Diffusion, Effusion, and Graham’s Law of Diffusion

What is diffusion? Low High The movement of particles from regions of higher concentrations to regions of lower concentration. Eventually, the particles will disperse evenly throughout the space. Low High

What is effusion? The passage of a gas under pressure through a tiny opening.

Graham’s law of diffusion Thomas Graham studied effusion in detail and determined that the rate of effusion is indirectly proportional to the square root of the molar mass of the gas, if pressure and temperature are kept constant. In other words: vA vB = Molar MassB Molar MassA 

Example Problems At the same temperature, which molecule travels faster, O2 or N2? How much faster? At room temperature, Xe atoms have an average speed of 240 m/s. At the same temperature, what is the speed of H2 molecules? What is the molar mass of a gas if it diffuses 0.907 times the speed of argon gas?

Answers 1) N2 (lower molar mass) (32/28) = 1.07 times faster 2) x/240 =  (131.3/2) x/240 = 8.10 x = 1944 m/s 3) 1/0.907 = (x/39.9) (1/0.907)2 = ((x/39.9))2 1.216 = x/39.9 x = 48.5 g/mol

Henry’s Law Effect of pressure on gas solubility The solubilities of solids and liquids are not affected appreciably by pressure When the pressure of a gas is increased, as in (b), the rate at which gas molecules enter the solution increases The concentration of solute molecules at equilibrium increases in proportion to the pressure So the solubility of a gas increases with pressure

Pressure and Solubility of Gases Solubility decreases as pressure decreases Soft drink bottled under CO2 pressure greater than 1 atm When the bottle is opened, partial pressure of CO2 above the solution decreases Solubility of CO2 decreases - > bubbles 13.5

Pressure and Solubility of Gases Solubility decreases as pressure decreases In many consumer beverages such as soft drinks, carbonation is used to give "bite". Contrary to popular belief, the fizzy taste is caused by the dilute carbonic acid inducing a slight burning sensation, and is not caused by the presence of bubbles. This can be shown by drinking a fizzy drink in a hyperbaric chamber at the same pressure as the beverage. This gives much the same taste, but the bubbles are completely absent. 13.5

Pressure and Solubility of Gases Solubility decreases as pressure decreases In many consumer beverages such as soft drinks, carbonation is used to give "bite". Contrary to popular belief, the fizzy taste is caused by the dilute carbonic acid inducing a slight burning sensation, and is not caused by the presence of bubbles. This can be shown by drinking a fizzy drink in a hyperbaric chamber at the same pressure as the beverage. This gives much the same taste, but the bubbles are completely absent. 13.5

Pressure and Solubility of Gases The solubility of a gas in a liquid is proportional to the pressure of the gas over the solution (Henry’s law). c is the concentration (M) of the dissolved gas c = kP P is the pressure of the gas over the solution k is a constant (mol/L•atm) that depends only on temperature C1/P1 =C2/P2 low P high P low c high c 13.5

SAMPLE EXERCISE A Henry’s Law Calculation Calculate the concentration of CO2 in a soft drink that is bottled with a partial pressure of CO2 of 4.0 atm over the liquid at 25°C. The Henry’s law constant for CO2 in water at this temperature is 3.1  10–2 mol/L-atm. Solution Analyze: We are given the partial pressure of CO2, and the Henry’s law constant, k, and asked to calculate the concentration of CO2 in the solution. Plan: With the information given, we can use Henry’s law to calculate the solubility. Solve:   Check: The units are correct for solubility, and the answer has two significant figures consistent with both the partial pressure of CO2 and the value of Henry’s constant. 2 PRACTICE EXERCISE Calculate the concentration of CO2 in a soft drink after the bottle is opened and equilibrates at 25°C under a CO2 partial pressure of 3.0  10–4 atm.

Blood gases and deep sea diving Solubility increases as pressure increases Divers who use compressed gases must be concerned about the solubility of the gases in their blood At depth, the blood contains higher concentrations of dissolved gases Ascension, if too rapid, will cause the blood to fizz similar to 7-UP when opened! This is called decompression sickness, or “the bends”, which is painful and can be fatal because the bubbles affect things like nerve impulses

Temperature and Solubility Solubility of most solid solutes in water increases with increasing temperature In contrast, solubility of gases in water decreases with increasing temperature 13.4

Temperature and Solubility Carbonated beverages go “flat” as they warm due to a decreased solubility of dissolved CO2 Bubbles form on the inside wall of a cooking pot when water is heated even though the temperature is well below boiling Thermal pollution of lakes and streams causes low oxygen levels in deeper layers In contrast, solubility of gases in water decreases with increasing temperature 13.4