the gaseous state chapter 5 suggested problems to start: 19, 23-27, 29, 31, 33, 35, 39, 41, 45

The Gaseous StateChapter 5

Suggested problems to start: 19, 23-27, 29, 31, 33, 35, 39, 41,

45

Chapter 5 2Copyright © by Houghton Mifflin Company. All rights reserved. 2

Operational Skills

Converting units of pressure.Using the empirical gas laws.Deriving empirical gas laws from the ideal gas law.Using the ideal gas law.Relating gas density and molecular weight.Solving stoichiometry problems involving gases.Calculating partial pressures and mole fractions.Calculating the amount of gas collected over water.Calculating the rms speed of gas molecules.Calculating the ratio of effusion rates of gases.Using the van der Waals equation.


PressureForce exerted per unit area of surface by molecules in motion.

1 atmosphere = 14.7 psi

1 atmosphere = 760 mm Hg (see Fig. 5.2)

1 atmosphere = 101,325 Pascals

1 Pascal = 1 kg/m.s2

P = Force/unit area

Force = mass x acceleration due to gravity (9.81 m/s2)


Figure 5.2: A mercury barometer.


P = gdhP = pressureg = acceleration due to gravity = 9.81 m/s2

d = denistyh = height of column


Figure 5.3: Atmospheric pressure from air mass.

760 mm Hg=1 atm=101 kPa

Pa = Pascal (Blaise--1623-62!)units = kg/(m-s2)

The force of gravity on the columnof air above the earth exerts a pressure at earth’s surface.


Figure 5.4: A flask equipped with a closed-tube manometer.

(a device used to measuregas pressure)


Figure 5.5: Robert Boyle’s experiment (1661.

Volume of gas at 1 atm

2 atm 3 atmGases are compressible!


Figure 5.6: Gas pressure-volume relationship.


The Empirical Gas Laws

Boyle’s Law: The volume of a sample of gas at a given temperature varies inversely with the applied pressure. (Figure 5.5)

V 1/P (constant moles and T)

or

iiff VPVP


A Problem to Consider

A sample of chlorine gas has a volume of 1.8 L at 1.0 atm. If the pressure increases to 4.0 atm (at constant temperature), what would be the new volume?

iiff VPVP using

)atm 0.4()L 8.1()atm 0.1(

PVP

Vf

iif

L 45.0Vf


Figure 5.13: Hot-air ballooning.

Jaques Alexander Charles--1787


Figure 5.7: Effect of temperature on a volume of gas. (A)

N2 (l)

John Dalton (1801) & Joseph Guy Lussac(1802


Figure 5.7: Effect of temperature on a volume of gas. (B)


Figure 5.8: Linear relationship of gas volume and temperature at constant

pressure.



Charles’s Law: The volume occupied by any sample of gas at constant pressure is directly proportional to its absolute temperature.

V Tabs (constant moles and P)

or

i

i

f

f

TV

TV



A sample of methane gas that has a volume of 3.8 L at 5.0 oC is heated to 86.0 oC at constant pressure. Calculate its new volume.

)K278()K359)(L8.3(

TTV

fi

fiV

L 9.4Vf

i

i

f

f

TV

TV

using



Gay-Lussac’s Law: The pressure exerted by a gas at constant volume is directly proportional to its absolute temperature.

P Tabs (constant moles and V)

or

i

i

f

f

TP

TP



An aerosol can has a pressure of 1.4 atm at 25 oC. What pressure would it attain at 1200 oC, assuming the volume remained constant?

i

i

f

f

TP

TP

using

)K298()K1473)(atm4.1(

TTP

fi

fiP

atm9.6Pf



Combined Gas Law: In the event that all three parameters, P, V, and T, are changing, their combined relationship is defined as follows:

f

ff

i

ii

TVP

TVP



A sample of carbon dioxide occupies 4.5 L at 30 oC and 650 mm Hg. What volume would it occupy at 800 mm Hg and 200 oC?

f

ff

i

iiTVP

TVP

using

)K 303)(Hg mm 800()K 473)(L 5.4)(Hg mm 650(

TPTVP

Vif

fiif

L7.5Vf


The volume of one mole of gas is called the molar gas volume, Vm. (See figure 5.10)

Volumes of gases are often compared at standard temperature and pressure (STP), chosen to be 0 oC and 1 atm pressure.


Avogadro’s Law: Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.


Figure 5.10: The molar volume of a gas.

22.4 L


At STP, the molar volume, Vm, that is, the volume occupied by one mole of any gas, is

22.4 L/molSo, the volume of a sample of gas is directly proportional to the number of moles of gas, n.


Avogadro’s Law

nV



A sample of fluorine gas has a volume of 5.80 L at 150.0 oC and 10.5 atm of pressure. How many moles of fluorine gas are present?

First, use the combined empirical gas law to determine the volume at STP.

)K423)(atm0.1()K273)(L80.5)(atm5.10(

TPTVP

Vistd

stdiiSTP

L3.39VSTP



Since Avogadro’s law states that at STP the molar volume is 22.4 L/mol, then

L/mol 22.4V

gas of moles STP

L/mol 22.4L 39.3

gas of moles

mol 1.75 gas of moles


The Ideal Gas Law

From the empirical gas laws, we see that volume varies in proportion to pressure, absolute temperature, and moles.

Law sBoyle' 1/PV

Law sAvogadro' nV Law Charles' TV abs


Combining the three proportionalities, we can obtain the following relationship.

The Ideal Gas Law

This implies that there must exist a proportionality constant governing these relationships.

)( PnTabs R""V

where “R” is the proportionality constant referred to as the ideal gas constant.


The Ideal Gas Law

The numerical value of R can be derived using Avogadro’s law, which states that one mole of any gas at STP will occupy 22.4 liters.

nTVP R

K) mol)(273 (1.00atm) L)(1.00 (22.4 R

KmolatmL 0.0821


The Ideal Gas Law

Thus, the ideal gas equation, is usually expressed in the following form:

nRT PV P is pressure (in atm)V is volume (in liters)n is number of atoms (in moles)R is universal gas constant 0.0821 L.atm/K.molT is temperature (in Kelvin)


An experiment calls for 3.50 moles of chlorine, Cl2. What volume would this be if the gas volume is measured at 34 oC and 2.45 atm?


PnRT V since

atm 2.45K) )(307 1mol)(0.082 (3.50 Kmol

atmL

V then

L 36.0 V then


Figure 5.14: A gas whose density is greater than that of air.


Figure 5.15: Finding the vapor density of a substance.


Figure 5.17: An illustration of Dalton’s law of partial pressures before mixing.

Return to Slide 33


Return to Slide 33



The “real” pressure exerted by 1.00 mol of SO2 at STP is slightly less than the “ideal” pressure.

2

2

V

an -

nb-VnRT

P

L/mol) 79mol)(0.056 (1.000 - L 22.41

)K2.273)( 06mol)(0.082 (1.000 P Kmol

atmL

2mol

atmL2

L) 41.22(

) (6.865mol) (1.000-

2

2

atm 0.989 P


Figure 5.22: Molecular description of Charles’s law.

Return to Slide 41


Figure 5.27: The hydrogen fountain.Photo courtesy of

American Color.

Return to Slide 44


Figure 5.26: Model of gaseous effusion.

Return to Slide 45

the gaseous state chapter 5 suggested problems to start: 19, 23-27, 29, 31, 33, 35, 39, 41, 45

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