Question

At 387.5 degrees C, the vapor pressure of K is 3.25 torr and that of Hg is 1280 torr. Over a solution 50 mol % of K in Hg, the vapor pressure of K is 1.07 and that of Hg 13.0 torr. Calculate the activities and activity coefficients of K and Hg in the solution. Calculate the $\Delta$ mixG of 0.5 mol of K and 0.5 mol Hg at 387.5 degrees C. If the $\Delta$ mixS is ideal, calculate the $\Delta$ mixH for the equimolar solution.

Answer 1

Activity = pi / p* [ pi = vapour pressure and p* = vapoure pressure of pure component]

Activity of K = 1.07/3.25 = 0.329

Activity of Hg = 0.01015

aK = yK * Xk

0.329 = yK * 0.5

yK = 0.658

aHg = yHg * XHg

yHg = 0.01015 / 0.5 = 0.203

delta mix G = nRT [ X1*lnX1 + X2*lnX2]

delta mix G = 0.5*8.314*[387.5+273] [ 0.5*ln 0.5 + 0.5 ln 0.5]

delta mix G = - 1.903 KJ

delta S mix = -nR [ X1*lnX1 + X2*lnX2]

delta H mix = delta G + T*delta S

delta H mix = nRT [ X1*lnX1 + X2*lnX2] -nRT [ X1*lnX1 + X2*lnX2] = 0