Lecture 14 10/3/05

Compare the heights of a Hg barometer and a water barometer if atmospheric pressure is 1 atm.

(Density of Hg = 13.53 g/cm3)

A scuba diver taking photos of a coral reef 60 ft below the ocean surface breathes out a stream of bubbles.

What is the total gas pressure of the bubbles at the moment they are released?

What is the pressure when the bubbles get to the surface?

Boyle’s Law

Pressure vs. Volume

As the volume of the air is reduced, its pressure goes up

P

1 V

2211

BB

VPVP

CPV V

1CP

Boyle’s Law

Assumes constant n and T

A sample of nitrogen gas has a pressure of 67.5 mm Hg in a 500-mL flask. What is the pressure of this gas sample when it is transferred to a 125-mL flask at the same temperature?

Charles’ LawVolume vs. Temperature(n and P are constant)

Charles’s Law

As temperature decreases, volume decreases

2

2

1

1

CC

T

V

T

V

CT

V TCV

T V

(n and P are constant)

A balloon is inflated with helium to a volume of 45 L at room temperature (25oC). If the balloon is cooled to -10oC, what is the new volume of the balloon? Assume no change in pressure.

General Gas Law (Combined Gas Law)

2

22

1

11

T

VP

T

VP

Assumes a constant n

Boyle’s Law and Charles’ Law are not independent

You have a 22-L cylinder of helium at a pressure of 150 atm and at 31˚C. How many balloons can you fill, each with a volume of 5.0L on a day when the atmospheric pressure is 755 mm Hg and the temperature is 22˚C.

Avagadros’s Hypothesis

2

2

1

1

n

V

n

V

n V

Assumes constant T and P

Name 3 ways the volume occupied by a sample of gas can be decreased.

IDEAL GAS LAW

Combines:Boyle’s LawCharles’s LawAvagadro’s Law

RnT

PV nRTPV

22

22

11

11

Tn

VP

Tn

VP

Gas Constant (R)

Kmol

torrL36.62R

Kmol

dmkPa314.8R

Kmol

J314.8R

Kmol

atmL08206.0R

3

RnT

PV

How much N2 is required to fill a small room with a volume of 27,000 L to a pressure of 745 mm Hg at 25 oC?

R = 0.082057 L•atm/K•mol

kg 8.30g 00308 28g/mol moles 1100grams

moles 1100)K298(

molKatmL

0.0821

)L 27000(mmHg 760atm 1

mmHg 745

n

A 1.00 g sample of water is allowed to vaporize completely inside a 10.0-L container. What is the pressure of the water vapor at a temperature of 150˚C?

What is the volume of 1 mole of gas at Standard Temperature (0˚C) and Pressure (1 atm)?

Gas Density

How do you introduce density into the ideal gas law?

nRTPV RT

M

mPV

RTmass Molecular

mPV

RT

PM

V

mD V

mD

Calculate the density of dry air at 25˚C and 1.00 atm if its molar mass (average) is 28.96 g/mol.

Prove that putting Helium in a balloon will make it rise.

In August 1986, 1700 people died from asphyxiation in the Lake Nyos valley, Camaroon, as a result of the lake’s massive release of carbon dioxide that blanketed the valley. Calculate the density of CO2 at 1 atm and 298 K.