#AP Chemistry: Gases - The Night Before 🚀

Hey there, future AP Chem master! Let's get you feeling confident and ready to rock that exam. We're going to break down the gas laws and make sure everything clicks. Remember, you've got this! 💪

#Pressure and Temperature: The Basics

#Pressure

Pressure is all about how often gas particles hit the walls of their container. Think of it like a bunch of tiny bouncy balls – the more they bounce against the walls, the higher the pressure! 💥

• Standard Pressure: This is just atmospheric pressure at sea level. It's good to know these values:
  • 1.00 atm
  • 760 mm Hg
  • 760 torr
  • 101.3 kPa

#Temperature

Temperature is a measure of the average kinetic energy of the particles. Higher temperature = faster-moving particles = more energy! 🔥

• Standard Temperature: 0 °C or 273.15 K. Remember to ALWAYS convert to Kelvin for gas law problems!
• Conversion: °C + 273.15 = K

#Standard Temperature and Pressure (STP)

• STP = 1 atm and 273.15 K. You'll see this a lot!

#Gas Laws & Relationships

These laws describe how gases behave when we change things like pressure, volume, and temperature. We'll focus on the relationships and how they affect each other. All of these laws assume the amount of gas (moles) is constant unless otherwise stated.

#Boyle's Law

• Relationship: Pressure and volume are inversely related at constant temperature. When one goes up, the other goes down. ⬇️⬆️
• Equation: $P_1V_1 = P_2V_2$
• Explanation: If you squeeze a gas into a smaller space (decrease volume), the particles hit the walls more often, increasing pressure.

#Charles' Law

• Relationship: Volume and temperature are directly related at constant pressure. If one goes up, the other goes up too. ⬆️⬆️
• Equation: $V_1/T_1 = V_2/T_2$
• Explanation: If you heat a gas (increase temperature), the particles move faster and need more space, increasing volume.

#Gay-Lussac's Law

• Relationship: Pressure and temperature are directly related at constant volume. ⬆️⬆️
• Equation: $P_1/T_1 = P_2/T_2$
• Explanation: If you heat a gas in a fixed container (increase temperature), the particles hit the walls more often and harder, increasing pressure.

#Avogadro's Law

• Relationship: Volume and the number of moles are directly related at constant temperature and pressure. ⬆️⬆️
• Equation: $V_1/n_1 = V_2/n_2$
• Explanation: If you add more gas particles to a container, the volume increases to keep pressure constant.
• Key Idea: Equal volumes of gases at the same temperature and pressure contain the same number of particles. (e.g., 5L of H2 and 5L of He at STP have the same number of particles)

#The Combined Gas Law

• Equation: $P_1V_1/T_1 = P_2V_2/T_2$
• Use: This combines Boyle's, Charles', and Gay-Lussac's laws. If a variable isn't mentioned, you can ignore it. For instance, if the temperature is constant, you can use $P_1V_1 = P_2V_2$.
• Memory Aid: Remember this one, and you can derive the others!

#Image Courtesy of Online Math Learning

#Ideal Gas Law

• Equation: $PV = nRT$
• Variables:
  • P = pressure (atm)
  • V = volume (L)
  • n = moles of gas
  • R = universal gas constant (0.08206 L⋅atm/mol⋅K)
  • T = temperature (K)
• Key Point: This law is used when you have a gas and you need to find one of these variables. It's on almost every AP exam, so make sure you know it well!

#Dalton's Law of Partial Pressures

• Concept: In a mixture of gases, each gas exerts its own pressure, and the total pressure is the sum of these partial pressures.
• Equation: $P_{total} = P_a + P_b + P_c + ...$
• Partial Pressure Calculation: $P_a = X_a * P_{total}$ where $X_a$ is the mole fraction of gas A.
• Mole Fraction: $X_a = \frac{moles , of , gas , A}{total , moles , of , gas}$
• Alternative Equation: $P_x = \frac{n_x}{n_{total}} * P_{total}$

#Image Courtesy of Science Notes

#AP Chemistry Reference Table

Here's what you get on the reference sheet. Focus on the highlighted parts for this unit:

#Final Exam Focus

• High Priority Topics: Ideal Gas Law, Dalton's Law, and understanding the relationships in Boyle's, Charles', and Gay-Lussac's laws.
• Common Question Types:
  • Calculations using PV=nRT (often with stoichiometry).
  • Partial pressure problems.
  • Conceptual questions about how changing one variable affects another.
• Time Management: Don't spend too long on one problem. If it's taking too long, move on and come back later.
• Common Pitfalls: Forgetting to convert to Kelvin, using the wrong units, and not understanding the relationships between variables.

#Practice Questions

Practice Question

#Multiple Choice Questions

1. A gas sample has a volume of 10.0 L at 27°C and 740 torr. What volume will the gas occupy at STP? (A) 7.2 L (B) 8.9 L (C) 9.2 L (D) 11.1 L

2. A rigid container holds a mixture of gases. If the temperature of the gas is increased, which of the following will increase? (A) The average speed of the gas molecules (B) The density of the gas (C) The total number of moles of gas (D) The volume of the gas

3. A container holds 2 moles of N2 gas and 1 mole of O2 gas. If the total pressure is 3 atm, what is the partial pressure of N2? (A) 1 atm (B) 1.5 atm (C) 2 atm (D) 2.5 atm

#Free Response Question

A 10.0 L rigid container is filled with 0.50 mol of H2 gas and 0.50 mol of N2 gas at 25°C.

(a) Calculate the partial pressure of each gas in the container.

(b) Calculate the total pressure in the container.

(c) If the temperature of the container is increased to 100°C, what will be the new total pressure in the container?

(d) If 0.25 mol of He gas is added to the container at 100°C, what will be the new total pressure in the container?

#FRQ Scoring Breakdown

(a) Partial pressure calculation (2 points)

• $P_{H_2} = \frac{nRT}{V} = \frac{(0.50 , mol)(0.08206 , L⋅atm/mol⋅K)(298 , K)}{10.0 , L} = 1.22 , atm$ (1 point)
• $P_{N_2} = \frac{nRT}{V} = \frac{(0.50 , mol)(0.08206 , L⋅atm/mol⋅K)(298 , K)}{10.0 , L} = 1.22 , atm$ (1 point)

(b) Total pressure calculation (1 point)

• $P_{total} = P_{H_2} + P_{N_2} = 1.22 , atm + 1.22 , atm = 2.44 , atm$ (1 point)

(c) New total pressure at 100°C (2 points)

• Using $P_1/T_1 = P_2/T_2$ (1 point)
• $P_2 = \frac{P_1T_2}{T_1} = \frac{(2.44 , atm)(373 , K)}{298 , K} = 3.06 , atm$ (1 point)

(d) New total pressure after adding He (2 points)

• Calculate moles of He: $P_{He} = \frac{nRT}{V} = \frac{(0.25 , mol)(0.08206 , L⋅atm/mol⋅K)(373 , K)}{10.0 , L} = 0.765 , atm$ (1 point)
• $P_{total} = 3.06 , atm + 0.765 , atm = 3.83 , atm$ (1 point)

You've got this! Go get 'em! 🌟