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 1662 Boyle’s Law

In mathematical terms: P x V = constant What 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 1787 Charles’s Law

In mathematical terms: V/T = constant

Absolute Zero If 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 ml has a mass of grams at C and 740. torr?

What is the density of carbon tetrachloride at 714 mmHg and 125 o C

NaN 3 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 of Partial 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, P total = P 1 + P 2 + P 3 + …

Collecting Gases Over Water 2KClO 3 →2KCl + 3O 2

Partial Pressures and Mole Fraction P g = X g P T

A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent CO 2, 18.0 mol percent O 2, and 80.5 mol percent Ar. (a) Calculate the partial pressure of O 2 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 O 2 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 mu 2

What does u depend on?

Calculate the rms speed of a nitrogen molecule at 25 o C.

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 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 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 - n 2 a V – nb V 2 Volume correction Attraction correction

Calculate the pressure exerted by 1.00 mole of hydrogen at 25 o C given a volume of 1.00 liter using (a)the ideal gas equation and (b)the van der Waals equation