Which of the following statements is always true for a liquid mixture of two components A and B 111equilibrium with a mixture of their vapours?(a) f.1A(l) = f.1B(l)and f.1A(g) = f.1B(g);(c) f.1A(I) = f.1A(g) and f.1B(I)= f.1B(g);(b) f.1A(l) = f.1A(g) = f.1B(I)= f.1B(g)(d) f.1A(l) -# f.1A(g) -# f.1B(l)-# f.1B(g)
Question
Which of the following statements is always true for a liquid mixture of two components A and B 111equilibrium with a mixture of their vapours?(a) f.1A(l) = f.1B(l)and f.1A(g) = f.1B(g);(c) f.1A(I) = f.1A(g) and f.1B(I)= f.1B(g);(b) f.1A(l) = f.1A(g) = f.1B(I)= f.1B(g)(d) f.1A(l) -# f.1A(g) -# f.1B(l)-# f.1B(g)
Solution
The statement that is always true for a liquid mixture of two components A and B in equilibrium with a mixture of their vapours is (c) f.1A(l) = f.1A(g) and f.1B(l)= f.1B(g).
This is based on Raoult's law which states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapour pressure of the pure component multiplied by its mole fraction in the mixture.
So, the fugacity (f) of component A in the liquid phase (l) is equal to the fugacity of component A in the gas phase (g), and the same applies to component B. This is because at equilibrium, the chemical potential (and therefore the fugacity, which is a measure of chemical potential in real gases) of each component is the same in the liquid and gas phases.
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