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Gases

Ch. 10 in Textbook bbc.co.uk

Intro: Bonds vs. IMFs

When 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 itl.chem.utl.edu

Properties of Gases

rapidly diffuse to fill container, homogeneously mixing shape and volume defined by container low density, molecules very spread out high kinetic energy possess vibrational, translational, and rotational motions high entropy high compressibility phy.cuhk.edu.hk

HW: 10.2

Pressure

force/area (N/m 2 ) atmospheric pressure = pushing force of 1 m 2 column of air on surface of Earth due to gravity standard atmospheric pressure (at sea level): 1 atm = 760 mmHg = 760 torr = 1.01325 x 10 5 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 from textbook (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

Example Calculation #0

You 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 Law

the volume of a gas is indirectly related to its pressure (at const. temperature) V = constant x 1/P PV = constant or ex) decrease volume of syringe, pressure of gas increases goiit.com

citycollegiate.com

wps.prenhall.com

Amonton’s Law

the pressure of a gas is directly related to its absolute temperature (at constant volume) P = constant x T P/T = constant or ex) pressure of tires increase as friction from the road heats them up library.thinkquest.com

chemed.chem.purdue.edu

Charles’s Law

the volume of a gas is directly proportional to its absolute temperature (at constant pressure) V = constant x T V/T = constant or ex) a balloon expands as it is heated mike66546.tripod.com

wps.prenhall.com

chemed.chem.purdue.edu

HW: 10.16

Gay-Lussac’s Law

when gases react with one another, the volume ratios in which they react are simple, whole numbers implies that atoms/molecules are reacting in whole-number ratios absoluteastronomy.com

from textbook

Avogadro’s Law

interpreted Gay-Lussac’s Law on a molecular level using Dalton’s atomic theory the volume of a gas is directly related to the number of gas molecules reich-chemistry.wikispaces.com

V = constant x n V/n = constant or

Avogadro’s Hypothesis

equal volumes of (different) gases at the same temperature and pressure contain an equal number of molecules (but not necessarily the same masses) cascience.wordpress.com

HW: 10.19

Ideal Gas Law

combine all gas laws and we get: V = constant x n x T P rearranging and designating R as our gas constant, we get: PV = nRT known as the ideal gas equation because it describes a theoretical gas that is accurately described by this equation used to describe a gas under unchanging conditions zazzle.co.nz

The Gas Constant

many possible values, but we will use R= 0.0821 L•atm/mol•K or R= 62.4 L•torr/mol•K this means that you must always convert volume to liters, pressure to atmospheres or torr, and temperature to Kelvin bytelove.com

Example Calculation #1

Nitrogen 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?

starringthecomputer.com

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

Molar Volume

the volume of 1.000 mol of gas at standard temperature and pressure STP= 1.000 atm and 273 K cartype.com

adozeneggs.com

Example Calculation #2

Calculate the molar volume at STP.

insanewn.info

HW: 10.22

Combined Gas Law

used to describe a gas under changing conditions P 1 T V 1 1 = P 2 V 2 T 2 remember to keep temperature in Kelvin, other units don’t matter so long as they are CONSISTENT if one variable remains constant, remove it from both sides of the equation rapidlearningcenter.com

Example Calculation #3

A 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? cybermentor.ca

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

Gas Density and Molar Mass

we want to find the density of the gas in g/L if we rearrange the ideal gas equation, we can at least get mol/L: n/V = P/RT we can convert moles to grams by multiplying by the molar mass M to maintain the equation, we have to do this to both sides of the equation pure carbon dioxide scienceclarified.com

nM/V = PM/RT d = PM/RT or we can also find the molar mass of an unknown gas by rearranging: M = dRT/P amiestreet.com

Example Calculation #4

What is the density of carbon dioxide at 766.6 torr and 56.1 °C?

themathteacher.org

HW: 10.36, 10.38

Ignore

volumes of gases in chemical reactions hurricansoftwares.com

Dalton’s Law of Partial Pressures

the total pressure of a mixture of gases is the sum of the pressures of the individual gases in other words, each gas exerts its own pressure, independently of the other gases and there are no interactions between different gases P total = P A + P B + P C + ….

chemistry.bd.psu.edu

wps.prenhall.com

we can REMIX! the ideal gas law as follows: P total = (n A + n B + n C + …)RT/V similarly we can use the mole fraction to find the partial pressure of a gas given the total pressure mole fraction, X A P A = X A P total = n A /n total (no units) nndb.com

reich-chemistry.wikispaces.com

Example Calculation #5

2.00 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?

newtonmathtutors.com

HW: 10.54

Gas Collection

a gas produced in a chemical reaction can be collected over water by a displacement method once 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 sciencebuddies.org

P total = P gas + P water P water can be looked up in Appendix B for various temperatures pitchfork.com

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Kinetic-Molecular Theory (KMT)

visual and mathematical model of how an ideal gas behaves according to the ideal gas equation anytime we describe the motion or collisions of a gas, we are using KMT there are 5 assumptions itl.chem.ufl.edu

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

chemprofessor.com

HW: 10.60

Root-Mean-Square Speed, u

rms

KE per molecule = ½mv 2 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

from textbook where k = 1.38 x 10

kg/mol

-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 final unit: m/s (don’t worry about it) shop.rockymountainskates.com

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 quickly see CD-ROM for example aykew.com

Example Calculation #6

What is the rms speed of an oxygen molecule at room temperature?

sodahead.com

HW: 10.62

Graham’s Law of Effusion

from textbook effusion is the escaping of a gas molecule through a tiny hole the faster the rms speed, the more likely that the gas molecule will escape thus, the larger the molecule, the slower it moves and the less likely it is to effuse ex) helium balloon vs. air balloon chem.ufl.edu

Example Calculation #7

By what factor does fluorine gas effuse faster than chlorine gas?

seowoman.com

HW: 10.66

Diffusion

the natural spreading of a gas to fill a space smaller molecules diffuse faster than larger molecules however, collisions limit the diffusion rate mean free path = the avg. distance traveled between collisions funfacts.com.au

tutorvista.com

Real Gases

unlike an ideal gas, real gases are not described perfectly by the ideal gas law real gases have a significant volume (relative to the container volume) and significant attractions or repulsions for one another zazzle.co.uk

neon.chem.uidaho.edu

neon.chem.uidaho.edu

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

HW: 10.67

van der Waals Equation

makes corrections for “real” gases P = _nRT_ – n

2 a

V – nb V

2

where a and b are van der waals constants for different substances nb is the correction for volume n 2 a/V 2 is the correction for attractions chemteam.info

rearranged to its more “familiar” form: (P + n 2 a) (V – nb) = nRT V 2 flickr.com

Example Calculation #8

24.5 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?

cyn.ca

HW: 10.73

inphotos.com