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Special question.

Ideal gas mixtures

The previous treatment of the behavior of gases applies only to single component gases. As the engineer rarely works with pure gases, the behavior of multi-component mixture of gases must be treated. This requires introduction of two additional ideal gases laws.

Dalton`s Law. Dalton`s Law states that each gas in a mixture of gases exerts a pressure equal to that which it would exert if it occupied the same volume as the total mixture. This pressure is called the partial pressure. The total pressure is the sum of the partial pressures. This law is valid only when the mixture and each component of the mixture obey the ideal gas law. It is sometimes called the Law of Additive Pressures.

The partial pressure exerted by each component of the gas mixture can be calculated using the ideal gas law.

Consider a mixture containing nA moles of component A, nB moles of component B, nC moles of component C. The partial pressure exerted by each component of the gas mixture may be determined with the ideal gas equation^

According to Dalton`s Law, the total pressure is the sum of the partial pressures

It follows that the ratio of the partial pressure of component j, pj, to the total pressure of the mixture p is:

(1)

where yj is defined as the mole fraction of its component in the gas mixture. Therefore, the partial pressure of a component of a gas mixture is the product of its mole fraction times the total pressure.

Amagat`s Law. Amagat`s Law states that the total volume of a gaseous mixture is the sum of the volumes that each component would occupy at the given pressure and temperature. The volumes occupied by the individual components are known as the partial volumes. This law is correct only if the mixture and each of the components obey the ideal gas law.

The partial volume occupied by each component of the gas mixture consisting of nA moles of component A, nB moles of component B, nC moles of component C, and so on, can be calculated using the ideal gas law.

Thus, according to Amagat, the total volume is

It follows that the ratio of the partial volume of component j to the total volume of the mixture is

. (2)

This implies that for an ideal gas the volume fraction is equal to the mole fraction.

Apparent Molecular Weight

Since a gas mixture is composed of molecules of various sizes, it is not strictly correct to say that a gas mixture has a molecular weight. However, a gas mixture behaves as if it were a pure gas with definite molecular weight. This molecular weight is known as an apparent molecular weight and is defined as

(3)

Exaple: dry air is a gas mixture consisting essentially of nitrogen (N2, mole fraction yN2=0.78, molecular weight MN2– 28.01), oxygen (O2, mole fraction yO2=0.21, molecular weight MO2– 32.00) and small amounts of other gases (such as argon – A, mole fraction yA=0.01, molecular weight MA– 39.94).

Lets computer the apparent molecular weight of air given its approximate composition.

A value of 29.0 is usually considered sufficiently accurate for engineering calculations.

The specific gravity of a gas is defined as the ratio of the density of the gas to the density of dry air taken at standard conditions of the temperature and pressure. Symbolically,

(4)

Assuming that the behavior of both the gas and air may be represented by the ideal gas law, specific gravity may be given as

where Mair is the apparent molecular weight of air. If the gas is a mixture, this equation becomes

(5)

where Ma is the apparent molecular weight of the gas mixture.

For engineering calculations the density of dry air taken at standard conditions of the temperature and pressure can be accepted at value 1.293.

So we can change the formula (4) into

(6)

The physical constants of hydrocarbons may be found in table 1.

Special lituretature (list):

Table 1 – Natural gas properties

Compound

Formula

Molecular weight

Describing (what is part of the natural gases at standard conditions?)

Critical pressure, psia

Critical temperature, 0F

1

Methane

CH4

16.043

dry gas

667.8

-116.63

2

Ethane

C2H6

30.070

dry gas

707.8

90.09

3

Propane

C3H8

44.097

liquid gas

616.3

206.01

4

n-Butane

C4H10

58.124

liquid gas

550.7

305.65

5

Isobutane

C4H10

58.124

liquid gas

529.1

274.98

6

n-Pentane

C5H12

72.151

condensate

488.6

385.7

7

Isopentane

C5H12

72.151

condensate

490.4

369.10

8

Neopentane

C5H12

72.151

condensate

464.0

321.13

9

n-Hexane

C6H14

86.178

condensate

436.9

453.7

10

Neohexane

C6H14

86.178

condensate

446.8

420.13

11

n-Heptane

C7H16

100.205

condensate

396.8

512.8

12

n-Octane

C8H18

114.232

condensate

360.6

564.22

13

Isooctane

C8H18

114.232

condensate

372.4

519.46

14

n-Nonane

C9H20

128.259

condensate

332.0

610.68

15

n-Decane

C10H22

142.286

condensate

304.0

652.1

16

Carbon Dioxide

CO2

44.010

non-hydrocarbon component

1071.(17)

87.9(23)

17

Hydrogen Sulfide

H2S

34.076

non-hydrocarbon component

1306.(17)

212.7(17)

18

Sulfur Dioxide

SO2

64.059

impurity

1145.(24)

315.5(17)

19

Air

N2O2

28.964

air

547.(2)

-221.3(2)

20

Hydrogen

H2

2.016

non-hydrocarbon component

188.1(17)

-399.8(17)

21

Oxygen

O2

31.999

non-hydrocarbon component

736.9(24)

-181.1(17)

22

Nitrogen

N2

28.013

non-hydrocarbon component

493.0(24)

-232.4(24)

23

Water

H2O

18.015

impurity

3208.(17)

705.6(17)

24

Helium

He

4.033

non-hydrocarbon component

-

-

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