A liquid mixture of two components A and B (binary mixture) has a molar volume, v~mixture. There are N moles of the mixture. The mixture is at standard state. (a) (i) Write down an equation that relates the total volume of the mixture (left hand side) to the partial molar volume of A,vA, and the partial molar volume of B,vB, the number of moles of A,NA, and number of moles of B,NB (right hand side). [1 marks] (ii) Explain how the equation in part (i) can be changed to refer to the mole fraction of component A,XA, and not the number of moles of A and B. Write down the new equation. [3 marks] (iii) For an ideal (perfect) binary, liquid mixture explain how the partial molar volumes of the two components change as their mole fraction changes from a value of zero, 0 , to one, 1 . [2 marks] (iv) For a liquid mixture of ethanol and water at standard state, sketch a graph which has partial molar volume of ethanol on the y axis (ordinate) and mole fraction of ethanol on the x axis (abscissa). You do not need to perform a calculation. Comment on the trend in the graph you have sketched. Assume the molar volume of pure ethanol is 58cm3mol1(5.8105m3 mol1). [4 marks] (b) The vapour pressure of pure liquid components benzene and ethyl benzene is given by the Antoine equation, Equation (6). The constants A,B and C are given in Table Q2 below. Here p0 is vapour pressure in kPa and T is temperature in C. ln(p0)=AT+CBTahla? (i) Use this information to calculate the bubble point temperatures of pure benzene and pure ethyl benzene at a pressure of 80kPa. [2 marks] (ii) Further, calculate the bubble point temperature and equilibrium vapour composition of a liquid mixture of benzene and ethyl benzene with a mole fraction of benzene of 0.5 at a pressure of 80kPa. Assume ideal behaviour for the liquid and vapour mixtures. Hint use 90C as an initial estimate. [4 marks] (iii) By calculating the bubble point temperature and equilibrium vapour composition at one other liquid composition, mole fraction of benzene equal to 0.25, plot a temperature composition, Txy, diagram for a mixture of benzene and ethyl benzene at a pressure of 80kPa. [4 marks]