In this problem you will determine an expression for the binary entropy of mixing. consider an isolated system composed of two types of particles a and b initially separated by a partition, as in fig. 3.13. the particles are constrained to occupy sites on a regular lattice, and there are exactly as many lattice sites as there are initial particles. the use of a lattice is an approximation, but it will give a very general expression for the entropy of mixing. there are no potential or kinetic energies, and swapping two particles of the same color is not considered a new configuration, i. e., particles of the same type are indistinguishable from each other. at some point the partition is removed, and particles freely mix. using its relationship to the density of states, write expressions for the entropy before and after the wall is removed. find the entropy difference, asmix = satter - sbefore. use stirling's approximation to simplify your answer. express your final answer in terms of the mole fractions, xana/n and xg = n/ny, and the total number of molecules nt = na + ng-

Astudent made a graph plotting the progress of a reaction over time. the student forgot to label the y-axis of the graph. a graph is shown with two graph lines. one graph line starts at a higher position on the y axis and slopes downwards towards the right. the other graph line starts at a lower position on the y axis and slopes upwards towards the right. the two graph lines stop short of intersecting each other and continue as separate lines which gradually become straight and parallel to the x axis. a vertical line is shown at a point where the two graph lines finally became parallel to the x axis. this vertical line is labeled equilibrium. the title on the x axis is time and an arrow pointing towards the right is shown above time. the title on the y axis is left blank. what best explains the label that the student should use on the y-axis? amount, because as the amount of product decreases, the amount of reactant increases over time. reaction rate, because forward and backward reaction become equal at equilibrium. amount, because the amounts of reactants and products become constant after equilibrium is reached. reaction rate, as the rate of forward reaction increases and rate of backward reaction decreases over time.