GAS LAWSJames Caudle

Wendy Cook

John Putnam

NOW THAT YOU HAVE SEEN AND DONE “CRUSH THE CAN”

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HERE IT IS ON A LITTLE BIGGER SCALE

crush 50 gallon drum.wmv

AND AN EVEN BIGGER SCALE

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THINK BACK TO THE PHET COMPUTER MODELS WE DID EARLIER, WHICH LAW DOES “CRUSH THE CAN” FOLLOW?

oil tanker.3gp

CHARLES’ LAW Connects how Temperature relates to

Volume of gases. (Pressure is held constant)

This is a direct proportion (one goes up the other goes up)

2

2

1

1

T

V

T

V

BOYLE’S LAW Connects how Pressure relates to

Volume of gases. (Temperature is held constant)

This is an inverse proportion (one goes up the other goes down)

2211 VPVP

AMONTONS’ LAW Connects how Pressure relates to

Temperature (Kelvin scale) of gases. (Volume is held constant)

This is a direct proportion (one goes up the other goes up)

2

2

1

1

T

P

T

P

ACTIVITY Take a piece of paper and fold in in half

length wise. With it folded still, do it again. Now evenly space out P, T, and V in that

order (very important that it is in alphabetical order)

HOW THE PTV RULER WORKS Pinch your finger over the P (Pivot point) Now raise the other end. This tells you that

as T increases so does V

Pinch your finger on T (Pivot point) Now raise the P on the end. This tells you

that as P increases then V decreases and vice versa

Pinch your finger on V (Pivot point) Now raise the other end. This tells you that

as P increases so does T

EXAMPLE 1 A balloon filled with helium gas has a

volume of 500 mL at a pressure of 1 atm. The balloon is released and reaches and altitude of 6.5 km, where the pressure is 0.5 atm. If the temperature has remained the same, what does the gas occupy at this height?

#1 Which law would you use? #2 How do you know? #3 Anything need to be converted? #4 Solve (don’t forget sig figs & labels)

EXAMPLE 1 ANSWER #1 Boyle’s Law # 2 Specifically says “Temp has

remained the same” (or your PTV ruler) #3 No

EXAMPLE 1 ANSWERS (CONT) #4

2

2

2

2211

1000

)5.0(

)*500(

))(5.0()500)(1(

VmL

Vatm

mLatm

VatmmLatm

VPVP

EXAMPLE 2 A sample of helium gas has a pressure

of 1.20 atm at 22 °C. At what Celsius temperature will the helium reach a pressure of 2.00 atm, assuming constant volume?

#1 Which law would you use? #2 How do you know? #3 Anything need to be converted? #4 Solve (don’t forget sig figs & labels)

EXAMPLE 2 ANSWER #1 Amontons #2 Says “assuming constant volume”

(or your PTV ruler) #3 Yes, Temp needs to be in Kelvin. (add

273.15)

EXAMPLE 2 ANSWER (CONT.)

CK

Tatm

Katm

atmTKatm

T

atm

K

atm

T

P

T

P

21927349249220.1

*.590

20.1*.590

00.2

295

20.1

2

2

2

2

2

1

1 #4

EXAMPLE 3 A sample of oxygen that occupies 1.00 x

106 mL at 575 mmHg is subjected to a pressure of 1.25 atm. What will the final volume be if the temperature is held constant?

#1 Which law would you use? #2 How do you know? #3 Anything need to be converted? #4 Solve (don’t forget sig figs & labels)

EXAMPLE 3 ANSWERS #1 Boyle’s Law # 2 Specifically says “Temp has

remained the same” (or your PTV ruler) #3 Yes, mmHg needs turned into atm or

vice versa—Don’t forget dimensional analysis

mmHgxatm

mmHgx

atm

or

atmmmHg

atmx

mmHg

76025.11

760

1

25.1

760

575

760

1

1

575

EXAMPLE 3 ANSWERS (CONT) #4

mLx

VatmmLxatm

VPVP

or

mLx

VmmHgxmLxmmHg

VPVP

5

26

2211

5

26

2211

1005.6

)25.1()1000.1)()760/575((

1005.6

))76025.1(()1000.1)(575(

EXAMPLE 4 A sample of nitrogen gas is contained in

a piston with a freely moving cylinder. At 0.0°C, the volume of the gas is 375 mL. To what temperature must the gas be heated to occupy a volume of 500.0 mL?

#1 Which law would you use? #2 How do you know? #3 Anything need to be converted? #4 Solve (don’t forget sig figs & labels)

EXAMPLE 4 ANSWERS #1 Charles’ Law #2 Pressure is not mentioned (or PTV

ruler) #3 Yes, Temp needs to be in Kelvin. (add

273.15)

EXAMPLE 4 ANSWERS (CONT) #4

CK

TmL

KmL

TmLKmL

T

mL

K

mL

T

V

T

V

91273364364

)375(

)2.273)(0.500(

)375()2.273)(0.500(

0.500

2.273

375

2

2

2

2

2

1

1

COMBINED GAS LAW If you noticed each of the three laws use

only two of three variables. Because of this we can combine all three laws into one.

We can do any of the four examples we just did using this by simply removing the variable that remains constant.

2

22

1

11

T

VP

T

VP

HOWEVER Nature does not keep one variable

constant most of the time. As one property changes it can change not just one other property but both. Especially if the container is an elastic container that can change its shape.

COMBINED GAS LAW EXAMPLE A 700.0 mL gas sample at STP is

compressed to a volume of 200.0 mL, and the temperature is increased 30.0 ºC. What is the new pressure of the gas in Pa?

#1 What is STP? #2 Anything need to be coverted? #3 Solve (don’t forget sig figs & labels)

COMBINED GAS LAW EXAMPLEANSWERS #1 Standard temp is 273.15 K and

standard pressure is 101325 Pa #2 Yes, Temp needs to be in Kelvin. (add

273.15)

COMBINED GAS LAW EXAMPLEANSWERS (CONT) #3

PaP

PKmL

KmLPa

KmLPKmLPaK

mLP

K

mLPa

39360

)2.273)(0.200(

)2.303)(0.700)(101325(

)2.273)(0.200()2.303)(0.700)(101325(2.303

)0.200(

2.273

)0.700)(101325(

2

2

2

2