Gas Laws

Kinetic Energy

Kinetic energy depends on both mass and velocity.
Formula: KE = \frac{1}{2}mv^2
- KE is kinetic energy.
- m is mass in kilograms (must be in kilograms).
- v is velocity in meters per second.

Temperature measures the average kinetic energy of molecules or particles (atoms) in a sample of matter.
This applies to all matter: gases, liquids (moving around), and solids (vibrating in place).

Gases can expand or contract to fill a container.
Liquids have a defined volume but an undefined shape; they take the shape of their container but don't fill it completely.
Solids have a defined volume and shape.

Gases flow due to the absence of significant attractive forces.
- Liquids also flow, but much slower.
Diffusion: The movement of one material through another.
- Example: Food coloring spreading in water, perfume spreading in a room.
Effusion: The escape of a gas through a tiny opening.
- Example: Air escaping from a punctured tire.

Graham's Law: Rate of effusion is inversely proportional to the square root of the molar mass.
- rate \propto \frac{1}{\sqrt{molar\ mass}}
Lighter gases diffuse or effuse faster than heavier gases.
- Example: Helium escapes a balloon faster than carbon dioxide.
- Helium (molar mass 4) vs. Carbon Dioxide (molar mass 44).
- Carbon dioxide is 11 times heavier, so it's \sqrt{11} \approx 3.3 times slower.

Pressure is defined as force per unit area.
Particles in Earth's atmosphere exert pressure in all directions.
- Pressure is greater near the surface due to gravity.
- Higher altitudes have less air and lower pressure.
The instructor mentions cities at high elevation, where it is harder to breathe.

Evangelista Torricelli invented the barometer to demonstrate and measure air pressure in the 1600s.
Barometer: A glass tube with a vacuum, submerged in mercury.
- Air pressure pushes down on the mercury, causing it to rise in the tube.
- The height of the mercury column indicates air pressure.
Normal air pressure at sea level: 760 millimeters of mercury (mmHg).
In the United States, inches of mercury are sometimes used.
- 1. 92 inches of mercury
Manometer: Used to study pressure changes in chemical reactions.
- Instead of mercury, safer alternatives like oil are used.
Other units for pressure:
- Pascal (Pa): SI unit, Newton per square meter (N/m^2).
- Kilopascal (kPa): 1000 Pascals.
Standard atmosphere:
- 1 atmosphere = 760 mmHg = 101.3 kPa.