cm1502 chapter 7thermodynamics part 1- ideal gas

8/12/2019 CM1502 Chapter 7Thermodynamics Part 1- Ideal Gas

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CM 1502 1

Properties of Gases and

Ideal Gas Law

1. States of Matter

2. Ideal Gas Law

3. Four Laws for Ideal Gases

4. Daltons Law of Partial Pressures and Mole Fraction

5. Real Gases

6. Virial (force) and Van der Waals Equations of State for

Real Gases


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CM 1502 2

Physical States of Matter

solid, liquid and gas.

http://www.grc.nasa.gov/WWW/K-12/airplane/state.html

Macroscopic description

Pressure

Volume

Temperature

Microscopic description

Shape of the molecule

Bond angle

Intermolecular forces


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3

The Ideal GasA dilute gas can be modeled as consisting

of point masses that do not interact withone another.

If the pressure of helium is measured as a

function of the volume for different

values of temperature, the set of nonintersecting hyperbolas are obtained.

These curves quantitatively fit the

functional form given below.

is determined to be proportional nR.


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4

Gas constant = R = 8.314 J K-1mol-1 = 0.0821 L atm mol-1 K-1

Volume (V) m3

1 L = 1 dm3= 0.001 m3= 1000 cm3 = 1000 mL

1 mL = 1 cm3= 10-6 m3

Amount (n) moles

n= no. of particles / no. of particles per mole (Avogradros no.)

[Avogradros no. = 6.022 x 1023mol-1]

n= m / Mr

Temperature (T) kelvin (K) 0 C = 273.15 K

Pressure = Force (N) / Area (m2) 1 Pa = 1 Nm-2

760 mm Hg = 760 Torr = 101325 Pa = 1 atm = 1.01325 bar = 14.7 psi(lb in-2)

PV = nRT

Equation of state


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CM 1502 5

A steel tank has a volume of 438 L and is filled with 0.885 kg of O2.

Calculate the pressure (in atm) of O2at 210C.

T = 21 C = (273.15 + 21) K = 294.15K

Equation

V

n

T

PV = nRT

438 L

n = m/Mr = 885 g/32 gmol-1= 27.7 mol

Answer

P =nRT

V=

27.7 mol 294.15 K0.0821 L atm K-1mol-1x

438 L= 1.5 atm

x

*


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CM 1502 6

4 variables P, V, n, T

In the ideal gas law PV = nRT, there are 4 variables P, V, n and T.

Vary one property, another will change, other two are constant.

1. Increase P, V decrease, constant n and T

Boyles Law (V 1/P)

2. Increase T, V increase, constant P and n

Charless Law (V T)

3. Increase T, P increase, constant V and nAmontomss Law(P T)

4. Increase n, V increase, constant P and T

Avogradros Law (V n)


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7

Molar volume.

Molar volume volume taken up per 1 mole. Vm= V/n

According to Avogradros principle, Vm should be the same for all ideal gases.

Figure 5.8 CM1401


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CM 1502 8


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CM 1502 9

Video

http://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swf

Fill in the table.

*

Laws defining ideal gases Description

Boyles Law V 1/P

Charless Law V T

Amontomss Law P T

Avogradros Law V n
http://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swfhttp://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swfhttp://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swfhttp://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swf


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CM 1502 10

In an industrial process, N2enters a constant volume vessel at 300 K

and exerts a pressure of 100 atm. If it is heated to 500 K, calculate the

pressure (in atm) it will exert.

According to Amontoms Law: Increase T, P increase, constant V and n

(P T). So increase T, expect an increase in P.

22

22

11

11

22

22

11

11

Tn

VP

Tn

VPSo,

RTn

VP

andRTn

VP

RnT

PVnRTPV

=

==

=

=

atm167P

500

P

300

100

T

P

T

Pconstant,arenandVSince

2

2

2

2

1

1

=

=

=


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CM 1502 11

Gases mix homogeneously in any proportions.

Each gas in a mixture behaves as if it were the only gas present.

The pressure exerted by each gas in a mixture is calledits partial pressure.

Daltons Law of partial pressures states that the total

pressure in a mixture is the sum of the partial pressures

of the component gases.

The partial pressure of a gas is proportional to its mole

fraction:

PA= XAx Ptotal

Daltons Law of Partial Pressures

XA=nA

ntotal

Gas A

PA= 5 kPa

Gas B

PB= 20 kPa

Gas A + B

PT= PA+ PB=25 kPa

+=


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CM 1502 12

Ideal vs. Real Gases Ideal gases are assumed to have no intermolecular

interactions. Real gases have attractions and repulsions

between molecules.

Real gases behave more and more like ideal gases as

the P is reduced, identical when P = 0 as gas molecules

are too far apart to interact.

In practice, at atmospheric P at sea level (P 100 kPa),

low enough for most real gases to behave ideally.

Ideal gases particles are assumed to occupy no space.

But the assumption is valid only if V is large or [gas] is

very low


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CM 1502 13

Real Gases:

Intermolecular Interactions

Distance between gas molecules:

None/small: repulsions, increase total E of

gas => positive potential E.HIGH PRESSURE

Intermediate: attractions, decrease total E of

gas => negative potential E.MODERATE PRESSURE

Large: no interactions, potential E = 0.

LOW PRESSURE

*


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CM 1502 14Far apart Very near

1nRT

PV=

For 1 mole of gas

The behavior of several

real gases with increasing

external pressure.

1nRT

PV

Boyles Law:

Increase P, V decrease

V 1/P

Attractive

forces

dominate

Repulsive

forces

dominate


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CM 1502 15

Equations of State for real gases

Variations to the ideal gas law has to be made to account for

intermolecular interactions in real gases.

- Van der Waals equations of state

- Others include Virial (force), Berthelot, Dieterici equations of state.

(P +n

2a

V2 )(V nb) = nRT

Van der Waals

equation for n

moles of a real gas

n2a/V2term account for intermolecular interactions and

nb account for volume of the gas particles


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CM 1502 16

0.034

0.211

1.35

2.32

4.19

0.2441.39

1.36

6.49

3.59

2.25

4.17

5.46

He

Ne

Ar

Kr

Xe

H2N2

O2

Cl2CO2

CH4

NH3

H2O

0.0237

0.0171

0.0322

0.0398

0.0511

0.02660.0391

0.0318

0.0562

0.0427

0.0428

0.0371

0.0305

Gas

aatm*L2

mol2

bL

mol

*

Van der Waals Constants for Some Common Gases

VDW

considers

both

attractive and

repulsive

forces.

Large a value : Intermolecular forces are significant

Large b value : Volume of particles is significant

cm1502 chapter 7thermodynamics part 1- ideal gas

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