Root Mean Square Velocity (u rms )

u rms = √(3RT/M)

• R = 8.3145 J/K(mol) • T = temp in KELVIN • M = mass of one mole in KILOGRAMS (use the molar mass from the periodic table and convert to kg/mol)

RMS Example • Calculate the root mean square velocity for the atoms in a sample of oxygen gas at 0 º C.

• Answer: 461 m/s • At 300 º C • Answer: 668 m/s

Graham’s Law of Effusion • Diffusion: Movement of particles from areas of higher concentration to lower concentration • Effusion: The process where molecules of a gas in a container randomly pass through a hole in the container.

Graham’s Law of Effusion Rate of Effusion for gas 1 Rate of Effusion for gas 2 = √M 2 √ M 1 M = molar masses of the gases Example 1: Compare the rate of effusion of carbon dioxide with that of hydrogen chloride at the same temperature and pressure.

Answer: CO 2 effuses 0.9X as fast as HCl.

Example #2 If a molecule of neon gas travels at an average of 400m/s at a given temp., estimate the average speed of a molecule of butane gas, C 4 H 10 , at the same temp.

Answer: 235m/s

Summary…

Larger GFM = slower rate of

effusion

.

Real Gases • No gas

actually

follows the ideal gas law • Some come close at low pressures and/or high temperatures • Under certain conditions (see above), gases behave more like ideal gases

Van der Waals Equation • Corrects the ideal gas equation to take nonideal conditions into account

(P + n 2 a)(V-nb) = nRT V 2

P= pressure of gas (atm) V = volume of gas (L) n = moles of gas T = temperature (K) R = 0.08206 L(atm)/mol(K)

Defining Variables…MORE.

a = a constant, different for each gas, that takes into account the attractive forces between molecules (table 5.3 pg. 216) b = a constant, different for each gas, that takes into account the volume of each molecule (table 5.3 pg. 216)

Example • Calculate the pressure exerted by 0.3000 mol of He in a 0.2000 L container at -25.0

º C – Using the ideal gas law – Answer: 30.53 atm – Using van der Waal’s equation – Where a = 0.0341 and b = 0.0237

– Answer: 31.60 atm • You can calculate percent error: 3% – |experimental – accepted|/accepted = ___ x 100 =

Pollution and Atmospheric Gases • Your book discusses these - you can read about them at the end of chapter 5, but we will not be going over them in class…