Table 2.7 Calculation for molecular mass of a gas mixture

Gas Component	Percentage by Volume (Vi)	Component Molecular Mass (Mi)	MiVi/ 100	Percentage by Mass
Methane	83.2	16.04	13.35	67.6
Ethane	8.5	30.07	2.56	13.0
Propane	4.4	44.09	1.94	9.8
Butane	2.7	58.12	1.57	7.9
Nitrogen	1.2	28.02	0.34	1.7
	100.00		19.76	100.00
		Mmix = 19.76
Relative density of mixture = 19.76 / 29 = 0.681

 

Vapour pressure of liquid mixtures

Dalton's Law of Partial Pressure states that when several gases occupy a common space, each behaves as though it occupies the space alone. The pressure which each gas exerts is called its partial pressure and the total pressure exerted within the enclosing space is the sum of the partial pressures of the components.

Using Dalton's Law, it is possible to calculate the saturated vapour pressure of a mixture of liquids at a given temperature. The partial pressure exerted by the vapour of a liquid component, is equal to the product of the saturated vapour pressure of that component, if it existed alone at that temperature, multiplied by the mole fraction of the component in the liquid mixture. The total saturated vapour pressure of the mixture will be the sum of the partial pressures of each component.

Thus, P_mt = S (P_nt x F_n)

where       P_mt is saturated vapour pressure of liquid mixture (m) at temperature (t)

                 P_nt is saturated vapour pressure of component (n) at temperature (t)

F_n is mole fraction of component (n) in liquid mixture. This is the mass of that

component divided by the mass of the whole mixture. For example, in

Table 2.7 the mole fraction of the gas mixture is given by:—

For example, for an LPG of the following composition at -40°C:—

Component (n)	Mole Fraction in mixture (Fn)	SVP of component at-40°C (Pnt) (bar)	Partial Pressure of component at -40°C (Pnt x Fn) (bar)	Composition of vapour (Partial Pressure/SVP of mixture x 100) (% by volume)
Ethane Propane n-Butane i-Butane	0.002 0.956 0.030 0.012 1.000	7.748 1.13 0.17 0.284	0.0155 1.0803 0.0051 0.0034 1.1043	1.4 97.8 0.5 0.3 100.0
Saturated Vapour Pressure of mixture = 1.1043 bar.

 

It is clear from the above example how the presence of a small amount of a very volatile component in the liquid mixture can add significantly to the vapour pressure. Because the components of the liquid mixture are in solution with each other, a low boiling component, such as the ethane in the above example, can remain in the liquid phase at temperatures well above the boiling point of the pure substance. However, the vapour phase will contain a higher proportion of such low boiling point material than does the liquid mixture.

2.18 BUBBLE POINTS AND DEW POINTS FOR MIXTURES

As outlined in 2.10 and illustrated in Figure 2.6, a pure liquid will commence to boil at a temperature depending upon the pressure above it. The liquid will continue to boil at

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