vodcast 9 2 gas laws pt1 rough ios

Summary

This 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

• 📜 Boyle's Law explains the inverse relationship between pressure and volume at constant temperature.
• 📐 Algebra is crucial when solving gas law problems, and all temperatures must be in Kelvin.
• 🌡 Temperature always needs to be converted to Kelvin by adding 273 to the Celsius value.
• 📉 Boyle's Law formula: P1 * V1 = P2 * V2, showing how pressure and volume change inversely.
• 📊 Charles's Law demonstrates the direct relationship between volume and temperature at constant pressure.
• 🚀 Charles's Law formula: V1 / T1 = V2 / T2, where temperature and volume rise and fall together.
• 🔄 Gay-Lussac's Law illustrates the direct relationship between pressure and temperature at constant volume.
• 🧮 The Combined Gas Law merges Boyle's, Charles's, and Gay-Lussac's laws into one formula: P1 * V1 / T1 = P2 * V2 / T2.
• 📝 When using the Combined Gas Law, if a variable is constant, it can be canceled out to simplify the equation.
• 🔧 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

00:00

📚 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.

05:01

🔍 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.

10:05

🌡️ 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.

15:08

📉 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.

20:10

🔄 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.

Keywords

💡Gas Laws

Gas laws are a series of fundamental relationships that govern the behavior of gases, particularly how they relate to changes in pressure, volume, and temperature. In the video, the host discusses several gas laws, including Boyle's Law, Charles's Law, and Gay-Lussac's Law, which are integral to understanding the properties of gases and their mathematical modeling. The script uses these laws to solve problems involving changes in gas properties.

💡Boyle's Law

Boyle's Law states that the volume of a fixed mass of gas varies inversely with the pressure when the temperature is held constant. This means that if the pressure increases, the volume decreases, and vice versa. The video script illustrates Boyle's Law with a problem where the pressure of a gas increases, resulting in a decrease in volume, showcasing the inverse relationship.

💡Charles's Law

Charles's Law indicates that the volume of a fixed mass of gas varies directly with the temperature in Kelvin when the pressure is held constant. The video explains this law by showing how an increase in temperature leads to an increase in volume, assuming the pressure remains the same. This law is crucial for understanding thermal expansion of gases.

💡Gay-Lussac's Law

Gay-Lussac's Law asserts that the pressure of a fixed mass of gas varies directly with the temperature in Kelvin when the volume is held constant. The script mentions this law in the context of explaining how changes in temperature directly affect pressure, which is essential for understanding how gases behave under varying temperature conditions.

💡Kelvin

Kelvin is the base unit of temperature in the International System of Units (SI). The video script emphasizes that all temperatures in gas law calculations must be in Kelvin, not Celsius. It provides the conversion formula (Kelvin = Celsius + 273), which is used in several examples to ensure that temperature values are correctly applied in the gas law equations.

💡Algebra

Algebra is a branch of mathematics concerning the study of symbols and the rules for manipulating these symbols. It is central to the video's theme as the host uses algebra to solve problems related to gas laws. The script provides detailed algebraic manipulations to isolate and solve for variables such as volume and pressure, which are key to understanding the quantitative relationships in gas laws.

💡Combined Gas Law

The Combined Gas Law is a principle that combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation, allowing for calculations when pressure, volume, and temperature can all change. The video script introduces this law as a comprehensive formula that simplifies the process of solving gas law problems by consolidating the individual laws into one equation.

💡Volume

Volume, in the context of the video, refers to the amount of space occupied by a gas. It is a key variable in the gas laws equations. The script discusses how volume changes in response to alterations in pressure and temperature, as dictated by Boyle's, Charles's, and Gay-Lussac's laws.

💡Pressure

Pressure, as used in the script, is the force applied per unit area. It is a critical variable in the gas laws and is discussed in relation to how it affects the volume of a gas, especially under conditions of constant temperature (Boyle's Law) and constant volume (Gay-Lussac's Law).

💡Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. The video script consistently refers to temperature, particularly in Kelvin, as a critical factor in the behavior of gases. It is shown to have a direct relationship with volume (Charles's Law) and pressure (Gay-Lussac's Law).

💡Algebraic Manipulation

Algebraic manipulation involves the systematic application of algebraic rules to solve equations. The script provides several examples of algebraic manipulation, such as cross-multiplication and division, to isolate and solve for variables in gas law equations, which is essential for understanding how to apply the laws mathematically.

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