םיזג - WordPress.com · 2010-07-06 · Charles’s and Gay-Lussac’s Law k T V 2 2 1 1 T V T V -273oC, [n,P], [n,P] “Absolute Zero” extrapolation Absolute temperature scale

19.07.101 © Prof. Zvi C. Koren

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Boyle

Charles

Gay-Lussac

AvogadroTorricelli

Kelvin

DaltonGraham

Maxwell Boltzmann


Example:

An automobile air bag is rapidly inflated by the explosion of

sodium azide (NaN3), which releases nitrogen gas when detonated:

2 NaN3(s) 2Na(s) + 3N2(g)

• How much sodium azide is required to

inflate an air bag with a volume of 50.0 L?

• Does the amount of sodium azide

required depend on the temperature of the

gas produced?

• Does altitude affect an air bag's

performance?

Gas Laws:A Practical Application - Air Bags

You will be able to answer these questions at the end of this chapter.


Air-Bag Chemistry

Products

Reactants

(Substances in red

are initially in

the air-bag)

Gas-Generator Reaction

extremely reactive

inert

Na(s)

N2(g)NaN3(s)

Initial Reaction Triggered by

Sensor.

reactive

reactive

inert

K2O(s)

Na2O(s)

N2

Na

KNO3(s)Second Reaction.

inert

Alkaline

silicate

(glass)

K2O

Na2O

SiO2(s)

Final Reaction.

Write balanced chemical reactions for each of these steps.

The signal from the deceleration sensor ignites the gas-generator mixture by an electrical

impulse, creating the high-temperature condition necessary for NaN3 to decompose.

Air-Bag Chemistry


The Mercury Barometer: Measuring Atmospheric Pressure

Evangelista Torricelli (1608 – 1647, Italy):

“We live submerged at the bottom of an ocean of air.”

Aristotle (4th century BCE): “Nature abhors a vacuum.”

Properties of Gases:

Gas Pressures, P


Patm

The Mercury Barometer: Measuring Atmospheric Pressure

Evangelista Torricelli

vacuum

PHg

meniscus

1 standard atmosphere is supported by a

mercury column that is 760 mm Hg in height:

The atmospheric pressure

(or barometric) pressure

can be described in terms of “mm Hg”

1 torr 1 mm Hg

1 atm 760 mm Hg

760 mm Hg 600 mm Hg


Pressure Units

dgh V

mgh

h

h

A

mg

A

w

A

f P

P = pressure

f = force

A = area

w = weight

m = mass

g = acceleration due to gravity = 9.80665 m/s2

h = height of column

d = density = m/V

P = d·g·h

For the mercury barometer (at 0 oC):

dHg = 13.5951 g/cm3 = 0.0135951 kg/cm3 x (102 cm / 1 m)3 = 1.35951 x 104 kg/m3

h = 760 mm Hg = 76 cm Hg = 0.76 m Hg

P = d · g · h

1 atm = (1.35951x104 kg/m3)·(9.80665 m/s2)·(0.76 m) = 1.01325x105 kg/m·s2

= 1.01325 x 105 Pa

= 101.325 kPa

= 1.01325 bar

= 14.6960 lb/in2 (“PSI”, Pounds per Square Inch)

760 (exactly) mm Hg

SI (and other) Units

Energy: 1 J = 1 kg·m2/s2

Force: 1 N = 1 kg·m/s2 (“kms”)

Pressure: 1 Pa = 1 N/m2 = 1 kg/m·s2

1 bar = 105 Pa

1 torr = 1 mm Hg

J = Joule, N = Newton, Pa = Pascal


The Mercury Manometer: Measuring Gas Pressure

OPENManometer

Pgas = Patm + PHg

Pgas PH

g

CLOSEDManometer

Pgas = PHg

vacuum

Pgas

Patm

PH

g

gas gas


Chemists use four basic measurements when

working with gases:

1. The quantity of the gas, n (in moles)

2. The temperature of the gas, T (in kelvins)

3. The volume of gas, V (in liters)

4. The pressure of the gas, P (in atmospheres)

• Changes in gas properties have been mathematically modeled for many years.

• These mathematical models are collectively called gas laws.

• They define the relationships between pairs of gas properties

and experiments confirm these gas laws.

Gas Laws


0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35

P

V

P • V = k or P = k •V–1 , [n,T]

P V-1, [n,T]

Boyle’s Law

hyperbolaP1V1 = P2V2 , [n,T]

gas

piston

Robert Boyle (1627 – 1691)

England


V

T

V = k T, [n,P]

V T, [n,P]

Charles’s and Gay-Lussac’s Law

k T

V

2

2

1

1

T

V

T

V

-273 oC

, [n,P]

, [n,P]

“Absolute

Zero”

extrapolation

Absolute temperature scale is in kelvins: T(K) = t(0C) + 273.15

Jacques Alexandre CésarCharles

(1746-1823)

Joseph LouisGay-Lussac(1778 – 1850)

William Thomson“Lord Kelvin”

(1824 -1907), Irish

The title “Baron Kelvin” was given in honor of his achievements, and named

after the River Kelvin, which flowed past his university in Glasgow, Scotland.


V n , [P,T]

Avogadro’s Law

V

n

V = k n , [P,T] k n

V

2

2

1

1

n

V

n

V , [P,T]

, [P,T]

Lorenzo Romano Amedeo Carlo Avogadro di Quareqa e di Carreto (1776 – 1854)


Combining all three gas laws:

P V

n

= k, [n,T]Boyle:

T+ Charles:

+ Avogadro:

P V= k, [n]

TP V

= k

At STP (Standard Temperature and Pressure), 0oC (= 273.15 K) & 1 atm:

1 mole of an ideal gas occupies 22.414 L of volume.

KmolatmLKmol

Latm

/ 0.082057

) 15.273() 1(

) 414.22() 1(

Tn

VP R

PV = nRT

R

= 8.31 J/mol·K

= 1.99 cal/mol·K

“Gas Constant”

Ideal Gas Law

= [energy/mol·K]

19.07.10

mole

Mole Day is celebrated on Oct. 23rd from 6:02 am to 6:02 pm

© Prof. Zvi C. Koren14 Happy Mole Day to You!!!


mole

Summary: Moles in Chemistry

# of items: Avogadro’s #

Mass: m/MW

Solution: MV

Gas: PV = nRT


Problem:

Potassium superoxide is used to purify air in a spacecraft.

What mass of KO2 is required to recycle 500.0 mL of CO2 at 25.00 oC and 750. mmHg?

4KO2(s) + 2CO2(g) 2K2CO3(s) + 3O2(g)

Solution:

Stoichiometric Flow-Chart:

RT

PV n

2CO 750. mmHg

Hgmm

atm

760

1 = 0.98684 atmP =

V = L500.0 mL

mL

L

1000

1 = 0.5000

25.00 + 273.15 = 298.15 K

2COn = 0.020168

0.020168 mol CO2

2

2

CO 2

KO 4

mol

mol

2

2

KO 1

KO 71.0971

mol

g= 2.87 g KO2

R = 0.082057 L·atm/mol·K

T =

? MWmass KO2 moles KO2 rxn PV=nRT

moles CO2 (V, T, P) of CO2

Gas Laws and Chemical Reactions: Stoichiometry


Ptotal = ΣPi = P1 + P2 + P3 + …

= n1RT/V + n2RT/V + n3RT/V + …

= RT/V

1

1

1

1

1

2

2

2 2

2

2

2 3

3

3

(n1 + n2 + n3 + …)

V

RTn P total

total

Pi = partial pressure of gas i

= niRT/V

RT/Vn

RT/Vn

P

P

total

i

total

i n

n

total

i Xi mole fraction of gas i ΣXi = 1

Pi = Xi•Ptotal

= ntotal RT/V

Gas Mixtures and Dalton’s Law of Partial Pressures

John Dalton (1766-1844), England


PV = nRTFrom:

RT

PV n

MW

m

MWRT

P

V

m

MWRT

P d d MW, [P,T]

For example:

)/ 00.32() )(273 (0.0821

1 STP @ d

2O molgKKatm/molL

atm

= 1.43 g/L

Gas Density


Determining the Molecular Weight of a Volatile Liquid

vent Measurements:

Mass of vapor = 1.2189 g

(measurements of empty and filled flask)

Volume of flask = 510.0 mL

(measured with water)

Temperature of vapor = 100.0 oC

Atmospheric pressure = 745 torr

MW = ?

Dumas Method



Ideal Gas Properties:

• No intermolecular forces

• Molecular volume is negligible

Tenets of KMT:

1. Gases consist of molecules whose separation is much larger than the volume of the

molecules themselves.

2. The gas molecules are in continuous random and rapid motion.

3. The average kinetic energy of the gas molecules is determined by the absolute gas

temperature.

Notes:

All gas molecules at the same T, regardless of mass, have the

same average kinetic energy.

Temperature is a bulk (macroscopic) property, and not one

based on an individual (microscopic) molecule)

4. Gas molecules collide with each other and with the walls of the container, but they

do so without loss of energy. These collisions are perfectly elastic.

Kinetic Molecular Theory (KMT) of Gases


KEmole3(½ RT) = = ½Mv2

1/21/2

M

3RT )(

2v

____

vrms = root-mean-square velocity (m/s)

R = (J/mol·K)

MW = (kg/mol)

Average Kinetic Energy for one mole KEmole T

Kinetic Energy for one molecule KEmolecule = ½mv2, m mass of one molecule

Kinetic Energy for one mole KEmole = ½Mv2, M MW, Molecular weight

Average Kinetic Energies, KE

Average Kinetic Energy for one mole KEmole = ½Mv2,

But also:

= 3(½ RT)

proof is not for this course

Combine these two

Graham’s Law

of Diffusion

for 2 Gases

at same T:

v1/v2 = (M2/M1)½

Thomas Graham(1805 – 1869), Scotland


Applications of KMT

1. Diffusion of NH3(g) vs. HCl(g)


2. Separation of Uranium Isotopes


Ludwig Eduard Boltzmann

(1844 – 1906), Austria James Clerk Maxwell

(1831 – 1879), Scotland

Maxwell-Boltzmann Distribution of Molecular Speeds

= f (T, MW)

Why do molecules, all at the same T,

have such a wide span of velocities?


Maxwell-Boltzmann Distribution of Molecular Velocities

MW Effects:

> >

(continued)


Temperature Effects 1:

(continued)


Temperature Effects 2:


Documents

םיזג - WordPress.com · 2010-07-06 · Charles’s and Gay-Lussac’s Law k T V 2 2 1 1 T V T V -273oC, [n,P], [n,P] “Absolute Zero” extrapolation Absolute temperature scale