PTV' model mentioned in the script?
-The 'PTV' model is a physical representation that helps visualize the relationships between pressure, temperature, and volume as described by the gas laws. It is a tool for understanding how changes in one variable affect the others.
Why is it crucial to perform algebraic manipulations step by step when solving gas law problems?
-Performing algebraic manipulations step by step ensures that each calculation is clear and accurate, reducing the chance of errors. It also helps in understanding the relationship between the variables in the gas laws.
Outlines
đ Introduction to Gas Laws
The script begins with an introduction to vodcast 9.1, focusing on the first section of gas laws. It emphasizes the algebraic nature of the topic and encourages the audience to refresh their algebra skills. The presenter instructs the audience to physically engage by folding a piece of paper 'hot dog style' and labeling it with P, T, and V, representing pressure, temperature, and volume. The importance of using Kelvin for temperature is stressed, with a reminder of the conversion from Celsius to Kelvin. The segment introduces Boyle's Law, which states that the volume of a fixed mass of gas is inversely proportional to its pressure at constant temperature. The presenter uses the folded paper to visually explain this concept and provides a mathematical formula for Boyle's Law, p1v1 = p2v2, and guides through a sample problem to demonstrate the concept.
đ Deep Dive into Boyle's Law
This paragraph continues the discussion on Boyle's Law with a detailed walkthrough of a problem. The problem involves calculating the new volume of a gas sample when the pressure increases from 2.5 to 5.0 atmospheres at a constant temperature. The presenter explains the algebraic manipulation required to solve for the new volume, emphasizing the inverse relationship between pressure and volume. The solution process involves dividing the initial volume by the pressure ratio to find the new volume, which is calculated to be 7.5 liters. The explanation reinforces the concept that if pressure doubles, the volume should theoretically be halved, aligning with Boyle's Law.
đĄïž Charles Law: Temperature and Volume Relationship
The script transitions to Charles Law, which describes the direct relationship between the volume of a fixed mass of gas and its temperature at constant pressure. The presenter uses the folded paper model to illustrate how increasing the temperature (in Kelvin) results in an increase in volume, and vice versa. The formula for Charles Law, v1/t1 = v2/t2, is introduced, and a problem is solved to demonstrate the application of this law. The problem involves calculating the final volume of a gas when its temperature is raised from 30°C to 90°C, starting from an initial volume of 5.5 liters. The solution involves converting the Celsius temperatures to Kelvin, applying the formula, and calculating the new volume to be 6.6 liters, reflecting a 20% increase in volume due to the temperature rise.
đ Gay-Lussac's Law: Constant Volume Analysis
The discussion moves to Gay-Lussac's Law, which focuses on the relationship between pressure and temperature when the volume is held constant. The law states that pressure and temperature are directly proportional under these conditions. A problem is presented where the initial pressure and temperature are given, and the task is to find the final temperature when the pressure changes. The formula P1/T1 = P2/T2 is used, and the presenter demonstrates how to cross-multiply and solve for the final temperature, which is found to be 894 Kelvin. The importance of correctly identifying initial and final conditions (1 and 2) is highlighted to avoid common mistakes in solving gas law problems.
đ Combined Gas Law: Unifying the Concepts
The script concludes with the combined gas law, which unifies Boyle's Law, Charles Law, and Gay-Lussac's Law into a single equation: PV/T = constant. This law is particularly useful when multiple variables are changing. The presenter explains how to simplify the combined gas law equation to match the specific conditions of a problem, effectively canceling out constants and applying the appropriate law. A comprehensive problem is solved involving a gas in a flexible container with changes in pressure, temperature, and volume. The presenter demonstrates the algebraic steps to isolate and solve for the final volume, emphasizing the need for careful algebraic manipulation and unit consistency. The solution process involves calculating the new volume to be 0.227 liters, considering the changes in pressure and temperature.
Mindmap
Keywords
đĄGas Laws
đĄBoyle's Law
đĄCharles's Law
đĄGay-Lussac's Law
đĄKelvin
đĄAlgebra
đĄCombined Gas Law
đĄVolume
đĄPressure
đĄTemperature
đĄAlgebraic Manipulation
Highlights
Introduction to vodcast 9.1 focusing on gas laws.
Emphasis on algebra skills for understanding gas laws.
Instruction to prepare a folded paper for visual aid.
Explanation of the importance of using Kelvin for temperature.
Boyle's Law introduced as the inverse relationship between pressure and volume at constant temperature.
Visual aid demonstration using the folded paper to explain Boyle's Law.
Mathematical formula for Boyle's Law presented.
Step-by-step problem-solving for Boyle's Law using the formula.
Charles Law introduced as the direct relationship between volume and temperature at constant pressure.
Visual aid demonstration for Charles Law using the folded paper.
Mathematical formula for Charles Law and its application.
Gay-Lussac's Law introduced as the direct relationship between pressure and temperature at constant volume.
Problem-solving for Gay-Lussac's Law using the formula.
Combined Gas Law formula that encompasses Boyle's, Charles, and Gay-Lussac's Laws.
Explanation of how to simplify the Combined Gas Law for specific scenarios.
Detailed problem-solving using the Combined Gas Law formula.
Emphasis on the importance of algebra in solving gas law problems.
Advice for students to practice algebraic manipulation when solving gas laws.
Transcripts
all right kiddos we're gonna jump into
vodcast 9.1 we're gonna talk about the
first section of gas laws today gonna be
very algebra intensive so if your
algebra skills are a little rusty
hopefully this will catch you back up
and you'll be okay with some mantra
after this so the first thing I want you
to do is grab a piece of paper okay into
four at once as I would say lengthwise
but as I've learned it's the right way
to say hot dog style and I want you to
fold it again hot dog style okay so you
should have sort of a kind of a fat rule
or looking thing here and then on that
what I want you to do is I want you to
write these letters I want you to write
P T V okay P on the side of V right in
the middle and then a T on the far other
side now there's stands for our three
times that we're going to be worried
about today for all of our gas laws and
those are pressure temperature and
volume and one thing I want to make real
sure that you keep track of while we're
doing this is that all of your
temperatures have to be in Kelvin now
yesterday we learned how to turn Celsius
into Kelvin so remember that Kelvin is
equal to degrees Celsius plus 273 okay
so hopefully that sort of rings a bell
for you the volume and the pressure they
can vary a little bit in this stuff
today although it wouldn't hurt to sort
of keep any in the back of your mind
that you want to get try to get pressure
in atmospheres most of the time and
volume in liters but it doesn't have to
be today but temperature always has to
be in Kelvin okay so let's dive in
because there's a lot of math and what
we're doing today I want to have time to
walk you through each of the steps of
the algebra so first look first of all
it's something called Boyle's law okay
and what Boyle's law says is that the
volume of a fixed mass of gas varies
inversely with the pressure at constant
temperature and you're like holy crap
that's a lot of crazy scientific jargon
you know what does that mean okay so
here's what that means if you take your
little friends here that you've
constructed okay your PTV alright if you
take that and then you
hold the temperature constant okay so
take your little friend there and put
your fingers over the T right there in
the middle and then you make the
pressure go up what happens to the
volume well if pressure goes up volume
goes down pressure goes down okay
volume goes up and the other way around
too so if volume goes up pressure has to
go down if volume goes down then
pressure has to go up okay we're going
to see that for each of the three major
ones we have today and that's why you've
made that's what you've made your little
friend here your little PTV
okay now mathematically this is what the
formula for Boyle's law looks like so
real quick let's just sort of add to our
scientific definition there just to you
know clear it up a little bit for you
that as pressure increases okay volume
decreases volume decreases okay
and vice versa okay
a simple way to say it is that as one
goes up the other one goes down okay so
one goes up the other one goes down
that's what your little PTV thing
there's going to show you so
mathematically or formula wise what that
means for us is this that we have p1 v1
p1 times v1 equals p2 times b3 now what
does that mean that means that I've got
an initial pressure initial volume that
that's going to be equal to a second
volume or a second pressure and a second
volume okay so they're the best way to
sort of understand this is to work a
problem so if you don't have this on a
sheet in front of you then copy this
problem down we're going to walk through
this okay a 15-point only der sample of
gas at a constant temperature in 2.5
atmospheres has its pressure increase
the 5.0 atmospheres what is the new
volume that you can make a pretty good
estimate anyway what you can sort of
know already is that pressure went from
2.5 to 5 points of pressure
way up okay so if pressure goes up then
that means the volume goes down okay so
I know that my final answer has to be
less than fifteen but let's actually
work the math for that now there are a
couple of ways to approach this I think
that one of the easiest ways is that
there's there's a couple of ways you can
write everything out which is what I
tend to do so my v1 is 15 point Oh
liters okay and so I write everything
out separately my p1 is 2.5 this is kind
of like regular given and your unknown
ain't so geometry problems except that
we're not gonna have any railroad tracks
in this particular problem and my p2 is
5.0 atmospheres now you don't
necessarily have to write it all out
like that you could just go in the
problem and write next to each one what
it is as long as it's clear to you and
you can tell what each thing is okay and
then what I'm looking for is it says
what is the new volume or in other words
what is v2 so in this case I'm looking
for v2 now there's no railroad tracks
here because I have a formula in
stoichiometry and in mole conversions
and all that stuff we don't have a
formula to plug stuff into it so that's
why we use the railroad tracks but in
gas laws we pretty much always have a
formula so we're gonna plug this stuff
in here okay so I'm gonna take each of
my values here from my problem and just
plug them into the equation so I've got
two point five atmospheres
let's start this business tonight okay
so we've got two point five atmospheres
okay what is that that's p1 right okay
times my v1 which is 15 point O liters
and that's me one that's equal to five
atmospheres
okay that's p2
and then that is multiplied by v2 okay
v2 of course is what I'm looking for
that's what I'm trying to solve for okay
so we got to do some algebra and I mean
simply statement algebra says that if I
want to get one thing by itself which I
want to get v2 by itself then I just
apply my rules of algebra and remember
that your general rule in algebra is
that you can do whatever you want to the
equation as long as you do it to both
sides so to get v2 by itself I'm gonna
divide both sides by 5 atmospheres okay
now what does that do for me
algebraically okay makes that cancel out
right and so then I'm gonna plug all
this stuff into the calculator now
there's a couple of ways you can do this
you could have done this math first this
red math right here first and then
divided by 5 it really doesn't make any
difference however you're most
comfortable plugging in the calculator
and when we plug this in what we're
gonna get out in this case is we're
going to get seven point five liters
equals v2 now again I sort of
intuitively knew that because my
pressure doubled and if we go back to
what Boyle's law says it says there they
vary inversely so if pressure doubles
that means volume should have okay
pressure went up by two volume should go
down by two a factor of two okay and so
therefore I cut the volume in half
basically and that's what the math is
going to show me there so that is my
correct answer okay so that's Boyle's
law um the next one we're gonna worry
about here is Charles law and Charles
law said states that in a volume of a
fixed mass of gas and constant pressure
R varies directly with the Kelvin
temperature okay now what does that mean
that means that volume and temperature
increase together okay and so again if
you take it if you grab your little
friend there okay where you've got your
P DV okay and this Rho should be a
little bit more spread out but you got
your little friend there if pressure is
constant then temperature and volume go
up together so T and V go together T and
V go down together
okay or we can look at that just as
easily or perhaps more easily on our
screen here well they would have made a
lot more sense
this little deal so if I keep my
pressure constant okay and then I do my
rotation temperature and volume both go
up together okay
temperature and volume go down together
in that case alright so how does that
work out to break low well here's the
formula v1 over t1 equals v2 over t2
okay and you're not gonna have to
memorize these formulas you're gonna
first stuff you have a formula sheet I'm
gonna show you away here at the end to
make it a little bit easier so let's
work problem and it cost the pressure
the temperature of a sample is raised
from 30 degrees to 90 degrees Celsius if
the initial volume is 5.5 liters what is
the final volume okay so I'm gonna write
now what everything is first I just like
to keep I think that these problems it
helps if you just keep everything as
neatly tied together as you can so I'm
looking for final volume right I have an
initial volume 5.5 liters okay and then
what else do I have
I have 81 and 82 given to me in the
problem t1 is 30 degrees t2 is 90
degrees but if you're crumbled back at
the beginning we said that we can't
leave everything in Celsius it has to be
in Kelvin so I have to add 273 to 273 to
each of these temperatures to get our
actual temperature that we want to plug
into from so in this case we're gonna
have 303 Kelvin then we're gonna get 363
kiln okay hopefully that that's a 6-3
you 63 okay
so plug that into our equation again
what's our equation in this case well
we've got v1 over t1 equals v2 over t2
okay and so we want to plug everything
in so my initial so 5.5 liters divided
by my initial temperature 303 Kelvin
that's equal to v2 over 363 Cal
now again a couple of ways out bravely
that you can solve this I could easily
get rid of so that stuff to make us some
room over here I could very easily
multiply both sides by this and then do
the math I could divide this out and
then multiply both sides by 363 really
again whatever algebra you're
comfortable with I'm will work I'm gonna
go ahead and get v2 by itself and to do
that I'm gonna multiply both sides by
363
okay so cancels and then that means over
here on the left hand side I've got 363
times 5.5 liters or that 5.5 does not
work for me tonight all over 303 Kelvin
and that is my v2 so now it's just a
matter of punching that into the
calculator we push that into the
calculator and we get six point six
liters okay
we actually get like 6.5 whatever but
sigfigs
now whenever I'm doing math here I
always want to go to my lowest number of
sig figs the temperature is usually sort
of worked out really wonky so I don't
worry about those most of time but the
volume here is what I'm going to stick
with sig figs and so since I am to here
I'm gonna keep two of my final answer
and once you get your answer you want to
take your little your little friend here
and you want to see if that answer makes
any sense well the temperature went up
so the volume should go up also and it
did it didn't go up by as much it seems
like because you're thinking with it in
the temperature triple not in the Kelvin
scale
okay moving from 303 to 363 so it's not
really a tripling it's more like a
percentage gain about 20% and that's
pretty much what we get here as well
okay so that's Charles long now just
real briefly they sort of go back just
just a tad to what we're talking about
before
I'm with each of the laws what's really
helpful is to go back and the way that I
like to memorize which laws which is to
memorize what's constant in each so
wools long has constant temperature
charles law has constant
pressure okay and then we've got our
third law which is gay lussac's law and
it has constant volume so something
different from in each of the three laws
that makes it different so what does
this one say well basically it says that
if we keep the volume constant okay then
pressure and temperature increase
together so volume stays the same
okay so if we brought volume in the same
place then temperature and pressure both
go up at the same rate together or they
both go down at the same rate together
okay so Boyle's law says the pressure
and volume are inversely related that
pressure goes up volume goes down the
other two laws Charles and vo sacks
basically say that two things go up
together it won't go down together
okay so let's work a problem real quick
just to make sure we know how this one
works same basic principles though I'm
gonna shorten things up here a little
bit um I'm gonna label in the problem
what each thing is so what do we have
here we're going to take we're gonna say
that my initial pressure is 75 kilo
Pascal's now I kind of prefer that
everything was in atmospheres but when
you're working a bunch of these problems
sometimes you just don't have time to do
all those conversions we're trying to
minimize that so just write down what
they are so P 1 P 2 my P 1 is 25 degrees
Celsius and again that's not gonna work
I need that in Kelvin so I add 273 that
gives me 298 Kelvin okay now our formula
again P 1 P over T 1 equals P 2 over T 2
now we plug this within the algebraic
it's a little Messier I mean not
terribly complicated but it's gonna look
a little weird so 75 okay kPa over my
initial temperature which is 298 Kelvin
and then 2 25 kilo Pascal's
/ what I'm looking for which is t2 final
temperatures what I'm looking for now
what do I do here easiest thing really
to do is to cross multiply so when I
multiply this times this and this times
this okay so what does that give me
that gives me 298 Kelvin times - 25 kilo
Pascal's equals 75 kilo Pascal's x times
t2 okay now why did I do that again
because what that is gonna allow me to
do is it makes it a little easier to get
t2 by itself it's real hard to get stuff
that's on the bottom by itself without
cross multiply possible but a little bit
easier this way now how do I am I
actually gonna get t2 by itself now that
I have on the multiplied by each other
I'm gonna divide both sides by 75
kiloPascals now like you guys this is
just all straight-up out over one stuff
a really pre out for stuff like solve
for X accept it instead of solve for X
and solve for t2 okay so I'm gonna plug
in these numbers into my calculator and
I'm gonna get out of this 894 Kelvin now
you should check this if you're not
getting those numbers then make sure
that you're doing your how to write and
then make sure that you're plugging
those things in right now will tell you
that the biggest mistake the students
usually make on gas laws is that they
don't pay attention to which is one of
which is two and they plug them in wrong
okay initial conditions is always 1
final conditions is always 2 and just be
real clear when you plug them into the
problems okay so you're thinking alright
great we've been fifteen minutes in the
video we're done right unfortunately not
um but here's the good news we're
actually gonna make all this a little
bit easier we're gonna take all three of
those laws okay so Boyle's Charles gay
lussac's and we're going to put them all
into one thing together called the
combined gas law
now here's the good news about this this
is the equation that you can use in
place of all of them and if you look at
this it's got all of them together okay
it's got p1 times v1 equals p2 times v2
that's Boyle's law okay um we've got v1
over t1 v2 over t2 Charles law p1 over T
1 P 2 over t2 that's gay lussac's law
but they're all put together here into
one equation now what's good here is
that this works well when nothing is
constant when basically everything is
changing and you're in the solvent for
one thing ok now before we actually work
a problem with it let me show you that
if you had a problem like the first one
we had so let's jump back to our Boyle's
law problem real quick 15 point leader
sample of gas at constant temperature
okay so here's the deal what we do here
is if you had a combined gas law problem
so you write you've got this formulas
form that's going to be given to you on
the test and it says constant
temperature that means they're the same
thing so just cancel them out and then
you just work the problem with what's
left
that would be Boyle's law okay
the same thing would be true for any of
the other problems when we did that
whoops when we did the Charles law
problem we could just as easily have
said okay I had constant volume in that
curve for constant pressure in that case
I'm gonna cancel my pressures out okay
gay lussac's constant volume cancel
those out and then I've got that left
okay so you can do that you can use that
in place of any of the other three laws
so let's do a problem lot of stuff
Riddler okay
so let's read through the problem and
then we'll talk about how to solve all
of this so simple gas on a flexible
container what that means is that the
volume can change
that's what flexible container means so
it's got a volume of 0.75 so since I've
got so much stuff I'm just I'm gonna
start writing it like right away so v1
is 0.75 meters okay at 25 degrees
Celsius so that's t1
remember that 25 degrees Celsius we're
gonna add 273 so that's gonna give us
298 Kelvin okay so that's t1 and a
pressure of one atmosphere okay so one
atm so that's that's like the initial
conditions all right there if the
pressure is increased to two point five
so that means P to two point five
atmospheres
okay temperatures decrease to zero now
this is really good because this shows
us why we can't plug in Celsius
temperatures because if I plug in a zero
to that formula I would get an undefined
answer and we can't do that
mathematically so remember everything's
in Kelvin so that's okay so I'm going to
add 273 and that's gonna mean that my
temperature is 273 Kelvin and then the
last thing is what is the final volume
so what I'm looking for is final volume
that's really to be honest with you that
is often what we're looking for okay
is that final volume stuff so um now
that we have everything we need I move
this out of the way just a tad just to
get by us a little bit more room here
okay slide all this stuff up just so
that we can sort of see what we're
dealing with a little bit better here
okay and then we're gonna write down our
equation so remember that this equation
basically has everything in it so p1 v1
all over t1 equals p2 v2 all over teach
it okay now there couple of ways but
really if you wanted to you could do the
algebra before you plugged in the
numbers okay that's kind of what I would
prefer to do like I would get v2 by
itself right now before I plugged in the
numbers but years of teaching chemistry
tells me that that's not what students
like to do you would much rather just
plug in the number so let's do that so
p1 is one atmosphere okay
times v1 which is 27 five liters all
over t1 t1
298 Kelvin okay and then we've got P 2
which is 2.5 atmospheres times v2 okay
all divided by t2 which is 273 and again
good thing I'm using Kelvin spider plug
in 0 right there I'm undefined whole
problem work said the hole in space-time
continuum okay not really but wouldn't
work out mathematically right so from
here a couple of ways that you can go
what a lot of students will want to do
is say hey can I just go and do the math
on both sides at this point like can I
just figure out what this side is and
what this side is and I think that's
kind of the easiest way to do it you can
do it any way you could go ahead and
cross multiply and we divide or you
could do this part and then multiply by
273 and then divide by 2.5 whatever way
you're most comfortable with really but
what I think is easy is I'm gonna do the
math on this side do the math that I
have on this side and then I'll then
I'll actually do a little bit more
algebra so if I just multiply this and
divide out I get point zero zero two
five one six over here I'm not going to
worry about the unit's at the moment cuz
I know that my units are gonna come out
to be the leaders because that's what's
not going to cancel okay over here on
this side two point five divided by two
273 gives me point zero nine one five
and then remember that all of that is
times B - okay so that's what's left so
these two things come to that those
three things become that I want to get V
2 by itself so I divide both sides by
point zero nine one five sorry for the
craziness there with the pen okay
cancels then we plug this into our
calculator and we get point two seven
liters equals V two okay so good now but
yeah you can't stop and say I mean does
that make any sense well my pressure
increased so my volume should probably
go down my temperature decrease
which would mean that my volume really
should decrease but my gain in pressure
was a lot bigger than my loss in
temperature so kind of makes sense in
regardless if you did the algebra right
your math should have everything work
out right okay now listen guys I know
and this is what makes this for most
students a lot harder than stoichiometry
because it's like geometry if you
understand how to set up the railroad
tracks you pretty much just plug
everything in punch it in your
calculator you're okay
and what makes gas laws a little bit
harder is that you have to do some
algebra okay so we're gonna work a bunch
of these do not skip working them
actually work out the algebra and work
out each step of the algebra like step
by step if you need to until you're
confident in how you solve these
problems all right
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