CL

Gas Laws – Combined vs. Ideal

Fundamental Variables in Gas Laws

  • P – Pressure of the gas
  • V – Volume occupied by the gas
  • n – Amount of gas in moles
  • T – Absolute temperature (must be expressed only in Kelvin for all gas‐law calculations)
  • R – Universal/Ideal gas constant (experimentally determined)

Why Kelvin Is Mandatory

  • Kelvin is denoted by an uppercase K.
  • Kelvin begins at absolute zero; therefore every possible temperature in Kelvin is positive.
  • Working in Kelvin prevents negative values inside proportional relationships, keeping ratios such as \frac{P1V1}{n1T1} physically meaningful.
    • Higher T ⇒ faster molecular motion ⇒ more frequent & forceful molecular collisions ⇒ generally higher P when volume is fixed.

Core Gas Laws Discussed

  • Only two equations will be used:
    1. Combined Gas Law
      \frac{P1 V1}{n1 T1}=\frac{P2 V2}{n2 T2}
    2. Ideal Gas Law
      PV = nRT

Combined Gas Law ("Two-State" Situations)

  • Contains two values for every property (initial 1-state and final 2-state).
  • Use when the problem describes a gas that changes: “before” vs “after” conditions.
  • Typical question pattern: “If I change the pressure from X to Y, what happens to the volume?”
    • Keep identical units for any matched pair (e.g., P1 & P2 both in atm or both in Torr).
    • Temperature must still be Kelvin in both numerator and denominator.

Ideal Gas Law ("Single-State" Situations)

  • One pressure, one volume, one temperature, one mole value, plus the constant R.
  • Use when the problem simply asks for an unknown property without comparing two separate states.
  • Emphasizes the proportionality discovered through experiments that introduced R.

The Gas Constant R

  • Experimental link connecting P, V, n, and T.
  • Common value in chemistry: R = 0.0821\,\text{L·atm·mol}^{-1}\text{K}^{-1} (other unit combinations exist, but units need to be consistent with the chosen pressure & volume units in your calculation).

Consistent Units Checklist

  • Pressure: atm with atm, Torr with Torr, Pa with Pa, etc.
  • Temperature: Convert °C → K before substituting anywhere.
  • Volume: Typically liters (L) if using R = 0.0821.

Temperature Conversion (implicit but vital)

  • Formula to convert whenever Celsius appears: T(\text{K}) = T(^{\circ}!C) + 273.15
    • Ensures temperatures remain positive and compatible with both gas laws.

Practical Decision Tree

  1. Does the problem mention initial and final conditions? → Use Combined Gas Law.
  2. Is there a single set of properties with only one unknown? → Use Ideal Gas Law.
  3. Always convert temperatures to Kelvin and match pressure units across equations.
  4. Plug, solve, and interpret (e.g., higher T tends to raise P at constant V).

Conceptual Takeaways & Connections

  • Gas behavior is fundamentally about molecular collisions; temperature directly controls collision frequency and energy.
  • Both laws derive from the same proportional relationships, but the combined law explicitly compares two snapshots in time, whereas the ideal law captures any one state provided the gas approximates ideal behavior.
  • Recognizing which variables duplicate (two of each vs. one of each) immediately signals which equation to select.