Worked examples: Ideal Gas Law and gas stoichiometry calculations.

📚 Quick Study Guide

• 🌡️ The Ideal Gas Law: $PV = nRT$, where P = pressure, V = volume, n = moles, R = ideal gas constant, and T = temperature (in Kelvin).
• 📏 Standard Temperature and Pressure (STP): 0°C (273.15 K) and 1 atm.
• ⚖️ Molar Mass: The mass of one mole of a substance (g/mol).
• 🔢 Gas Stoichiometry: Use mole ratios from balanced chemical equations to relate the amounts of gaseous reactants and products.
• 🧮 Dalton's Law of Partial Pressures: The total pressure of a mixture of gases is the sum of the partial pressures of each individual gas: $P_{total} = P_1 + P_2 + ... + P_n$.
• 💡Remember to always use consistent units!

🧪 Practice Quiz

1. Question 1: What is the volume occupied by 2 moles of an ideal gas at STP?
   1. A) 11.2 L
   2. B) 22.4 L
   3. C) 44.8 L
   4. D) 67.2 L
2. Question 2: A gas occupies 10 L at 27°C and 1 atm. What is the volume if the temperature is increased to 327°C while keeping the pressure constant?
   1. A) 5 L
   2. B) 15 L
   3. C) 20 L
   4. D) 25 L
3. Question 3: How many grams of $O_2$ are needed to react completely with 4 grams of $H_2$ to form water, according to the equation $2H_2 + O_2 \rightarrow 2H_2O$?
   1. A) 8 g
   2. B) 16 g
   3. C) 32 g
   4. D) 64 g
4. Question 4: If 5 L of $N_2$ and 5 L of $H_2$ react, what is the volume of $NH_3$ produced according to the equation $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, assuming the reaction goes to completion and the temperature and pressure remain constant?
   1. A) 2.5 L
   2. B) 3.33 L
   3. C) 5 L
   4. D) 10 L
5. Question 5: A container holds 2 moles of nitrogen gas and 3 moles of oxygen gas. If the total pressure is 10 atm, what is the partial pressure of nitrogen?
   1. A) 2 atm
   2. B) 4 atm
   3. C) 6 atm
   4. D) 8 atm
6. Question 6: What is the density of methane ($CH_4$) gas at STP?
   1. A) 0.714 g/L
   2. B) 0.800 g/L
   3. C) 1.00 g/L
   4. D) 1.43 g/L
7. Question 7: If 10 grams of $CaCO_3$ decompose according to the equation $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$, what volume of $CO_2$ is produced at STP?
   1. A) 2.24 L
   2. B) 4.48 L
   3. C) 11.2 L
   4. D) 22.4 L