Gas Laws and Diffusion Notes

Density

• Density is the ratio of a substance's mass to its volume.
• Density of a gas = Molecular weight ÷ Universal molar volume (22.4)
• Density of a gas mixture = the sum of the % of each gas density in the mixture.
• Density of air = [(gmw x \%N2) + (gmw x \%O2)] ÷ 22.4 L = (28 x .79) gm + (32 x .21) gm ÷ 22.4 L = 1.29 gm/L

Problem 1

• The atomic weight of nitrogen is 14.
• The formula for nitrogen is N2, and its gram molecular weight is 28 grams.
• At normal temperature and pressure, the density of Nitrogen needs to be determined.

Problem 2

• Given:
  • Gram molecular weight of gas X is 15, gas Y is 8, and gas Z is 21
  • Gas mixture composition: gas X = 20\%, gas Y = 30\%, gas Z = 50\%.
• Calculate the density of the gas mixture at normal temperature and pressure.

Diffusion

• Diffusion is the process whereby molecules move from an area of higher concentration to areas of lower concentration.
• Gases with high kinetic energy diffuse more rapidly.

Graham’s Law

• Graham’s Law states that the rate of diffusion of a gas (D) is inversely proportional to the square root of its gram molecular weight.
• D_{gas} = 1 ÷
  \sqrt{gmw}
• Diffusion is based on kinetic activity; anything that increases molecular activity quickens diffusion.
• Lighter gases diffuse rapidly, whereas heavier gases diffuse more slowly.

Fick’s First Law of Diffusion

• Fick’s First Law of Diffusion states that the rate of diffusion of a gas into another gas is proportional to its concentration.
• The bulk movement of gas through a biologic membrane (Vgas) is given by:
  • (A = \text{Cross Sectional area}; D = \text{Diffusion coefficient}; T = \text{Thickness}; P1-2 = \text{Partial pressure gradient})
  • V_{gas} = \frac{A X D}{T} (P1 –P2)
• CO2 and O2 move between and through alveoli, capillary blood, cells, and tissues, driven by pressure gradients of the lungs to maintain cellular metabolism and gas exchange.
• How transport occurs depends on:
  • Surface area (how far is it going)
  • Diffusion constant (what’s diffusing across the membrane)
  • Concentration (pressure) gradient (higher to lower concentration across the capillary membrane)

Solubility of Gases in a Liquid

• Henry’s Law: As the kinetic energy of the gaseous solute increases, its molecules have a greater tendency to escape the attraction of the solvent molecules and return to the gas phase. Therefore, the solubility of a gas decreases as the temperature increases and vice versa.
• Gases can dissolve in liquids.
• Henry’s law predicts how much of a given gas will dissolve in a liquid.
• At a given temperature, the volume of a gas that dissolves in a liquid (V) equals its solubility coefficient (α) times its partial pressure (P_{GAS}).
  • V = α x P_{GAS}
• Carbonated water and soda are good examples of gas (CO2) dissolved in water (H2O).
• Temperature plays a major role in gas solubility.

Solubility Coefficient

• The solubility coefficient equals the volume of a gas that will dissolve in 1ml of a given liquid at standard pressure and specified temperature.
• The Sol Coefficient of O2 at 37 degrees Celsius and 760 torr is .023
• The Sol Coefficient of CO2 at 37 degrees Celsius and 760 torr is .510

Gas Laws

• Boyle’s Law:
  • At constant temperature, the volume of gas varies inversely with the pressure exerted on it.
  • Smaller container, particles travel faster, they hit the walls more often.
  • Kinetic energy increases, increase in frequency leads to an increase in pressure.
  • Pressure becomes larger as gas (volume) becomes smaller.
• Charles’ Law:
  • If the pressure and the mass of a gas remain constant, the volume of the gas varies directly with the absolute temperature.
  • Average kinetic energy in a gas is proportional to the temperature of a gas.
  • Mass is constant.
  • Particles move faster as the temperature gets warmer, increasing kinetic energy.
  • As they move faster, the force exerted on the wall leads to an increase in pressure.
  • If the container is flexible, it will expand until the pressures of gas balance the pressure of the atmosphere.
  • Volume becomes larger as temperature increases.
• Gay Lussac’s Law:
  • If the volume and mass of a gas remain constant, the pressure of the gas varies directly with the absolute temperature.
  • Kinetic energy only increases if the average velocity of the particles increases; the faster particles hit the wall of the container, the greater the force exerted.
  • As temperature increases, kinetic energy/activity increases, and pressure increases.