= let’s build it… = if the temperature of the gases in the soda increase, what happens to the...

THE IDEAL GAS LAW

IT ALL STARTS WITH A FORMULA

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Let’s Build It…


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If the temperature of the gases in the soda increase, what happens to the pressure inside the can?


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So Pressure and Temperature are __________ related


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So Pressure and Temperature are directly related


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They must go on opposite sides of the equation. “If one increases, the other must increase”.

P T


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If the temperature of the gas in the balloon decreases, what happens to the volume of the balloon?

P T


=

So Volume and Temperature are __________ related

P T


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So Volume and Temperature are directly related

P T


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They must go on opposite sides of the equation. “If one decreases, the other must decrease”.

P TV


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If you add moles of gas to the tire, what happens to the volume and the pressure in the tire?

P TV


=P TV

So Volume and Pressure are __________ related to Moles


=P TV

So Volume and Pressure are directly related to Moles


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They must go on opposite sides of the equation. “If one increases, the other must increase”.

P TV n


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There is also a “constant” of proportionality in the equation

P TV n


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It is called “R”, the “Universal Gas Law Constant”

P TV n R

THE IDEAL GAS LAW FORMULA

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This law is valid under most normal conditions so don’t break it!

P TV n R

THE UNITS FOR EACH VARIABLE

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Volume is measured in Liters (L)

P TV n R


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Amount is measured in Moles (mol)

P TV n R


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Temperature is measured in Kelvins (K)

P TV n R


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Pressure has many units. The S.I. unit for pressure is the Pascal (Pa)

P TV n R

*See the notes on “Pressure” to learn more


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“R” has 4 units.Rearrange this equation to solve it for “R”

P TV n R

THE UNIVERSAL GAS LAW CONSTANT

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See why it has 4 units, now?

P TV n R


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“R” has units of pressure

PTV

nR


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“R” has units of pressure, volume

PTV

nR


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“R” has units of pressure, volume, moles

PTV

nR


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“R” has units of pressure, volume, moles and temperature

PTV

nR


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To get the numerical value of “R”, you must substitute in all the standard values:

PTV

nR

(1 atm)(22.4L) (1mol)(273K)R = atm L

mol K= 0.0821


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There are many different standard pressure units you could plug in:

PTV

nR

(760mmHg)(22.4L) (1mol)(273K)R = mmHg L

mol K= 62.4


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There are many different standard pressure units you could plug in:

PTV

nR

(101.3kPa)(22.4L) (1mol)(273K)R = kPa L

mol K= 8.31

EXAMPLE #1

What is the volume of 2.3 moles of hydrogen gas at a pressure of 1.2 atm

and a temperature of 20 oC?

If PV=nRT, then V =

nRT P

EXAMPLE #1



V =

(2.3 mol)

0.0821 atm L mol K

(293 K)

(1.2 atm)

EXAMPLE #1

V =

(2.3 mol)

0.0821 atm L mol K

(293 K)

(1.2 atm)

This “R”

value has atmin it

EXAMPLE #1

V =

(2.3 mol)

0.0821 atm L mol K

(293 K)

(1.2 atm)

This “R”

value has atmin it

which cancels with units of “P”

EXAMPLE #1

V =

(2.3 mol)

0.0821 atm L mol K

(293 K)

(1.2 atm)

Every unit cancels except “L” which is good because we are solving for volume!

EXAMPLE #1



V =

46 L

EXAMPLE #2

What is the temperature of 2.50 moles of helium gas at a pressure of 795 mmHg

in a 3.25 liter container?

If PV=nRT, then T =

PVnR

EXAMPLE #2



If you want to use 0.0821 atm L for “R”, mol Kyou have to convert 795 mmHg to atm so they will cancel

EXAMPLE #2



795 mmHg x

1 atm =760 mmHg

1.05 atm

EXAMPLE #2



T =

(2.50 mol)

0.0821 atm L mol K

(3.25 L)(1.05 atm)

EXAMPLE #2

T =

(2.50 mol)

0.0821 atm L mol K

(3.25 L)(1.05 atm)

Every unit cancels except “K” which is good because we are solving for temperature!

EXAMPLE #1



T =

16.6 K

WHAT IS AN “IDEAL” GAS?

A gas that behaves according to the Kinetic Molecular Theory*

(It obeys all the postulates of KMT)

*See KMT Notes for more information

WHEN IS A GAS “IDEAL”?

Never!!!!Ideal gases don’t exist

However, real gases act like “ideal” gases at most normal conditions of temperature and pressure

HUH?

Real gases follow the Kinetic Molecular Theory until…….

The temperature gets extremely lowORThe pressure gets extremely high

KMT FAILS AT LOW TEMPERATURES

The KMT says particles don’t attract or repel each other, but at very low temperatures, gas particles move very slowly and this

allows particles to attract each other when they get close

If no attractive forces, the particles will spread out

If attractive forces are present,The particles would clump together

KMT FAILS AT LOW TEMPERATURES

The KMT says particles don’t attract or repel each other, but at very low temperatures, gas particles move very slowly and this

allows particles to attract each other when they get close

If no attractive forces, the particles will spread out

And the volume would be smallerThan our gas law would predict

KMT FAILS AT HIGH PRESSURES

The KMT says particles have negligible volume, but at very high pressures, the

gas particles are smashed close together thus reducing the empty

space between them, but NOT to zero volume because the particles

themselves have some volume.

WHY USE THE KMT IF IT IS NOT TRUE?

Because it is a useful “model” that helps us understand and predict what gases

will do under most conditions

The KMT only breaks down under extremely low temperatures and

extremely high pressures

= let’s build it… = if the temperature of the gases in the soda increase, what happens to the...

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