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AP Notes Chapter 11 Properties Of Gases

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Temperature An indirect measure of the average kinetic energy of a collection of particles An indirect measure of the average kinetic energy of a collection of particles KE avg = kT Boltzman Plot Boltzman Plot

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Pressure Measure of the number of collisions between gas particles and a unit area of the wall of the container Pressure = force / unit area

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Force/area English system: pounds/in 2 (psi) pounds/in 2 (psi) Metric system: Newton/m 2 (pascal) Newton/m 2 (pascal)

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Torricelli Barometer h = 760 mm Hg 1 atmosphere pressure

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1 atm = 760 torr (mm Hg) = kPa = bar =14.70 psi

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Manometer P gas P atm h

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Manometer P gas P atm h

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Volume Total space of a container that gases occupy due to the free random motion of the gas molecules

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Relationship between Volume & Pressure of Gases P-V

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V P (at constant T)

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V 1/P (at constant T) Slope = k

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In mathematical terms: y = mx + b Boyles Law

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Relationship between Volume & Temperature of Gases V-T

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In mathematical terms: y = mx + b V = mT + b Charles Law

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Where T must be in Kelvin (K) temperature K = 0 C + 273

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Relationship between Pressure & Temperature of Gases P-T

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In mathematical terms: y = mx + b P = mT + b Gay-Lussacs Law

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Relationship between Volume & Moles of Gases V-n

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In mathematical terms: y = mx + b V = mn + b Avogadros Law

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Avogadros Hypothesis At constant temperature and pressure, equal volumes of gases contain equal number of particles

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3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 37 0 C and 100 kPa. What volume of ammonia is produced at these same conditions?

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Combined Gas Law

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Ideal & Real Gasses

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Kinetic Molecular Theory 1. Gases consist of small particles that are far apart in comparison to their own size. These particles are considered to be tiny points occupying a negligible volume compared to that of their container.

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2. Molecules are in rapid and random straight-line motion. This motion can be described by well-defined and established laws of motion. Kinetic Molecular Theory

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3. The collisions of molecules with the walls of a container or with other molecules are perfectly elastic. That is, no loss of energy occurs. Kinetic Molecular Theory

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4. There are no attractive forces between molecules or between molecules and the walls with which they collide. Kinetic Molecular Theory

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5. At any particular instant, the molecules in a given sample of gas do not all possess the same amount of energy. Kinetic Molecular Theory

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Have 1 particle, with mass m, with velocity PARTICLE IN THE BOX

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Consider the P exerted:

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But: f = ?

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But: f = ma where

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Change in velocity = (

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Thus, the pressure exerted by one particle on a wall is:

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But,

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and, the distance a particle travels between collisions with the same wall is ?

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Substituting into we get:

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Simplifying:

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but,

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This represents the pressure (P) that one particle exerts striking opposite walls in the box.

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Now assume the box contains N particles. Then, N/3 particles are traveling between opposite walls.

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Thus, the total pressure on opposite walls is:

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Substitute & rearrange

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From classical physics where k is the Boltzman constant

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where R = universal gas constant N 0 = Avogadros number

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Ideal Gas Equation

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Note that is similar to the Combined Gas Law derived earlier.

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Variations on Ideal Gas Equation

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4. What is the molar mass of methylamine if g of the gas occupies 125 mL with a pressure of 99.5 kPa at 22 0 C?

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Variations on Ideal Gas Equation Bromine

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5. Calculate the density of fluorine gas at: 30 0 C and 725 torr C and 725 torr. STP STP

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Real Gas Behavior

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Ideal Gas Equation P V = n R T

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Ideal gas P (atm) PV nRT CO 2 H2H2 N2N2 CH 4

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correct for volume of molecules (V - b)

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also correct for attractive forces between molecules

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van der Waals Equation for 1 mole

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van der Waals Equation for n moles

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from CRC Handbook a* b* He Ne *when P(atm) & V(L)

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from CRC Handbook a* b* NH H 2 O *when P(atm) & V(L)

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from CRC Handbook a* b* CCl C 5 H *when P(atm) & V(L)

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Cl 2 gas has a = 6.49, b = Cl 2 gas has a = 6.49, b = For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. P (ideal) = nRT/V = 49.3 atm P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm P (van der Waals) = 29.5 atm

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T & P conditions where a real gas approximates an ideal gas?

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203 K 293 K 673 K Ideal gas P (atm) PV nRT N 2 gas

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T & P conditions where a real gas approximates an ideal gas? high temperature low pressure

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Gaseous Molecular Movement

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Partial Pressure pressure exerted by each component in a mixture of gases

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this assumes that NO interactions occurs between the molecules of gas

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must conclude 1. each gas acts as if it is in container alone 2. each gas collides with the container wall as an event

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where n = # components or P T = P 1 + P 2 + P

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P i V = n i R T or

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thus:

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or

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therefore: n T = n i and P T sum of mols of gas

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Mole Fraction

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Since: and

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Then

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and P i = X i P T

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diffusion is the gradual mixing of molecules of different gases. diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container. effusion is the movement of molecules through a small hole into an empty container.

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rate of average effusion speed

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But... where

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thus then RMS speed

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substituting:

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simplifying Grahams Law NH 3 -HCl

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if d is constant

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if t is constant

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GAS LAW STOICHIOMETRY

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1. Ethanol, C 2 H 5 OH, is often prepared by fermentation of sugars such as glucose, C 6 H 12 O 6, with carbon dioxide as the other product.

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[A] What volume of CO 2 is produced from 125 g of glucose if the reaction is 97.5% efficient?

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[B] Ethanol can also be made from ethylene, C 2 H 4 according to the following chemical system:

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3 C 2 H 4 (g) + 2 H 2 SO 4 C 2 H 5 HSO 4 + (C 2 H 5 ) 2 SO 4 then C 2 H 5 HSO 4 + (C 2 H 5 ) 2 SO 4 + 3H 2 O 3C 2 H 5 OH + 2 H 2 SO 4

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What volume (mL) of 95% ethanol is produced from dm 3 of C 2 H 4 ? The density of 95% ethanol is g/mL.

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2. What is the final pressure [kPa] if g uranium reacts with sufficient fluorine gas to produce gaseous uranium hexafluoride at 32 o C in a 300. L container?

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3. What mass of sodium metal is needed to produce 250 mL of hydrogen gas at 24 o C and 740 Torr?

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