Question

You are fractionally distilling 100 mL of a 1:1 solution of cyclohexane and toluene. After 2 mL has distilled you collect a sample for analysis. It is determined that your sample contains a mixture that is 92:8 cyclohexane/toluene. Calculate the number of theoretical plates if the relative volatility (?) of the original solution is 2.33

Answer 1

100 mL of a 1:1 solution of cyclohexane and toluene, it means that we have the same cuantity for the cyclohexane ando toluene, 50ml of cyclohexane + 50ml of toluene =100ml of solution. Then in the solution of 2ml we will have 1.84 ml of cyclohexane + 0.16 ml of toluene =2ml of sample.

for calculate the number of theorical plates we will use the Fenske equation:

mol_cyclohexane=1.84gr/84.16g/mol=0.022mol

mol_toluene=0.16gr/92.14g/mol=0.0017

X_cyclohexane=0.022/(0.022+0.0017)=0.928

X_toluene=0.0017/(0.022+0.0017)=0.072

making the substitution in the above equation we have to:

N=log(12.8*12.8)/log(2.33)=2.21/0.36=6.14=6 plates