Determine the parameters a, b, and c given the data on table 11.3. Please do not
ID: 1061139 • Letter: D
Question
Determine the parameters a, b, and c given the data on table 11.3. Please do not use the solutions manual.
11.36. The data in Table 11.3 are experimental values of HE for binary liquid mixtures of 1,2-dichloroethane (1) and dimethyl carbonate(2) at 313.15 K (40 C) and l atm. (a) Determine from the data numerical values of parameters a, b, and c in the correlating equation: x1x2(a bx1 cxi) (b) Determine from the results of part (a) the minimum value of HE. At what value of x1 does this occur? (c) Determine from the results of part (a) expressions for H1 and H2. Prepare a plot of these quantities vs. x1, and discuss its features. Table 11.3 HE Values for 1,2-Dichloroethane(1)/ Dimethyl Carbonate(2) at 313.15 K (40 C) R. Francesconi et al., Int. DATA Ser, Ser. A, vol. 25. no. 3, p. 225, 1997. HEIJ mol HE/J mol x1 0.0426 23.3 0.5163 204.2 0.6156 0.0817 45.7 191.7 66.5 0.6810 174.1 0.1510 0.7621 86.6 141.0 0.2107 118.2 0.8181 116.8 0.2624 0.8650 144.6 85.6 0.9276 176.6 0.3472 43.5 0.4158 0.9624 195.7 22.6Explanation / Answer
The equation can be written as HE/x1x2= a+bx1+cx2
The plot of HE/x1x2 along vs x1 is plotted and shown below
accordingly a+bx1+cx12= 1036x12-1118.3x1-523.6
comparing the coefficients,
a= -523.6, b=-1118.3 and c= 1036
HE= x1x2( 1036x12- 1118.3x1-523.6)= x1*(1-x1){ 1036x12- 1118.3x1- 523.6)= (x1-x12) (1036x12-1118.3x1-523.6)
= -1036x14 +2154.3x13-594.7x12- 523.6x1
dHE/dx1= 0 gives the values of x , -4144x13 +6462x12-1189.4x1- 523.6 =0
dHE/dx1= 4144x13 +6462.9x12- 1189.4x1-523.6 =0
when solved using excel, x1=0.536
d2HE/dx12>0 at x1=0.536
hence x1 is minimum
H1-E= HE+x2(dHE/dx1)=-1036x14+2154.3x13-594.7x12-523.6x1 +(1-x1)*(4144x13 +6462.9x12- 1189.4x1-523.6)
=-3108x14 -164.6x13-5868.2x12- 1189.4x1- 523.6
H2-e= HE- x1*dHE/dx1= 1036x14+2154.3x13-594.7x12-523.6x1- x1*(4144x13 +6462.9x12- 1189.4x1-523.6 )
=-5180x14-4308.6x13=594.7x12
the plots are drawn and shown below
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