Unit 8: Gases

KMT · Gas Laws · Ideal Gas Law · Dalton's Law · Gas Stoichiometry

💨 Concept Overview

8.1–8.3 — Gas Variables & Unit Conversions

  • P = pressure, V = volume, T = temperature (always in Kelvin!), n = moles
  • Temperature conversion: K = °C + 273
UnitEquivalent to 1 atm
atm1 atm
mmHg / torr760 mmHg = 760 torr
kPa101.325 kPa
Pa101,325 Pa
psi14.7 psi

8.4–8.8 — Kinetic Molecular Theory (KMT)

KMT explains gas behavior at the molecular level:

  • Gas particles are in constant, random motion and are very far apart (mostly empty space)
  • Collisions between particles are elastic (no net energy loss)
  • There are no intermolecular attractive forces between ideal gas particles
  • Temperature is proportional to average kinetic energy of particles
  • Pressure is caused by particle collisions with container walls — more collisions = higher pressure

Relationships from KMT:

  • P ↑ when V ↓ (inverse) — same particles in less space → more collisions
  • P ↑ when T ↑ (direct) — faster particles → harder/more frequent collisions
  • V ↑ when T ↑ (direct) — for flexible containers
  • P ↑ when n ↑ (direct) — more particles → more collisions

8.9–8.11 — Combined Gas Law & STP

(P₁V₁)/T₁ = (P₂V₂)/T₂  |  T must be in Kelvin!
  • STP: Standard Temperature and Pressure = 0°C (273 K) and 1 atm
  • Standard molar volume: 1 mole of any ideal gas = 22.4 L at STP
  • If a variable doesn't change, cancel it out of the combined gas law

8.12 — Ideal Gas Law

PV = nRT  |  R = 0.0821 L·atm/(mol·K)
  • Use when you have 3 of the 4 variables (P, V, n, T) and need the 4th
  • P must be in atm, V in liters, T in Kelvin, n in moles
  • R = 0.0821 L·atm/(mol·K) — the gas constant (provided on test)

8.13 — Dalton's Law of Partial Pressures

P_total = P₁ + P₂ + P₃ + ...
  • In a gas mixture, each gas exerts pressure independently (partial pressure)
  • Total pressure = sum of all partial pressures
  • Mole fraction: χ = n_i / n_total → P_i = χ_i × P_total

8.14–8.16 — Gas Stoichiometry

  • Liter ratios (same T & P): coefficients give L ratios directly (e.g., 2 L H₂ needs 1 L O₂)
  • At STP: use 22.4 L/mol as a conversion factor
  • Non-STP: use PV = nRT to find V or n, then connect to stoichiometry via moles

🃏 Flashcards

Click any card to flip it.

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Kinetic Molecular Theory
Model explaining gas behavior: particles are in constant random motion, far apart, elastic collisions, no intermolecular forces, and temperature = average KE.
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STP
Standard Temperature and Pressure: 0°C (273 K) and 1 atm. At STP, one mole of any ideal gas occupies 22.4 L (standard molar volume).
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Combined Gas Law
(P₁V₁)/T₁ = (P₂V₂)/T₂. Used when amount (n) is constant and conditions change. Temperature MUST be in Kelvin. Cancel any variable held constant.
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Ideal Gas Law
PV = nRT. P in atm, V in L, n in mol, T in K. R = 0.0821 L·atm/(mol·K). Use when you have 3 variables and need the 4th, especially when n changes.
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Dalton's Law
P_total = P₁ + P₂ + P₃ + ... Total pressure of a gas mixture = sum of partial pressures. Each gas acts independently regardless of the others present.
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Pressure (KMT)
Caused by gas particle collisions with the walls of the container. More particles, higher temperature, or smaller volume all increase collision frequency → higher pressure.
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Kelvin Conversion
K = °C + 273. ALWAYS convert to Kelvin before using any gas law formula. 0°C = 273 K; 25°C = 298 K; 100°C = 373 K. Absolute zero = 0 K = −273°C.
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Flexible vs. Rigid Containers
Rigid: volume is fixed — heating increases P. Flexible (balloon/piston): pressure adjusts to stay constant — heating increases V. Knowing the container type tells you which variable is held constant.
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Pressure Conversions
1 atm = 760 mmHg = 760 torr = 101.325 kPa = 101,325 Pa = 14.7 psi. Memorize: 1 atm = 760 mmHg = 101.3 kPa.
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Standard Molar Volume
22.4 L/mol at STP. Any ideal gas occupies 22.4 L per mole at 0°C and 1 atm. Conversion factor: 22.4 L ↔ 1 mol (only valid at STP).
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Explosion vs. Implosion (KMT)
Explosion: pressure inside > outside → container bursts outward. Implosion: pressure outside > inside → container collapses inward. Both caused by pressure imbalance between inside and outside.
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Gas Stoichiometry (STP)
At STP, use 22.4 L/mol to convert between liters of gas and moles, then apply mole ratios. For gases at same T and P, volume ratios = mole ratios from coefficients.

⚡ Quick Review

📝 Practice Quiz

20 multiple choice + 3 short answer.

1. Convert 200.°C to Kelvin.

2. Convert 3.200 atm to mmHg.

3. According to KMT, gas pressure is caused by:

4. A gas occupies 400. mL at 0.00°C. What volume does it occupy at 27.0°C (pressure constant)?

5. A gas occupies 700. mL at 1.70 atm. At what pressure will it occupy 1.00 L (temperature constant)?

6. Calculate the volume of 500. mL of gas collected at 27.0°C and 750. mmHg when converted to STP (0°C, 760 mmHg).

7. What volume does 3.50 mol of gas occupy at 35.0°C and 2.25 atm? (R = 0.0821 L·atm/mol·K)

8. The Goodyear blimp has a volume of 2.00 × 10⁶ L. What mass of helium (MM = 4.003 g/mol) fills it at 27.0°C and 1.00 atm?

9. A mixture of gases has a total pressure of 7.00 atm. It contains 0.683 mol O₂, 0.821 mol He, and 1.09 mol CO. What is the partial pressure of He?

10. The total pressure of a mixture of N₂, H₂, and Cl₂ is 891 mmHg. If P(N₂) = 421 mmHg and P(H₂) = 135 mmHg, what is P(Cl₂)?

11. Which relationship between gas variables is INVERSE?

12. A gas cylinder contains N₂ at 10.00 atm and 20.0°C. The cylinder is left in the sun and heats to 50.0°C. What is the new pressure?

13. What is NOT a postulate of KMT for ideal gases?

14. How many grams of KClO₃ (MM = 122.6 g/mol) are needed to produce 100.0 L of O₂ at STP? (2KClO₃ → 2KCl + 3O₂)

15. For the reaction: 2CO(g) + O₂(g) → 2CO₂(g). When 5.00 L of CO reacts, what volume of O₂ is required at the same temperature and pressure?

16. At what temperature must 2.10 mol of O₂ be for the gas to exist at 15.0 L and 2.60 atm?

17. A container holds Xe at 297.4 kPa, He at 1380. mmHg, and Ar at 3.872 atm. What is the total pressure in atm? (1 atm = 760 mmHg = 101.325 kPa)

18. When a sealed metal can is cooled rapidly, it implodes. The best KMT explanation is:

19. 108 g of CH₄ (MM = 16.05 g/mol) occupies 37.9 L at 8.10 atm. What is the temperature?

20. How many liters of CO₂ at 30.0°C and 1.10 atm are produced when 2.00 g of NaHCO₃ (MM = 84.01) decomposes? 2NaHCO₃ → Na₂CO₃ + H₂O + CO₂

Short Answer Questions

SA1. A 2.50 L sample of gas at 25.0°C and 1.20 atm is heated to 75.0°C and compressed to 0.850 L. (a) Set up the combined gas law with all values. (b) Calculate the new pressure. (c) Using KMT, explain why both the temperature increase AND volume decrease contributed to raising the pressure.

(a) P₁=1.20 atm, V₁=2.50 L, T₁=298 K; P₂=?, V₂=0.850 L, T₂=348 K
(P₁V₁)/T₁ = (P₂V₂)/T₂ → P₂ = (P₁V₁T₂)/(T₁V₂)

(b) P₂ = (1.20 × 2.50 × 348)/(298 × 0.850) = 1044/253.3 = 4.12 atm

(c) Temperature increase (KMT): Higher T → particles move faster → hit walls harder and more frequently → higher pressure. Volume decrease: same number of particles in smaller space → more frequent collisions per unit area → higher pressure. Both effects together multiply to create the large pressure increase.

SA2. A mixture contains O₂ at 50 mmHg, N₂ at 175 mmHg, and CO₂. The total pressure is 250 mmHg. (a) What is the partial pressure of CO₂? (b) If the container holds 21.8 total moles of gas at this total pressure, and the partial pressure of O₂ is 101.3 kPa, how many moles of O₂ are present? (1 atm = 101.325 kPa; P_total = 395.3 kPa for this part)

(a) P_CO₂ = P_total − P_O₂ − P_N₂ = 250 − 50 − 175 = 25 mmHg

(b) Mole fraction of O₂ = P_O₂/P_total = 101.3/395.3 = 0.2563
mol O₂ = 0.2563 × 21.8 = 5.59 mol O₂

SA3. Magnesium reacts with CO₂: 2Mg(s) + CO₂(g) → 2MgO(s) + C(s). How many liters of CO₂ at 0.82 atm and 300. K would react with 5.00 g of Mg (MM = 24.31 g/mol)? Show all steps.

Step 1: mol Mg = 5.00 g ÷ 24.31 g/mol = 0.2057 mol Mg
Step 2: mol CO₂ = 0.2057 mol Mg × (1 mol CO₂ / 2 mol Mg) = 0.1029 mol CO₂
Step 3: Use PV = nRT → V = nRT/P = (0.1029 × 0.0821 × 300) / 0.82
V = 2.534 / 0.82 = 3.09 L CO₂