Consider a case in which initially all of the molecules of some component A of a gas mixture are confined by a partition in one region of a system. The partition is then removed. Random movement among the gas molecules will, in time, distribute component A through the mixture. The greater the concentration of A in the partitioned region, the more rapidly will diffusion occur across the boundary once the partition is removed.
The relative proportions of the components in a mixture or a solution are expressed in terms of the concentrations. Any convenient units may be used for concentration, such as g g-1, g kg-1, mg g-1, percentages, parts per million, and so on.
Because the gas laws are based on numbers of molecules, it is often convenient to express concentrations in terms of the relative numbers of molecules of the components. The unit in this case is called the molecular fraction, shortened to mole fraction, which has been introduced in Chapter 2. The mole fraction of a component in a mixture is the proportion of the number of molecules of the component present to the total number of the molecules of all the components.
In a mixture which contains wA kg of component A of molecular weight MA and wB kg of component B of molecular weight MB, the mole fraction:
Notice that (xA + xB) = 1, and so, xB = (1 - xA)
The definition of the mole fraction can be extended to any number of components in a multicomponent mixture. The mole fraction of any one component again expresses the relative number of molecules of that component, to the total number of molecules of all the components in the mixture. Exactly the same method is followed if the weights of the components are expressed in grams. The mole fraction is a ratio, and so has no dimensions.
of ethanol, C2H5OH, is 46 and the molecular weight of water, H2O, is 18.
the components in gas mixtures can be expressed as weight fractions, mole
fractions, and so on. When expressed as mole fractions, they can be related
to the partial pressure of the components. The partial
pressure of a component is that pressure which the component would exert
if it alone occupied the whole volume of the mixture. Partial pressures
of the components are additive, and their sum is equal to the total pressure
of the mixture. The partial pressures and the mole fractions are proportional,
so that the total pressure is made up from the sum of all the partial
pressures, which are in the ratios of the mole fractions of the components.
In the case of gas mixtures, it is also possible to relate weight and volume proportions, as Avogadro's Law states that under equal conditions of temperature and pressure, equal volumes of gases contain equal numbers of molecules. This can be put in another way by saying that in a gas mixture, volume fractions will be proportional to mole fractions.
Since mole fractions are proportional to volume fractions,
The molecular weight
of nitrogen, N2, is 28 and of oxygen, O2, is 32.
Similarly the weight
fraction of oxygen = (21 x 32) / [(79 x 28)
+ (21 x 32)]
As the sum of the two weight fractions must add to 1, the weight fraction of the oxygen could have been found by the subtraction of (1 - 0.77) = 0.23.
To find the mean molecular weight, we must find the weight of one mole of the gas:
Contact-Equilibrium Processes - THEORY > GAS-LIQUID EQUILIBRIA
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