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 n_A moles of component A, n_B moles of component B, n_C 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 y_j 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 n_A moles of component A, n_B moles of component B, n_C 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 y_N2=0.78, molecular weight M_N2– 28.01), oxygen (O2, mole fraction y_O2=0.21, molecular weight M_O2– 32.00) and small amounts of other gases (such as argon – A, mole fraction y_A=0.01, molecular weight M_A– 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 M_air is the apparent molecular weight of air. If the gas is a mixture, this equation becomes

(5)

where M_a 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	-	-