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!