AT

Gas Laws and Variables

Gas Variables

  • Key Variables to Understand Gas Behavior:
  • P (Pressure): The force exerted by gas particles colliding with the walls of a container.
  • V (Volume): The space occupied by the gas, defined by the size of the container.
  • N (Moles): The number of gas particles in the container.
  • T (Temperature): The measure of the average kinetic energy of the gas particles, usually expressed in Kelvin.

Relationships Between Variables

  • Ideal Gas Assumptions:

  • Gas particles are in constant motion.

  • Particle collisions are elastic.

  • Boyle's Law: (P1V1 = P2V2)

  • Relationship: Pressure is inversely proportional to volume when temperature and the moles of gas are constant.

  • Example: If the volume is halved, the pressure doubles if the temperature remains constant.

  • Charles's Law: (V1/T1 = V2/T2)

  • Relationship: Volume is directly proportional to temperature when pressure and the number of moles are constant.

  • Example: If the temperature doubles, the volume must also double, provided pressure remains the same.

  • Avogadro's Law: (V1/n1 = V2/n2)

  • Relationship: Equal volumes of gases at the same temperature and pressure contain the same number of molecules.

  • Example: If you double the moles of gas, the volume must also double when temperature and pressure are constant.

Combined Gas Law

  • Formula:
  • (P1V1/T1 = P2V2/T2)
  • Combines Boyle’s Law, Charles’s Law, and Avogadro’s Law.
  • Useful for situations where you are adjusting one or more of the gas variables.

Ideal Gas Law

  • Formula: PV = nRT
  • Where R is the gas constant and varies based on the units used (0.0821 L·atm/(K·mol) is a common value).
  • This law assumes ideal behavior, which can be used to calculate one variable if the others are known.

Temperature and Units

  • Temperature must be in Kelvin for gas calculations.
  • To convert °C to K: K = °C + 273
  • Example: To convert 100°C to Kelvin: 100 + 273 = 373 K.

Practical Applications

  • Standard Molar Volume: 1 mole of gas at standard temperature and pressure (STP) occupies 22.4 liters.
  • Report Outputs: Always report your final answer with the correct number of significant figures based on the inputs you are given.

Solving Gas Law Problems

  1. List knowns and unknowns: Identify what information is provided and what is being sought.
  2. Write the raw formula: Use the appropriate gas law formula for the problem.
  3. Rearrange for the unknown: Solve the formula algebraically to isolate the variable you need.
  4. Plug and chug: Insert the known values into the formula and calculate the answer.

Example Problem

  • A balloon has a volume of 5.15 L and a pressure of 1.35 atm. If it is compressed to a volume of 3.43 L, what is the new pressure?
  • Step 1: Known values: P1 = 1.35 atm, V1 = 5.15 L, V2 = 3.43 L, find P2.
  • Step 2: Use Boyle's Law: P1V1 = P2V2
  • Step 3: Rearrange to find P2: P2 = (P1V1)/V2
  • Step 4: Plug in: P2 = (1.35 * 5.15) / 3.43.

Conclusion

  • Understanding and memorizing the relationships and laws of gases helps predict how changes in conditions will affect gas behavior in practical and theoretical applications.
  • Keep practicing problems to reinforce understanding!