Particle Theory of Matter

Are able to move independently Random motion Move is straight lines until course is altered by collisions with other particles Motion is fast Liquids flow because they are influences by gravity Gas particles move so fast that gravity does not affect them as much Compressible Motion in all directions until all available empty space is filled (expand)

Kinetic Molecular Theory Theory developed to explain gas behavior. Theory of moving molecules.

Assumptions: Gases consist of a large number of molecules in constant random motion. Volume of individual molecules negligible compared to volume of container. Intermolecular forces (forces between gas molecules) negligible. Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. Average kinetic energy of molecules is proportional to temperature.

Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level. Gas molecules have an average kinetic energy. Each molecule has a different energy.

When particles are heated: Particles move faster and have more collisions Higher kinetic energy helps overcome attractive forces Particles need more space, making the object expand

Pressure of a gas results from the number of collisions per unit time on the walls of container Magnitude of pressure given by how often and how hard the molecules strike.

There is a spread of individual energies of gas molecules in any sample of gas. As the temperature increases, the average kinetic energy of the gas molecules increases.

Pressure Pressure is the force acting on an object per unit area: Gravity exerts a force on the earth’s atmosphere Atmospheric pressure is the force per unit area exerted against a surface by the weight of the air above that surface. A column of air 1 m2 in cross section exerts a force of 105 N. The pressure of a 1 m2 column of air is 100 kPa.

Barometer

A Torricellian Barometer At sea level, the average atmospheric pressure supports a column of mercury 760 mm high in a simple mercury barometer at 0oC This average pressure is called one atmosphere. A Torricellian Barometer

The height changes as atmospheric pressure changes. Atmosphere Pressure and the Barometer The height of the mercury column is a measure of the atmosphere’s pressure. The height changes as atmospheric pressure changes.

Pressure and the Manometer A manometer consists of a bulb of gas attached to a U-tube containing Hg The pressures of gases not open to the atmosphere are measured in manometers. The height of the mercury is in millimeters (mmHg) If Pgas < Patm then Pgas + Ph = Patm. If Pgas > Patm then Pgas = Patm + Ph.

Units of Pressure atmospheres (symbol = atm) millimeters of mercury (symbol = mm Hg). This unit is also called a torr. Pascals (symbol = Pa). A Pa is N/m2. More commonly used is kiloPascals (symbol = kPa). This is the SI unit for pressure.

Conversion Between Units 1 atm = 760 mm Hg = 101.325 kPa = 101325 Pa

Example #1 - Convert 0.875 atm to mmHg 1 atm = 760 mmHg 0.875 atm ? ? = 665 mmHg Example #2 - Convert 745.0 mmHg to atm. ? 745.0 mmHg ? = 0.9802 atm

Example #3 - Convert 0.955 atm to kPa 1 atm = 101.325 kPa 0.955 atm ? ? = 96.8 kPa Example #4 - Convert 98.35 kPa to atm 1 atm = 101.325 kPa ? 98.35 kPa ? = 1.030 atm

Example #5 - Convert 740.0 mmHg to kPa 760 mmHg = 101.325 kPa 740 mmHg ? ? = 98.6 (99) kPa Example #6 - Convert 99.25 kPa to mmHg ? 99.25 kPa ? = 744.4 mmHg

Convert the following pressures: 658.2 mm Hg to kPa 1.85 atm to torr 337.3 kPa to atm 6.6 x 10-2 torr to atm 147.2 kPa to torr

Convert the following pressures: 658.2 mm Hg to kPa 87.75 kPa 1.85 atm to torr 1.41 x 103 torr 337.3 kPa to atm 3.329 atm 6.6 x 10-2 torr to atm 8.7 x 10-5 atm 147.2 kPa to torr 1104 torr

The mercury in a manometer is 46 mm higher on the open end than on the gas bulb end. If atmospheric pressure is 102.2 kPa, what is the pressure of the gas in the bulb?

On a certain day the barometer in a laboratory indicates that the atmospheric pressure is 764.7 torr. A sample of gas is placed in a vessel attached to an open-end mercury manometer. A meter stick is used to measure the height of the mercury above the bottom of the manometer. The level of mercury in the open end arm of the manometer has a measured height of 136.4 mm. In the arm that is in contact with the gas has a height of 103.8 mm. What is the pressure of the gas (a) in atm and (b) in kPa?