Gases

Ch. 10 in Textbook

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Intro: Bonds vs. IMFsWhen separating an ionic solid, BONDS must be broken to separate the ions (strong)When separating molecules in a molecular solid, INTERMOLECULAR FORCES (IMFs) must be broken to separate the molecules (weak)The behavior of gases is governed by IMFs, not bonds

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Properties of Gasesrapidly diffuse to fill container, homogeneously mixingshape and volume defined by containerlow density, molecules very spread outhigh kinetic energypossess vibrational, translational, and rotational motionshigh entropyhigh compressibility

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HW: 10.2

Pressureforce/area (N/m2)atmospheric pressure = pushing force of 1 m2 column of air on surface of Earth due to gravitystandard atmospheric pressure (at sea level): 1 atm = 760 mmHg = 760 torr = 1.01325 x 105 Pa = 101.325 kPa

mercury barometer

from textbook

HW: 10.8 (a)-(c)

Manometers

similar to barometer, good for low pressure gases(a) closed-tube manometer(b) open-tube manometer when atmospheric pressure is greater than that of the gas(c) open-tube manometer when atmospheric pressure is lower than that of the gas

from textbook

Example Calculation #0You are given an open-end manometer. If the atmospheric pressure is 0.975 atm and the height of the mercury is 67 mm higher on the end open to the atmosphere, what is the pressure of the enclosed gas in atm?

HW: 10.14

Boyle’s Lawthe volume of a gas is indirectly related to its pressure (at const. temperature)V = constant x 1/P or

PV = constantex) decrease volume of syringe, pressure of gas increases

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Amonton’s Lawthe pressure of a gas is directly related to its absolute temperature (at constant volume)P = constant x T orP/T = constantex) pressure of tires increase as friction from the road heats them up

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Charles’s Lawthe volume of a gas is directly proportional to its absolute temperature (at constant pressure)V = constant x T orV/T = constantex) a balloon expands as it is heated

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HW: 10.16

Gay-Lussac’s Lawwhen gases react with one another, the volume ratios in which they react are simple, whole numbersimplies that atoms/molecules are reacting in whole-number ratios

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from textbook

Avogadro’s Lawinterpreted Gay-Lussac’s Law on a molecular level using Dalton’s atomic theorythe volume of a gas is directly related to the number of gas moleculesV = constant x n or

V/n = constant

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Avogadro’s Hypothesisequal volumes of (different) gases at the same temperature and pressure contain an equal number of molecules (but not necessarily the same masses)

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HW: 10.19

Ideal Gas Lawcombine all gas laws and we get: V = constant x n x T Prearranging and designating R as our gas constant, we get:PV = nRTknown as the ideal gas equation because it describes a theoretical gas that is accurately described by this equationused to describe a gas under unchanging conditions

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The Gas Constantmany possible values, but we will use R= 0.0821 L•atm/mol•K or

R= 62.4 L•torr/mol•Kthis means that you must always convert volume to liters, pressure to atmospheres or torr, and temperature to Kelvin

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Example Calculation #1Nitrogen gas fills a syringe at 28.5 °C. The pressure equals 111.3 kPa when the syringe expands to 35.6 mL. How many grams of nitrogen are present?

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HW: 10.24 (c) & (d), 10.30 (a)

Molar Volumethe volume of 1.000 mol of gas at standard temperature and pressureSTP= 1.000 atm and 273 K

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Example Calculation #2Calculate the molar volume at STP.

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HW: 10.22

Combined Gas Lawused to describe a gas under changing conditionsP1V1 = P2V2

T1 T2

remember to keep temperature in Kelvin, other units don’t matter so long as they are CONSISTENTif one variable remains constant, remove it from both sides of the equation

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Example Calculation #3A gas at STP is heated to a temperature of 88.0 °C, pressure of 768 torr, and a volume of 56.7 mL. What was the original volume of the gas?

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HW: 10.18, 10.32 (a) & (b)

Gas Density and Molar Masswe want to find the density of the gas in g/Lif we rearrange the ideal gas equation, we can at least get mol/L:

n/V = P/RTwe can convert moles to grams by multiplying by the molar mass Mto maintain the equation, we have to do this to both sides of the equation

pure carbon dioxide

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nM/V = PM/RT ord = PM/RT

we can also find the molar mass of an unknown gas by rearranging: M = dRT/P

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Example Calculation #4What is the density of carbon dioxide at 766.6 torr and 56.1 °C?

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HW: 10.36, 10.38

Ignore volumes of gases in chemical reactions

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Dalton’s Law of Partial Pressuresthe total pressure of a mixture of gases is the sum of the pressures of the individual gasesin other words, each gas exerts its own pressure, independently of the other gases and there are no interactions between different gasesPtotal = PA + PB + PC + ….

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we can REMIX! the ideal gas law as follows:

Ptotal = (nA + nB + nC + …)RT/V

similarly we can use the mole fraction to find the partial pressure of a gas given the total pressuremole fraction, XA = nA/ntotal (no units)

PA = XA Ptotal

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Example Calculation #52.00 g of oxygen and 2.00 g of nitrogen are mixed in a 2.0 L vessel at 25.0 °C. What is the total pressure of the vessel and the partial pressure of each gas component?

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HW: 10.54

Gas Collection a gas produced in a chemical reaction can be collected over water by a displacement methodonce the gas is collected, the container must be lowered or raised to equalize outside and inside pressures (water levels equalize)because water vaporizes (even at room temp.) we must include this in our calcs

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Ptotal = Pgas + Pwater

Pwater can be looked up in Appendix B for various temperatures

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Kinetic-Molecular Theory (KMT)visual and mathematical model of how an ideal gas behaves according to the ideal gas equationanytime we describe the motion or collisions of a gas, we are using KMTthere are 5 assumptions

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many molecules in continuous, random motionsmolecular volume is negligible compared to container volumeattractive and repulsive forces between molecules are negligibleKE is transferred during collisions, but the avg. KE does not (at const. temp.)avg. KE is proportional to the absolute temp.

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HW: 10.60

Root-Mean-Square Speed, urms

KE per molecule = ½mv2

each molecule in a gas has its own KE, but the avg. KE remains the same at a given temp.the rms speed, u, is the speed of a molecule that possesses avg. KE (center of curve)notice how the distribution of speeds changes with increasing temperature

from textbook

where k = 1.38 x 10-23 J/K (Boltzmann’s constant) and m = mass of molecule in kg or where R = 8.31 J/mol•K and M = molar mass in kg/molfinal unit: m/s (don’t worry about it)

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from textbook

based on formula, at the same temp, the more massive the molecule the more slowly it moves compared to a less massive molecule which moves more quicklysee CD-ROM for example

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Example Calculation #6What is the rms speed of an oxygen molecule at room temperature?

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HW: 10.62

Graham’s Law of Effusion

effusion is the escaping of a gas molecule through a tiny holethe faster the rms speed, the more likely that the gas molecule will escapethus, the larger the molecule, the slower it moves and the less likely it is to effuseex) helium balloon vs. air balloon

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from textbook

Example Calculation #7By what factor does fluorine gas effuse faster than chlorine gas?

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HW: 10.66

Diffusionthe natural spreading of a gas to fill a spacesmaller molecules diffuse faster than larger moleculeshowever, collisions limit the diffusion ratemean free path = the avg. distance traveled between collisions

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Real Gasesunlike an ideal gas, real gases are not described perfectly by the ideal gas lawreal gases have a significant volume (relative to the container volume) and significant attractions or repulsions for one another

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real gases are most ideal at a higher temperatures and a lower pressures

from textbook

HW: 10.67

van der Waals Equationmakes corrections for “real” gasesP = _nRT_ – n2a V – nb V2

where a and b are van der waals constants for different substancesnb is the correction for volumen2a/V2 is the correction for attractions

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rearranged to its more “familiar” form:(P + n2a) (V – nb) = nRT

V2

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Example Calculation #824.5 g of carbon dioxide exerts a pressure of 1.12 atm at a volume of 0.2452 L. What is the temperature of the gas?

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HW: 10.73

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