dr. williamson’s notes for gases - chemistry educationchemed.tamu.edu/chem101/pptnotes/gas laws...

Dr. Williamson’s Notes for Gases

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Gases

Dr. V. M. WilliamsonStudent Version

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Properties of Gases, Liquids

and Solids Properties

Definite shape

Compressibility

Density Fluid

Diffusing Rate

Particle Motion

Gas No

High

Low

Rapid

Rapid

Solid Yes

High No

Very slow

Vibra-tional

Liquid No

Intermediate Yes

Moderate Slow

Restricted

Pressure

3

!  1 atm = pressure of air at sea level

!  Pressure in Denver vs. CS?

Pressure!  Atmospheric

pressure is measured using a barometer.

!  Definitions of standard pressure"  76 cm Hg"  ______ mm Hg"  ______ torr"  _____ atmosphere"  101.3 kPa"  14.69 PSI

4

Manometer

Pgas = Patm

Pgas = ______ Pgas = ________

Kinetic Molecular Theory1.  Gases consist of tiny particles (atoms or molecules)2.  These particles are so small, compared to the

distance between them that the volume of the individual particles can be assumed to be _______ ______

3.  These particles move in rapid, random, straight line motion until they collide with another particle or the walls of the container (causing ___________). The collisions are ______________.

4.  There is __ force of attraction between gas particles or between the particles and the walls of the container.

5.  The ______ _______ ________ of a collection of gas particles depends on the temperature of the gas and nothing else.


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Temperature___ , Average KE__

Volume___ , Pressure__

Pressure____, Volume_____

!  ___________ relationship between P and V

!  Robert Boyle (1627-1691)

Boyle’s Law: Volume-Pressure Relationship

!  V ∝ 1/P or P ∝ 1/V !  V= k (1/P) !  PV = k!  P1V1 = k1 for one sample of a

gas.!  P2V2 = k2 for a sample of the

gas.!  ______for the same gas at the

constant T.!  Boyle’s Law is:

12


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Pressure and Volume Volume and Temperature

Temp__, Volume__#______ Relationship


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Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale

!  J.L. Gay-Lussac in 1802 from unpublished work of Jacques Charles in ~ 1780.

!  Mathematical form of Charles’ law.!  V ∝ T!  V / T = k!  V1 / T1 = k1 for one sample of a gas.!  V2 / T 2 = k2 for a second sample of the gas.!  _________for the same gas at the constant P.!  Charles’ Law is:

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Absolute Zero, Std Temp and Pressure

!  Absolute Zero = _ K!  Standard

Temperature = _____˚C or ________________

!  Standard Pressure = _________

Pressure and Temperature

Temperature___, Pressure____ ___________ Relationship

Pressure and Temperature! P ∝ T! P / T = k! P1 / T1 = k1 for one sample of a gas.! P2 / T 2 = k2 for a second sample of the

gas.!  _______for the same sample of a gas at

the constant V.! So: ! OR

Pressure & Amount


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Pressure and Amount

P ∝___ P= ____

Particles are

Volume-Amount Relationship!  V ∝ n

!  V= k n

!  Avogadro’s Law = 1 mole of any gas at same P and T contains the same ________________ and the same ________________.

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Summary of Gas Laws: The Ideal Gas Law!  Boyle’s Law – V ∝ 1/P (at constant T & n)!  Charles’ Law – V ∝ T (at constant P & n)!  Avogadro’s Law – V ∝ n (at constant T & P)!  Combine these three laws into one statement

V ∝ ____________!  Convert the proportionality into an equality

with a constant (R).V = __________

!  This provides the Ideal Gas Law.__________________ (memorize this one)

!  R is a proportionality constant called the universal gas constant. (R = _____________ L*atm/mol*K)

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Summary of Gas Laws: The Ideal Gas Law!  R has other values if the units are changed.!  R = 8.314 J/mol K

" Use this value in thermodynamics.

!  R = 8.314 kg m2/s2 K mol" Use this later in this chapter for gas velocities.

!  R = 8.314 dm3 kPa/K mol"  This is R in all metric units.

!  R = 1.987 cal/K mol"  This the value of R in calories rather than J.

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Summary of Gas Laws: The Ideal Gas Law!  Find the volume of 1 mol of gas at STP!  PV = nRT

!  V = ________L = molar volume of a gas at STP

29

€

V = nRTP

=

Volume-Amount Relationship

30


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The Combined Gas Law Equation!  A given gas (n) with change of conditions. Useful

when the V, T, and P of a gas are changing.

!  For a given sample of gas: PV = nRT or:

31

€

P VT

= nR

At condition 1 then : P1 V1T1

= nR

At condition 2 then : P2 V2T2

= nR

The Combined Gas Law Equation

!  If T is constant then this becomes Boyles’ Law

!  If P is constant then this becomes Charles’ Law

€

Boyle's LawP1V1 = P2V2

32

€

The combined gas law is :

€

Charles' Law

V1T1

=V2T2

Gas Density!  PV = nRT

€

PRT

= nV

€

But n = mMM

where m = mass; MM = Molar Mass

so PRT

=

€

But density = mV

so

!  Is NH3 lighter than air at STP? Air density =

!  (A) Yes (B) No (C) no enough info

Dalton’s Law of Partial Pressures!  Dalton’s law states that the pressure

exerted by a mixture of gases is the sum of the partial pressures of the individual gases.

Ptotal = PA + PB + PC + .....

35

Partial Pressures/ Mole Fractions!  The partial pressure (PA) of each gas in a

mixture is equal to its mole fraction (XA) times the total pressure:

PA = XA (Ptotal)PB = XB (Ptotal)PC = XC (Ptotal) etc...

where:XA = nA/ntotalXB = nB/ntotalXC = nC/ntotal etc....


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Dalton’s Law: Molecular View

Dalton’s Law: An ApplicationCollecting Gas over Water

The Kinetic-Molecular Theory

u RTMrmsm

=3

!  The root-mean square velocity of gases is a very close approximation to the average gas velocity.

!  Calculating the root-mean square velocity is simple:

40

$  Tocalculatethiscorrectly:%  ThevalueofR=8.314kgm2/s2Kmol%  AndMmustbemolarmassinkg/mol.

Diffusion and Effusion of Gases!  Diffusion is the

!  Effusion is the

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Diffusion and Effusion of Gases!  This is a demonstration of diffusion.

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Diffusion and Effusion of Gases•  The rate of effusion is inversely

proportional to the square roots of the molecular weights or densities.

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1

2

2

1

1

2

2

1

DD

RR

or

MM

RR

=

=

!  Rate of N2 = 1molecule /millisec

!  What is rate of H2?

!  Let 1=H2 and 2 = N2

!  R1 =

KE = ½ m v2

Real Gases: Deviations from Ideality!  PV = nRT assumes that all points of the Kinetic

Molecular Theory are correct.!  Real gases behave ideally at ordinary temperatures

and pressures.!  At ___ temperatures and ____ pressures real gases

do not behave ideally. !  The reasons for the deviations from ideality are:

1.  A GAS PARTICLE DOES HAVE VOLUME, SO VOLUME IS OFF. When the molecules are very close to one another, their volume is important (high pressure-low volume).

2.  GAS PARTICLES DO ATTRACT, SO PRESSURE IS OFF. The molecular interactions become important as the particles slow down at low temperatures.

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P ___, deviation __

n= (PV)/(RT) T = 273 K Different Gases


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T___, deviation __

n= (PV)/(RT) One Gas - Vary T van der Waal’s Equation of State

!  P, V, T and n are measured values of pressure, volume, temperature and moles

!  a and b are obtained experimentally for a gas!  a adjusts P up to account for decrease due to

attractive forces!  b adjusts V down to reflect free volume, not

entire container V

€

(P +n2aV2)(V − nb) = nRT

van der Waal’s Constants

Gas a b (L2.atm/mol2) (L/mol)H2 0.244 0.0266He 0.034 0.0237N2 1.39 0.0391NH3 4.17 0.0371CO2 3.59 0.0427CH4 2.25 0.0428

2H2 + O2 ! 2H2O

O2

Mass-Volume Relationships in Reactions Involving Gases

54


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Mass-Volume Relationships in Reactions Involving Gases

2 mol KClO3 yields 2 mol KCl and 3 mol O22(122.6g) yields 2 (74.6g) and 3 (32.0g)

Those 3 moles of O2 can also be thought of as:

at STP

Or if T and P is known, you could solve for V using

55

g)(2(s)&MnO

(s)3 O 3 + KCl 2KClO 2 2!!! →! Δ

!  What volume of oxygen gas will be collected over water at 26 ˚C and 740 mm Hg when 1.60 g of potassium chlorate is heated, producing potassium chloride?

KClO3! KCl + O22KClO3! 2KCl + 3O2Plan = g KClO3!mol KClO3!mol O2!gas lawMol O2 =

=

!  b) Gas Law to get Volume of O2!  V = nRT/P!  T = 26 + 273 = 299K!  P = P of water + P of oxygen!  From table: at 26 ˚C vp of water = 25 mmHg)!  P of oxygen =!  ____ mmHg (1 atm/760 mmHg) = ____ atm

!  V =€

V = nRTP

=

If 1.8 L of oxygen gas reacts with sufficient hydrogen gas at 25.0˚C and 1.0 atmospheres, how many moles of water will be formed? (Hint: balance equation first!)

(A) ___ moles (B) _____ moles(C) ___ moles (D) _____ moles

dr. williamson’s notes for gases - chemistry educationchemed.tamu.edu/chem101/pptnotes/gas laws...

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