Gas Laws

Gas Pressure

Just means that gas is “pushing” on something.

Gas Pressure

Tire

What’s going on inside?

Air:Nitrogen 78%Oxygen 21%Argon ~1%Carbon Dioxide <1%

Each of these particles are constantly flying around. Like a lotto ball!

They slam against the container and keep the tire “full”. The particles press against the walls.

Measuring Gas PressureAir:Nitrogen 78%Oxygen 21%Argon ~1%Carbon Dioxide <1%

Think of a giant ball pit miles and miles up.

At the bottom of the ball pit, is like us walking around. That’s the atmospheric pressure.

Measuring Gas Pressure

U-TubeCan’t use it to

measure atmospheric

pressure, because atmospheric

pressure presses on everything

equally.

Vacuum

So how do we measure it?

Vacuum

It pushes down on this side, and it moves up on the other side.

Measuring Gas Pressure

Vacuum

We can measure that!Take a ruler and measure low to high in milimeters!

The fluid that is contained in this U tube, is mercury. If we measure this at sea level, we get. 760mmHg between the bottom and the top.

760 mmHg

Measuring Gas Pressure

What if we go up a mountain or down into a mine?Think about that ball pit again. If you’re at the bottom of the ball pit will it weigh more or less than at the top?

Sea Level

More Pressure

760mmHg

Less Pressure

Measuring Gas Pressure of Containers

800 mmHg

40 mmHg

What if I snap off the vacuum bulb?

Because atmospheric pressure is pushing down!

760 mmHg

Measuring Gas Pressure

Barometer Manometer

Gas Pressure Conversions

How do we measure things? Lots of ways! Same goes with gas pressure.

Gas Pressure UnitsmmHg atmosphere kilopascalTorr

atm kPa

Conversions760 mmHg = 1 atm = 101.3kpa

Gas Pressure Conversions

The pressure inside a car tire is 225 kPa. Express this value in both atm and mmHg.

760 mmHg = 1 atm = 101.3 kPa

225 kPa x 1 atm 101.3 kPa

=2.22 atm

225 kPa x 760 mmHg 101.3 kPa

=1688 mmHg

Boyle’s Law

If we keep the temperature the same, we can predict what pressure and volume will do.

Boyle’s Law

Pressure and Volume

Gas particles have a bunch of room. Gas particles are

squeezed into smaller space.

What about volume?

V=HighV=Low

As pressure goes up, volume goes down. That means inverse relationship.

P= LowP=High

Boyle’s Teeter Totter

• When volume is high, pressure is low

• When the volume is low, pressure is high

• An Inverse relationship.

Pressure

Volume

Boyle’s Law

Boyle’s law is explained by the equation P1V1=P2V2Let’s get right to it!

At 1.70 atm, a sample of gas takes up 4.35 L. If the pressure on the gas is increased to 2.40 atm, what will the new volume be?

P1V1 = P2V2

(before) (after)What do you know?

P1 (before pressure) = V1 (before volume)=P2 (after pressure) =V2 = ??

(1.70 atm)(4.35L)=(2.40 atm)V2

7.40atm/L = (2.40atm)V2V2 =3.01L

1.70 atm4.35 L2.4 atm

Boyle’s Law

Does that answer make sense?At 1.70 atm, a sample of gas takes up 4.35 L. If the pressure on the gas is increased to 2.40 atm, what will the new volume be?

We increased the pressure, so we pushed down that piston. We squeezed the molecules into a smaller space. So the volume should go down!

Boyle’s Law

If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be? P1V1 = P2V2

(before) (after)P1 (before pressure) =V1 (before volume)=P2 (after pressure) =V2 =

(1.5atm)(5.6L) = (P2)(4.8L)

8.4 atm/L = (4.8L)P2

1.8 atm = P2

1.5 atm

5.6 L

?

4.8L

Charles’ Law

Charles’ law relates volume and temperature, while keeping pressure the same

V1 = V2

T1 T2

Charles’ Law

How could we test the theory that temperature and volume are related?

Think about kinetic theory and molecules.

Charles’ Law

HOTCOLD

T= High T = LowV= High V = Low

Charles’ law says that as the temp increases, so does volume. A direct relationship.

What’s going on with the temp?

Charles’ Law

So now we can relate volume and temperature. V1 = V2

T1 T2

MUST ALWAYS USE KELVIN TEMPERATURE in gas lawsA balloon takes up 625 L at 0°C. If it is heated to 80°C, what will its new volume be?

Must convert to Kelvin.0 °C + 273 = 273K80 °C + 273 = 353K

625 L

0 °C

??

V1 =T1 =

T2 =

V2 =80 °C

Charles’ Law

V1 = V2

T1 T2

A balloon takes up 625 L at 0°C. If it is heated to 80°C, what will its new volume be?

V1 = 625 LT1 = 273KT2 = 353KV2 = ??L

625L = V2

273K 353K

2.29L/K= V2

353K808L = V2

Charles’ Law

At 27.00 °C a gas has a volume of 6.00 L. What will the volume be at 150.0 °C?

What’s the equation?V1 = V2

T1 T2

V1=

T1=

V2=

T2=

6.00 L27 °C

??

150.0 °C

Must convert to Kelvin.27 °C + 273 = 300K150°C + 273 = 423K

Charles’ Law

At 27.00 °C a gas has a volume of 6.00 L. What will the volume be at 150.0 °C?

V1 = V2

T1 T2

V1=

T1=

V2=

T2=

6.00 L

??

300K

423K

6.00L = V2

300K 423K

0.02L/K = V2

423K

8.46L = V2

Avogadro’s Law

Relationship between:Amount of gas (n) and the Volume.

What happens to one, when I change the other?

I start with the first balloon, and then blow more air into it…will the volume increase?

Yes, a direct relationship

Avogadro’s Law

As the amount (in moles) goes up, so does the volume.If we double the amount, it doubles the volume.

Avogadro’s Law

We only changed TWO things. The volume and the amount of particles. We didn’t mess with the pressure or the temperature, they were held constant.

V1 = V2

n1 n2

Avogadro’s Law

V1 = V2

n1 n2

Let’s try!In a sample of gas, 50.0 g of oxygen gas (O2) take up 48L of volume. Keeping the pressure constant, the amount of gas is changed until the volume is 79 L. How many mols of gas are now in the container?

n1= n2 = V1 = V2 =

When doing Avogadro's law, “n” MUST be in moles!

50g

40L

mol?79L

Avogadro’s Law

V1 = V2

n1 n2

Before Aftern1=50g n2 = g?V1 = 48L V2 = 79L

When doing Avogadro's law, “n” MUST be in moles!

50g O2 x 1 mol O2

32g O2

= 1.6 mol O2

1.6mol

1.6 mol O2 48L

= n2

79L0.03 = n2

79L2.6 mol = n2

Gay-Lussac’s LawThe pressure and Kelvin temperature of a gas are directly proportional, when the volume remains constant.

Gay Lussac’s Law

This law only applies to gases held at a constant volume. Only the pressure and temperature will change.

P1 = P2

T1 T2

Pi =initial pressurePf = final pressureTi = initial temperature (kelvin)Tf = final temperature (kelvin)

The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20C). If the can is warmed to 48C, what will the new pressure inside the can be?

Gay Lussac’s Law

The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20°C). If the can is warmed to 48°C, what will the new pressure inside the can be?

P1 = P2

T1 T2

Must convert to Kelvin20°C + 273 = 293K48°C + 273 = 321K

P1 =

P2 =

T1 =

T2 =

235 kPa?

20°C

48°C

235293

= Pf

3210.80 = Pf

321257.5 kPa = Pf

P1 =

P2 =

T1 =

T2 =

235 kPa?

The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20°C). If the can is warmed to 48°C, what will the new pressure inside the can be?

P1 = P2

T1 T2

293K

321K

How to use these formulas

Charle’s LawV1 = V2

T1 T2Avogadro’s LawV1 = V2

n1 n2

Gay Lussac’s LawP1 = P2

T1 T2

They are all pretty much the same equation, just different variables!

Combined Gas Law

Charle’s LawV1 = V2

T1 T2Boyle’s Law(P1)(V1) = (P2)(V2)Gay Lussac’s LawP1 = P2

T1 T2

What if I had a balloon. I wanted to increase the pressure and cool it down. What is the volume? Do we have an equation for that? P, T, V.We can combine the laws!

Combined Gas Law(P1)(V1) = (P2)(V2) T1 T2

Combined Gas LawA 40.0L balloon is filled with air at sea level (1.00 atm, 25.0 °C). It's tied to a rock and thrown in a a cold body of water, and it sinks to the point where the temperature is 4.0 ° C and the pressure is 11.00 atm. What will its new volume be?(P1)(V1) = (P2)(V2) T1 T2

Convert to Kelvin25°C + 273 = 298K4°C + 273 = 277K

P1= 1 atmP2= 11 atmV1= 40 LV2= ??T1= 298KT2= 277K

(1)(40) = (11)(V2) 298K 277K

0.13 = (11)(V2) 277K36.01 = (11)(V2)

3.27 L = V2

P1 =P2 = V1 =V2 =T1 =

T2 =

1 atm11 atm40 L??25°C

4°C

Ideal Gas Law

How can we describe what’s going on in this container? What variables can we think of?

Temperature (T) 313KPressure (P) 3.18 atmVolume (V) 95.2 L

Amount of Gas (n)

7.5 mol

Did you know that if we know 3 of the 4 variables, we can find the last one?

Ideal Gas LawIdeal gas law: PV = nRT

Temperature (T) 313KPressure (P)

Volume (V) 95.2 LAmount of Gas (n)

7.5 mol

How would we rearrange the problem to find P?

??

P =nRT V

What if we needed the amount of gas (n)?

3.18 atm

??

PV = nRT

Ideal Gas Law

PV = nRTSo what is R?

R is a constant! For most cases, R = 0.0821 L▪atm/mol ▪K

Those units look familiar.

V = LP = atmT = Kn = mol The units on

“R” MUST match the units in the problem!

Ideal Gas Law

“R” will come in many forms.R = 62.4 L▪mmHg /K ▪mol

R = 8.31 L▪kPa /K ▪mol

NOT A BIG DEAL! The “R” constant will always be given, just use the right constant.

Ideal Gas Law

2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is volume of the gas?

PV = nRT

P =

V =

n =

R = T =

0.0821 L▪atm/K ▪mol

1.70 atm

??

2.3 mol

41°C

Convert to Kelvin41°C + 273 = 314K

Ideal Gas Law

PV = nRT

P =

V =

n =

R = T =

0.0821 L▪atm/K ▪mol

1.70 atm

??

2.3 mol

314K

2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is volume of the gas?

Rearrange the equation.

V = nRT P

V = (2.3 mol)(314K) x 0.0821 L ▪atm 1.70 atm K ▪ mol

V = 59.3 1.7

V = 34.9 L

Ideal Gas Law

At a certain temperature, 3.24 moles of CO2 gas at 2.15 atm takes up a volume of 35.28 L. What is this temperature (in Celsius)?

P = V =T =

n =

R =

2.15 atm35.28 L??

3.24 mol

0.0821 L▪atm/K ▪mol

Do the units given match the R?

Ideal Gas Law

V =T =

n =

R =

2.15 atm35.28 L??

3.24 mol

0.0821 L▪atm/K ▪mol

At a certain temperature, 3.24 moles of CO2 gas at 2.15 atm takes up a volume of 35.28 L. What is this temperature (in Celsius)?

P =

PV = nRT

Rearrange the equation.T = PV

nR

T = (2.15 atm)(35.28L) X K ▪ mol (3.24 mol) 0.0821 L ▪ atm

Ideal Gas LawCharle’s LawV1 = V2

T1 T2Avogadro’s LawV1 = V2

n1 n2Gay Lussac’s LawP1 = P2

T1 T2

Who wants to memorize all of these?!?!

Ideal Gas LawPV = nRT

Combined Law(P1)(V1) = (P2)(V2) T1 T2

You don’t have to!

Gas LawJust memorize one!

Ideal Gas LawPV = nRT

Can use it for any of the gas law problems!

Warning:If this blows your mind and you get totally confused, just memorize the equations.

Gas Law

Before AfterP1 = 3 atm P2 = 7atmT1 = ?? T2 = 150k

Rearrange the ideal equation so that the variables given are on the same “side”

PV =nRT

PV = nRTV VP = nRTT VT

P= nRT V

You’ve found the equation you need to use. You don’t need “n, R, or V”.

P1 = P2

T1 T2

Gas Law

P1 = 1,217 mmHgP2 = 732 mmHgV1 = ??V2 = 42L

PV = nRT

Rearrange the equation so the variables you’re looking for are on the same side of the equation.

Easy! PV is already on the same side. Now just double it.

P1V1 = P2V2

Gas Law

V1 = 7.5LV2 = 1.2Ln1= 32 moln2 = ?

PV = nRT

Rearrange the equation so V and n are on the same side.PV = nRT P P

V = nRT PV = nRTn Pn

V1 = V2

n1 n2

Gas Law

Before AfterV1 = ? V2 = 54LP1 = 96 kPa P2 = 112 kPaT1 = 12K T2 = 42K

PV = nRT

Rearrange so V, T, P are on same side.

PV = nRT T T

P1V1 = P2V2

T1 T2