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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 KEavg = kT 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/in2 (psi) Metric system:**

Newton/m2 (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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Patm Manometer h Pgas

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Patm Manometer h Pgas

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

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**In mathematical terms:**

y = mx + b Boyle’s 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 = 0C + 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-Lussac’s 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 Avogadro’s Law

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**Avogadro’s 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**

3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 370C 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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**Kinetic Molecular Theory**

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

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**Kinetic Molecular Theory**

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.

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**Kinetic Molecular Theory**

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

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**Kinetic Molecular Theory**

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

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

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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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But, 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**

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

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**the total pressure on opposite walls is:**

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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**R = universal gas constant**

where R = universal gas constant N0 = Avogadro’s 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 220C?

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**Variations on Ideal Gas Equation**

Bromine Variations on Ideal Gas Equation

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**5. Calculate the density of fluorine gas at:**

300C and 725 torr. STP

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Real Gas Behavior

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Ideal Gas Equation P V = n R T

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N2 2.0 CH4 H2 PV nRT 1.0 Ideal gas CO2 P (atm)

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**“correct” for volume of molecules**

(V - b)

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**attractive forces between molecules**

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 H2O *when P(atm) & V(L)

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from CRC Handbook a* b* CCl C5H *when P(atm) & V(L)

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Cl2 gas has a = 6.49, b = For 8.0 mol Cl2 in a 4.0 L tank at 27oC. P (ideal) = nRT/V = 49.3 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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**N2 gas PV nRT 203 K 293 K 1.8 1.4 673 K Ideal 1.0 gas 0.6**

P (atm)

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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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**pressure exerted by each component in a mixture of gases**

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 PT = P1 + P2 + P

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Pi V = ni R T or

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thus:

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or

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therefore: nT = ni and PT 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 Pi = Xi PT

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**diffusion is the gradual mixing of molecules of different gases.**

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 Graham’s Law NH3-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, C2H5OH, is often prepared by fermentation of sugars such as glucose, C6H12O6, with carbon dioxide as the other product.

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**[A] What volume of CO2 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, C2H4 according to the following chemical system:**

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3 C2H4(g) + 2 H2SO4 C2H5HSO4 + (C2H5)2SO4 then C2H5HSO4 + (C2H5)2SO4 + 3H2O 3C2H5OH H2SO4

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**What volume (mL) of 95% ethanol is produced from 142. 5 dm3 of C2H4**

What volume (mL) of 95% ethanol is produced from dm3 of C2H4? 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 32oC 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 24oC and 740 Torr?

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