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DAT Review · General Chemistry

Gases and Gas Laws

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On this page 7 sections
  1. In 30 seconds
  2. The college version
  3. Eli explains
  4. Key takeaway
  5. Check yourself
  6. Study tools
  7. Sources & references

In 30 seconds

Gas law problems are reliable DAT points — typically 2–4 questions. You must know the Ideal Gas Law (PV = nRT) cold, be able to apply Boyle's, Charles's, and the Combined Gas Law, and understand Dalton's Law of Partial Pressures. Kinetic Molecular Theory postulates are frequently tested. Always convert temperature to Kelvin — this is the single most common error.

The college version

Core Review

Pressure and Temperature

Pressure is force per unit area. Standard atmospheric pressure: 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 14.7 psi. All gas law calculations require Kelvin temperature: K = °C + 273.15. Using Celsius in any gas law will produce a wrong answer.

The Simple Gas Laws

Boyle's Law (constant T, n): Pressure and volume are inversely proportional.

P₁V₁ = P₂V₂

If volume halves, pressure doubles.

Charles's Law (constant P, n): Volume and absolute temperature are directly proportional.

V₁ / T₁ = V₂ / T₂

A gas expands when heated and contracts when cooled — only if T is in Kelvin.

Avogadro's Law (constant P, T): Volume is directly proportional to moles of gas.

V₁ / n₁ = V₂ / n₂

Combined Gas Law integrates Boyle's, Charles's, and Avogadro's:

P₁V₁ / n₁T₁ = P₂V₂ / n₂T₂

When moles are constant (sealed container), n₁ = n₂ and they cancel.

The Ideal Gas Law

The Ideal Gas Law unifies all simple gas laws:

PV = nRT

P = pressure (atm), V = volume (L), n = moles, T = temperature (K), R = gas constant.

Crucial: choose the correct R value based on pressure units:

  • R = 0.08206 L·atm/mol·K (most common on DAT)
  • R = 8.314 J/mol·K (energy calculations)
  • R = 62.36 L·mmHg/mol·K

Worked Example: What volume does 2.00 mol of an ideal gas occupy at 25°C and 1.50 atm?

  • T = 25 + 273.15 = 298.15 K
  • V = nRT / P = (2.00 × 0.08206 × 298.15) / 1.50 = 48.9 / 1.50 = 32.6 L

STP (Standard Temperature and Pressure): 0°C (273.15 K) and 1 atm. At STP, one mole of any ideal gas occupies 22.4 L (molar volume). For SATP (25°C, 1 atm), molar volume is approximately 24.5 L.

Density of a gas can be derived from the Ideal Gas Law:

d = PM / RT    (where M = molar mass in g/mol)

Dalton's Law of Partial Pressures

In a mixture of non-reactive gases, the total pressure equals the sum of the partial pressures:

P_total = P₁ + P₂ + P₃ + ...

Each gas behaves independently. The partial pressure of gas A is Pₐ = Xₐ × P_total, where Xₐ is the mole fraction (moles A / total moles).

Collected over water: When a gas is collected by water displacement, the total pressure includes water vapor. Subtract the vapor pressure of water at the given temperature to obtain the pressure of the dry gas:

P_dry gas = P_total − P_H₂O

Kinetic Molecular Theory (KMT)

The five postulates:

  1. Gases consist of tiny particles (atoms/molecules) in constant, random motion.
  2. The volume of the gas particles themselves is negligible compared to the volume of the container.
  3. Gas particles exert no attractive or repulsive forces on each other (no intermolecular forces).
  4. Collisions between particles and container walls are perfectly elastic (no kinetic energy lost).
  5. The average kinetic energy of gas particles is directly proportional to Kelvin temperature: KE_avg = (3/2)RT (per mole) or (3/2)k_BT (per particle).

Key KMT consequence: at the same temperature, lighter gas molecules move faster than heavier ones (Graham's Law: rate₁/rate₂ = √(M₂/M₁)).

Key Equations

EquationName
P₁V₁ = P₂V₂Boyle's Law
V₁/T₁ = V₂/T₂Charles's Law
P₁V₁/T₁ = P₂V₂/T₂Combined Gas Law
PV = nRTIdeal Gas Law
P_total = ΣPᵢDalton's Law
Pₐ = Xₐ·P_totalPartial pressure from mole fraction
d = PM/RTGas density

Common Traps

  • Using °C instead of K in any gas law — always add 273.15.
  • Forgetting to subtract water vapor pressure in "collected over water" problems.
  • Mixing up direct and inverse relationships (Boyle's = inverse, Charles's = direct).
  • Using the wrong R value (0.08206 is atm; 8.314 is Joules).
  • Assuming real gases behave ideally at high pressure / low temperature.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a bouncy castle filled with kids bouncing around. If you squeeze the castle walls (smaller volume), the kids hit the walls more often — that's higher pressure (Boyle's Law). If the kids get more energetic (higher temperature), they bounce harder and need more space — the castle expands (Charles's Law). The Ideal Gas Law is just the rulebook that ties together how much space, how much bouncing, how many kids, and how energetic they are. Dalton's Law says if you add grown-ups to the bouncy castle, the total bounciness on the walls is the sum of the kids' bounces plus the grown-ups' bounces.

Key takeaways

  • Kelvin conversion: this is tested explicitly — expect a trap answer in Celsius.
  • Dalton's Law with water vapor subtraction.
  • The relationship between molar mass and gas density/effusion rate.
  • Which R value to use based on pressure units.
  • STP definition and molar volume (22.4 L/mol).

Check yourself

3 review questions from the chapter. Try each one, then open the answer.

  1. A balloon has a volume of 2.50 L at 25°C and 1.00 atm. What is its volume at 50°C and 0.800 atm?

    Show answer

    T₁ = 298 K, T₂ = 323 K. P₁V₁/T₁ = P₂V₂/T₂ → V₂ = (P₁V₁T₂)/(T₁P₂) = (1.00 × 2.50 × 323) / (298 × 0.800) = 808 / 238 = 3.39 L.

  2. What is the density of O₂ gas at 1.00 atm and 273 K? (M(O₂) = 32.00 g/mol, R = 0.08206 L·atm/mol·K)

    Show answer

    d = PM/RT = (1.00 × 32.00) / (0.08206 × 273) = 32.00 / 22.4 = 1.43 g/L.

  3. A mixture contains 0.500 mol N₂ and 1.50 mol O₂ at a total pressure of 2.40 atm. What is the partial pressure of N₂?

    Show answer

    X(N₂) = 0.500 / (0.500 + 1.50) = 0.500 / 2.00 = 0.250. P(N₂) = 0.250 × 2.40 atm = 0.600 atm.

Keep learning

Ready to build on this? Continue to the next lesson.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • State and apply Boyle's Law, Charles's Law, Avogadro's Law, and the Combined Gas Law.
  • Use the Ideal Gas Law (PV = nRT) to solve for any variable.
  • Convert between common pressure units (atm, mmHg, torr, kPa).
  • Apply Dalton's Law of Partial Pressures to gas mixtures.
  • List the five postulates of Kinetic Molecular Theory.
  • Define STP and calculate molar volume.

Sources & references

  1. OpenStax Chemistry 2e, Chapter 9: Gases.
  2. Chemistry LibreTexts: Gas Laws.
  3. NIST: Standard Temperature and Pressure.

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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