Gases• All molecules move to some

extent.–Vibrational–Rotational–Translational*

Pressure

(1 square inch)

This column of air weighs 14.7 pounds

Point “X”

Measuring Air pressure

Average air pressure at sea level is…

Four variables are used to describe a gas:

Pressure

Volume

Temperature

Amount of a gas

Pressure Volume Relationship

Robert Boyle

Pressure Volume Relationship

“For a fixed amount of gas, the volume of a gas varies

inversely with pressure at a constant temperature”

Robert Boyle 1662Boyle’s Law

In mathematical terms:

P x V = constantWhat does this

mean?

P x V = constant

Volume Temperature Relationship

Jacques Charles

Volume Temperature Relationship

“The volume of a gas varies directly with Kelvin temperature

at a constant pressure”

Jacques Charles 1787Charles’s Law

In mathematical terms:

V/T = constant

V/T = constant

Absolute ZeroIf a gas is cooled enough it would

occupy zero volume, this temperature is called absolute zero. At this temperature, the molecules have minimal or no

vibrational motion

Coldest place in the solar system

-128 O F or -89 O C Antarctica

-391 O F or -235 O C Triton-454 O F or -270 O C Deep Space

This is the lowest natural temperature.

Lowest man made temperature

• MIT scientists have cooled a sodium gas to the lowest temperature

ever recorded, only half-a-billionth of a degree above absolute zero.

Absolute zero is a bone chilling…

Combined Gas Law

Avogadro’s Hypothesis

• Equal volumes of gases contain the same number of particles at the same

temperature and pressure.

Avogadro’s Law

At constant T and P, the volume of a gas is directly proportional to the number of

moles of the gas.

Avogadro’s Law

At constant T and P, the volume of a gas is directly proportional to the number of

moles of the gas.

Ideal Gas Law

• An “ideal gas” is a gas that obeys the ideal gas equation

Ideal Gas Law

• An “ideal gas” is a gas that obeys the ideal gas equation

• There is no such thing as an ideal gas

Further Applications of the Ideal Gas Law

• Density

• Molar mass

• Stoichiometry

What is the molecular weight of a gas if 1000. ml has a mass of 0.975 grams at 77.00C and 740. torr?

 

What is the density of carbon tetrachloride at 714 mmHg and

125oC

NaN3 decomposes to form nitrogen and sodium. How

many grams of reactant must be used to inflate an air bag

with a volume of 36.0 liters to a pressure of 1.15 atm. at 26.0 degrees centigrade?

Dalton’s Law ofPartial Pressures

Dalton’s Law ofPartial Pressures

• The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.

• In other words,

Ptotal = P1 + P2 + P3 + …

Collecting Gases Over Water 2KClO3→2KCl + 3O2

Partial Pressures and Mole Fraction

Pg = Xg PT

A study of the effects of certain gases on plant growth requires a synthetic

atmosphere composed of 1.5 mol percent CO2, 18.0 mol percent O2, and 80.5 mol

percent Ar. (a) Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 121-L space at 295 K, how many

moles of O2 are needed?

Kinetic Molecular Theory

Explains why gases move as they do

1. Gases are made up of molecules or atoms which travel in straight lines. The energy they possess is called

kinetic energy.

2. The actual volume of all the particles of a gas are very

small compared to the volume of the container

they are in.

3. The attractive and repulsive forces between

gas particles is negligible. In other words they do not

interact.

4. When gas particles do collide with each other or

the walls of a container, the collisions are elastic.

 

5. The kinetic energy of a gas particle depends on its temperature .

At any given temperature the molecules of all gases have the

same average KE.

KE =1/2 mu2

What does u depend on?

MWRTu /3

Calculate the rms speed of a nitrogen molecule at 25oC.

Diffusion Effusion spreading of one gas into another escape of gas through a tiny hole

•

Both depend on the molar mass of the gas particle.

The smaller the particle, the faster the rate of diffusion and effusion.

Graham’s Law

A nitrogen molecule is found to move at 1000. mi/hr. How fast would a molecule of

hydrogen move under these same conditions?

How many times faster does a helium atom diffuse compared to

argon?

Ideal Gases

• An ideal gas is a gas that:Obeys the Ideal Gas Equation

Ideal Gases

• An ideal gas is a gas that:Obeys the Ideal Gas Equation

Exerts no attractive force

Occupies no volume (relative to the container)

Real vs Ideal Gases

Real vs Ideal Gases

• Real Gases

Real Gases

.

Real Gases

Corrections for Nonideal Behavior

• The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.

• The corrected ideal-gas equation is known as the van der Waals equation.

The van der Waals equation.

P = nRT - n2a

V – nb V2

Volume correction

Attraction correction

Calculate the pressure exerted by 1.00 mole of hydrogen at 25oC given a volume of 1.00 liter using (a)the ideal gas

equation and (b)the van der Waals equation