Ch. 5 Gases 5.1 Pressure

I. Kinetic Theory A. Refers to the kinetic (motion) energy of particles particularly gases: 1. Gases composed of particles with practically insignificant volumes (mostly empty space between) 2. No attractive/repulsive forces 3. Move rapidly in constant random motion 4. All collisions perfectly elastic (no energy lost when particles hit each other)

II. Pressure Demo: Sudden changes in pressure A. Gas Pressure: force of quickly moving gas particles pushing on an object (ex. Inside of balloon) B. Atmospheric Pressure: force of air above us being pulled down by gravity C. Gas pressure depends on volume of gas, amount of gas (moles) and temperature D. Atmospheric pressure depends on altitude

III. Barometer A. Measures atmospheric pressure B. Based on pushing down Mercury and observing height it travels up tube

C. Atmospheric pressure measured in how many millimeters the Hg travels D. At sea level = 760 mmHg (a.k.a. Torr’s after inventor of barometer) E. 760 millimeters Hg = 760 Torrs = 1 Atmosphere = KiloPascals *** Make sure you can convert between them***

IV. Measuring Gas Pressure A. Manometer: uses Hg to compare the pressure of a gas to the pressure of the atmosphere B. Calculate gas pressure by difference in height of Hg in two tubes P gas = P atmosphere P gas = P atm + h P gas = Patm - h h h

5.2: I. Boyles, Charles, Avogadro A. Boyles Law says Pressure and Volume of gas are inversely related B. P x V = Constant (k) C. Can compare two gas conditions P 1 V 1 = P 2 V 2 D. Works better at low pressure for real gases

II. Charles Law A. Direct relationship between Volume and Temperature at constant pressure B. V/T = constant (k), V 1 /T 1 = V 2 /T 2 C. Plotting V vs. T for different gases, they all intersect at -273º Celsius or 0 Kelvin D. Absolute Zero: theoretical temperature when volume of gas goes to zero or motion stops, never been reached

III. Avogadro’s Law A. Equal volumes of gases at same temperature and constant pressure have same number of particles (n) in moles B. V/n = constant (k)

5.3: I. Ideal Gas Law A. Combination of other gas laws B. PV = k, V/T = k, V/n = k C. PV/Tn = constant called “R” ideal gas constant D. Written as PV = nRT E. R is in units L Atm/ K moles (# depends on units in problem) F L Atm/K mole

5.4: I. Gas Stoichiometry A. Standard Temperature and Pressure: 273 K and 1 Atm, common references for ideal gas calculations B. Molar Volume: volume of one mole of an ideal gas at STP = 22.4 Liters C. Can be used as a conversion factor for stoichiometric calculations

II. Molar Mass of a Gas A. Calculate using gas density and ideal gas law B. Moles (n) = gas mass/molar mass C. P V=[gas mass/molar mass] R T D. P = (gas mass RT)/ (molar mass V) E. gas mass/volume = Density F. P = (Density R T) molar mass G. molar mass = (D R T) P

5.5: I. Dalton’s Law and Partial Pressures A. Dalton’s Law: Total pressure of a mixture of gases equals the sum of the partial pressure of each gas in mixture B. P Total = P 1 + P 2 + … C. Mole fraction (ҳ): ratio of moles of a gas in a mixture to the total number of moles in the mixture D. X = n 1 /ntotal = n 1 /(n 1 + n 2 + …) E. Since in a mixture all the Vol’s and Temp’s are the same: n 1 /ntotal = p 1 /ptotal

5.6: I. Kinetic Theory of Gases A. Assumed that average kinetic energy (motion energy) of gas particles is directly proportional to Kelvin B. KE ave = (3/2) RT C. We can use the derived form of the ave. K.E. equation to come up with an equation for the average velocity of gas particles called “Root Mean Square Velocity” (Urms) D. Urms =, “M” is the molar mass in Kilograms (kg/mole)

E. The “R” value cannot be in L Atm/K mole because there is no Volume or Pressure in the equation to cancel out those units F. R value modified with an energy unit related to Velocity called “Joules”; R = J/Kelvin moles G. Joules is Kilogram meter 2 /second 2 U rms = √(3 x (Kg m 2 /s 2 K mole) x Kelvin)/(Kg/mole) U rms = √(3 x (m 2 /s 2 )) which when the sq.root is taken leaves U rms = (√3) m/s

II. Velocity vs. Particle # at Temp. A. There are more particles at similar velocities at low temp because there is less of a range of possible temps to spread out the particles

5.7: I. Effusion/Diffusion A. Effusion: speed at which gas is transferred into a chamber B. Graham’s Law of Effusion: Rate of effusion gas 1 = √M 2 Rate of effusion gas 2 √M 1 C. M is the molar mass of the gases

A. Diffusion: Rate at which particles mix together B. Particles travel extremely fast, but when mixed with other particles there are collisions that affect their distance C. Smaller particles (less molecular weight) travel faster because they collide less often with other particles II. Diffusion

5.8: I. Real Gases A. Most gases exhibit ideal gas behavior at low pressure and high temperature

II. Correction Factors A. To account for real gas behavior we have to look at the assumptions: B. Ideal gases have negligible volume, be it still has to be considered for real gases C. P = nRT/(V-nb) D. Subtract the volume of container by volume the gas particles take up E. n = # moles of gas, b is an experimentally determined constant

F. Ideal gas have no attractive or repulsive forces, real gases have forces that decrease the pressure in a container G. P observed = P – correction factor H. P obs = (nRT/V-nb) – correction factor I. Since the correction factor depends on the concentration of gas particles per liter (n/V) with a constant for “attractiveness” (a) J. P obs = P – a(n/v) 2

III. Van der Waals Equation A. P obs = (nRT/V-nb) – a(n/V) 2 rearranged to get: B. [P obs + a(n/V) 2 ] x [V-nb] = nRT C. Values for a, b are experimentally determined for each gas, values found in table 5.3