(16) Gas Law Formulas and Equations - College Chemistry Study Guide

Pressure Definition

  • Pressure is defined as force divided by area.

  • Standard unit of pressure in physics: pascals (Pa).

    • 1 Pascal = 1 Newton/m².

  • In chemistry, pressure is often measured in:

    • ATM (atmospheres)

      • 1 atm = 101.3 kPa

      • 1 atm = 764 torr

      • 1 atm = 760 mmHg

      • 1 atm = 14.7 psi (pounds per square inch)

Ideal Gas Law

  • The ideal gas law formula is: PV = nRT.

    • P: Pressure (in ATM)

    • V: Volume (in liters)

    • n: Number of moles

    • R: Gas constant

      • R = 0.08206 L·ATM/(mol·K)

      • Alternatively, R = 8.3145 J/(mol·K) (use this with units in pascals and cubic meters)

    • T: Temperature (in Kelvin)

  • To convert Celsius to Kelvin: K = °C + 273.15.

  • To convert Fahrenheit to Celsius: use the appropriate conversion formula.

Combined Gas Law

  • Rearranging the ideal gas law: R = PV/nT.

  • Combined gas law: P1V1/(n1T1) = P2V2/(n2T2); it applies when moles are constant.

  • Combined gas law simplifies to: T1V1/T1 = T2V2/T2 when moles are constant.

  • Requirements: Pressure and Volume must match units; Temperature must be in Kelvin.

Boyle's Law

  • For constant moles and temperature: P1V1 = P2V2.

  • Shows an inverse relationship between volume and pressure.

    • Increasing volume decreases pressure.

Charles's Law

  • For constant pressure and moles: V1/T1 = V2/T2.

  • Demonstrates a direct relationship between volume and temperature.

    • As temperature increases, volume also increases.

Gay-Lussac's Law

  • For constant volume and moles: P1/T1 = P2/T2.

  • Shows direct relationship between pressure and temperature.

    • Increasing temperature results in increasing pressure.

Avogadro's Law

  • For constant pressure and temperature: V1/N1 = V2/N2.

  • Establishes a direct relationship between volume and the number of moles.

    • More moles lead to a larger volume.

Molar Mass and Density

  • Moles can be expressed as n = mass/MW (molar mass).

  • Formula for calculating pressure with molar mass: P × V × MW = mass × R × T.

  • Density of a gas can be calculated: Density = (P × MW) / (RT).

Standard Temperature and Pressure (STP)

  • At STP:

    • Standard temperature = 273 K (0 °C).

    • Standard pressure = 1 atm (760 torr).

    • At STP, one mole occupies a volume of 22.4 L.

Dalton's Law of Partial Pressures

  • Total pressure = sum of partial pressures from each gas: P_total = P1 + P2 + P3....

  • Partial pressure of substance A: PA = mole fraction × total pressure.

  • Mole fraction: Mole fraction = moles of A / total moles.

  • The sum of all mole fractions = 1.

Kinetic Energy and Temperature Relation

  • Average kinetic energy proportional to temperature: KE_avg ∝ T.

  • Use R = 8.3145 J/(mol·K) for kinetic energy calculations.

Root Mean Square Velocity

  • Formula: v_rms = √(3RT/MW) (where MW in kg/mol).

  • For O2: 32 g/mol converts to 0.032 kg/mol.

Graham's Law of Effusion

  • Rate of effusion inversely related to the square root of molecular weight: R2/R1 = √(MW1/MW2).

  • Heavier gases effuse slower, and lighter gases effuse faster.

  • Time ∝ 1/Rate: heaver gases take longer to effuse.