Gas Law Chemistry Notes

Gas Properties

Units of Measurement

• If a substance is given in a shot, it's measured in cc's, which stands for cubic centimeters.
• cc's are a unit of liquid volume.

Kinetic Molecular Theory of Gases (KMT)

Assumptions About Ideal Gases

• Attractive and repulsive forces between gas molecules are negligible (negative).
• Collisions between gas molecules are perfectly elastic; when molecules collide, they move and bounce back.
• Collisions between the walls of a container and gas molecules are elastic, implying there's no loss of kinetic energy during collisions.
• When gas particles collide, they gain momentum, similar to a chain reaction where energy transfers from one particle to another.
• More particles within a container lead to more collisions because they are closer together within the space.
• The size of the container affects the frequency of collisions.

Ideal vs. Real Gases:

• Ideal gases conform entirely to the kinetic molecular theory, but no real gas perfectly conforms.
• Ideal gases are imaginary constructs to serve as a point of reference for understanding real gas behavior.
• Real gases experience attractive and repulsive forces and can lose energy during collisions.
• Real gases behave more like ideal gases at high temperatures and low pressures.

Importance of Ideal Gases

• Ideal gases serve as a reference point for comparison.
• Understanding ideal gases helps in approximating and understanding real gas behavior.

Historical Context

• Early chemists struggled with gas chemistry because gases were difficult to contain and study.
• The KMT was developed to make assumptions that simplify the understanding of gas behavior.
• Real gases behave closely enough to ideal gases that KMT can be used to understand gas behavior.

Overriding Principle of KMT

• Understanding small gas molecules' behavior allows extrapolation to understanding the behavior of all molecules in a gas.

Properties of Ideal Gases

1. Infinitely Small Molecules:
   • Gas molecules are assumed to be infinitely small.
   • While not entirely true, the space between gas molecules is substantial, making their volume negligible.
   • This assumption simplifies mathematical calculations because the size of the molecules is irrelevant.
2. Constant Random Motion:
   • Gas molecules are in constant, random motion with no set path.
   • Constant motion implies gases are dynamic.
   • Random motion enables statistical treatment; instead of tracking individual molecules, they can be summed up overall mathematically.
   • Collisions of gas molecules with each other and the container walls generate heat, and the force of these collisions creates pressure.
3. Elastic Collisions:
   • All collisions are assumed to be elastic, meaning no energy is lost during collisions.
4. No Intermolecular Forces:
   • Ideal gas molecules do not interact with each other except during collisions.
   • This is a reasonable assumption because gas molecules are small and move quickly, reducing their chance to interact.
5. Kinetic Energy and Temperature:
   • Kinetic energy of gas molecules is proportional to temperature in Kelvin.
   • Heating a gas increases the velocity of its molecules.
   • Temperature is a measure of how fast molecules in a material are traveling; higher temperatures correspond to higher molecular velocity.
   • Kelvin is used because negative degrees would imply negative molecular energy, which is impossible.

Quick Recap: Properties of Ideal Gases

1. Molecules are infinitely small.
2. Gas molecules are in constant random motion.
3. Gas molecules don't experience intermolecular forces.
4. Kinetic energy of gas molecules is proportional to temperature in Kelvin.

Real Gases

• Real gases have different degrees of ideality based on their specific properties.

Properties of Real Gases

1. Low Density:
   • Gas molecules don't interact with each other and travel at high speeds, so they are generally far apart.
   • Gases have low density: example, the density of water is $1$, while the density of steam is $0.00596$.
2. Compression and Expansion:
   • Gases can be compressed and expanded due to the substantial space between molecules.
   • Gases expand to the size of the container they are in because the molecules don't stick together.
   • For example, air in a scuba tank can be compressed to a maximum pressure of $3,442$ PSI, or about $234$ times the atmospheric pressure (one ATM).
3. Diffusion:
   • Gases diffuse; they mix if put in the same container.
   • Air consists of gases like nitrogen (78%), oxygen (21%), argon, and carbon dioxide.
   • Increased oxygen levels can allow things to grow larger.
4. Velocity
   • The velocity at which gas molecules move depends on temperature and mass.

Graham's Law (Mentioned, but not covered in detail)

• Graham's Law describes the root mean square velocities of gas molecules, indicating how fast gas particles move.
• $Root Mean Square = \sqrt{\frac{3RT}{m}}$
• Where:
  • R is the gas law constant
  • T is the absolute temperature in Kelvin
  • m is the mass of a mole of the gas in kilograms