MCAT Chapter 8 General Chemistry: The Gas Phase

Variable Distinguishing Gas Phase

• Pressure 

• Volume 

• Temperature 

• Moles (n)

• Expressed in atm, mmHG, toor, or Pascal (Pa) 

  • 1 atm = 760 mmHG = 760 torr = 101.325 kPA

Standard Temperature and Pressure (STP)

describes conditions in which gas processes usually take place

• 273 degrees kelvin, and 1 atm

• 1 mol of gas occupies 22.4 L

  • STP is not identical to standard state conditions (298 K, 1atm, 1M)

Ideal Gases

• represents a hypothetical gas with molecules that have no intermolecular forces and occupy no volume 

  • Many compressed real gases demonstrate behavior close to ideal 

Ideal Gas Law

• Shows the relationship among four variables that define a sample of gas 

• Can be used to analyze relationship between P and V when all other variables are constant

• Can be used to analyze gas density and molar mass 

Equation 8.1: Ideal Gas Law 

PV = nRT

R = ideal gas constant, 8.21*10^-2 (L*atm/ mol * K)

Or 8.314 (J/K*mol)

n = mol of gas

Density

• : the ratio of the mass per unit volume of a substance 

Equation 8.2: Density of Gas 

⍴ = m/V = PM /RT

• m= mass

• M = molar mass 

Combined gas Law

• Used to related changes in temperature, volume and pressure of a gas 

• Relates Boyle’s, Charles’s, and Gay-Lussac’s laws

• Usually when that gas differs from STP conditions 

P₁V₁ / T₁ = P₂V₂ / T₂ 

Molar Mass (M) og Gas

• Can calculate the molar mass of a gas experimentally using density equation derived from ideal gas law 

  • Can be calculated a the product of the gas’s density at STP and the STP volume of one mol of gas 

    • M = (⍴_STP)(22.4 L/mol)

Avogadro’s Principle

• all gases at a constant temperature and pressure occupy volumes that are directly proportional to the number of moles of gas present 

  • One mol of an gas, will occupy 22.4 liters at STP 
    

Equation 8.4: Avogadro’s Principle 

n/V = k   OR  n₁/V₁ = n₂ / V₂ 

Boyle’s Law

• For a given gaseous sample held at constant temperature (isothermal condition), the volume of the gas is inversely proportional to its pressure

  Equation 8.5: 
  

  PV = k   OR     P₁V₁ = P₂V₂ 

  • K is a constant

  • Special version of ideal gas law where temperature is constant 

Charles’s Law

• At constant pressure, the volume of a gas is proportional to its absolute temperature, expressed in Kelvins 

• Equation 8.4: Charles’s Law 

  V/T = k      OR      V₁/T₁ = V₂/T₂ 
  

  • K is proportionality constant 

  • Special case of ideal gas law where n and pressure are held constant 

Gay-Lussac’s Law

• Complementary to Charles’s law in its derivation of ideal gas law 

• Relates pressure to temperature when volume is constant (isovlumetric)

  Equation 8.4: Gay-Lussac’s Law
  

  P/T = k or  P₁ / T₁ = P₂/ T₂

  • K is proportionality constant 

  • Special case of ideal gas law where n and volume are constant

Dalton’s Law of Partial Pressrues

• When two or more gases that do not chemically interact are found in one vessel, each gas will behave independently of the other 

• Pressure or partial pressure exerted by each gas in mixture will be equal to pressure exerted if it were the only one in the container 
  

Equation 8.8: …… Law of ……….

• Total pressure of a gaseous mixture is equal to the sum of the partial pressures of hte individual components 

P_T = P_A + P_B + P_C …….

Henry’s Law

• At various applied pressures, the concentration of a gas in a liquid increased or decreased 

• Characteristic of a gas’s vapor pressure 

Equation 8.10: …….. Law 

• Relates solubility and pressure 

• Depicted in alveolar gas exchange 

[A] = k_H * P_A or  [A]₁/P₁ = [A]₂ / P₂ = k_H

Vapor Pressure

• the pressure exerted by evaporated particles above the surface of a liquid 

  • Pressure from evaporated molecules forces some of the gas back into the liquid phase, and equilibrium is reached between evaporation and condensation 

Kinetic Molecular Theory

• Used to explain the behavior of gases while other laws mainly described 

• Demonstrate that all gases show similar physical characteristics and behavior irrespective of their particular chemical identity 

• Behavior of real gases deviates from ideal behavior under this theory, but these can corrected via calculations

Assumptions of Kinetic Molecular THeory

• Gases are made up of particles with volumes negligible compared to container volume

• Gases exhibit no intermolecular attractions/repulsions

• Gas particles are in continuous, random motion, undergoing collisions w/ other gases and container walls 

• Collisions between any two gas particles are elastic 

  • No conservation of momentum and kinetic energy

  
  

• Average kinetic energy of gas particles is proportional to the absolute temperature of the gas 

Relating Kinetic Energy of Gas Particles to Temperature and Motion

Equation 8.11: Average Molecular Speeds 

• Using kinetic molecular theory, average kinetic energy of a gas particle can be determined from absolute temperature 

KE = ½,v² = 1.5K_BT

• K_B = Boltzmann constant
  

Equation 8.12: Root-mean-squared-speed

• Defines an average speed by determining the average kinetic energy per particle and calculating the speed to which it corresponds 
  

𝜇_rms = √3RT/M

Maxwell Boltzmann Distribution Curve

• shows the distribution of gas particle speeds at a given temperature 

Diffusion

• the movement of molecules from high concentration to low concentration through a medium 

• Kinetic molecular theory of gases predicts that heavier gases diffuse more slowly than lighter ones because of their differing average speeds 

Graham’s Law

• Under isothermal and isobaric conditions, the rates at which two gases diffuse are inversely proportional to the square roots of their molar mass 

Equation 8.13: ……… Law

r₁/r₂ = √M₂/M₁

Effusion

• The flow of gas particles under pressure from one compartment to another through a small opening 

• Graham used kinetic molecular theory to show that two gases at the same temperature have rates of effusion proportional to the average speeds

Real Gases

• Under nonideal conditions, intermolecular forces and the particles’ volumes become significant for gases

• Figure shows real gas isothermal curves, compare to figure 8.2

  

Deviations Due to Pressure (real gases)

• At moderately high pressure a gas’s volume is less than would be predicted by the ideal gas law due to intermolecular attraction (higher pressure pushes gases closer together)

• At extremely high pressures, the size of the particles become relatively large compared to the distance between

  • This causes gases to take a larger volume than would be predicted by the ideal gas law; 

  • Directly, conflicts ideal gas law which says that gas does not take up space

Deviations Due to Temperature (real gases)

• As the temperature of a gas is decreased, the average speed of the gas molecules decreases and the attractive intermolecular forces become increasingly significant 

• As the temperature of a gas is reduced towards its condensation point, intermolecular attraction causes the gas to have a smaller volume than that which would be predicted by the ideal gas law 

Van der Waals Equation of State

One of many equations that attempt to correct for deviations from ideality that occur when a gas does not closely follow the ideal gas law 

Equation 8.14 

( P + n²a/V²) (V-nb) = nRT

•  a and b are physical constants experimentally determined for each gas 

  • a corrects for attractive forces 

  • b corrects for volume of the molecules themselves