In an ideal mixture of liquids A and B the mole fraction of A is 0.25.If the ratio of P_A^@ to P_B^@ is 7//3.how many repeated distillations would be required as a "minimum" to obtain a small quantity to distillate which has a mole fraction A, better than 0.80 ?

In an ideal mixture of liquids A and B the mole fraction of A is 0.25.

1.	In an ideal mixture of liquids A and B the mole fraction of A is 0.25.If the ratio of P_A^@ to P_B^@ is 7//3.how many repeated distillations would be required as a "minimum" to obtain a small quantity to distillate which has a mole fraction A, better than 0.80 ?
Answer» 4 2 3 5 Solution :A=0.25B=0.75 `P_4^C/P_3^C=7/3implies P_B^0=3/7P_A^0` `P_T=0.25xxP_A^0+0.75xx3/7P_A^0=P_A^0(1/4+9/28)` `y_AP_T=P_A^0X_Aimplies y_A=(X0.25)/((1/4+9/28))=(((1//4)/(7+9))/28)=7/16 & y_B=9/16` `P_T^1=7/16xxP_A^0+9/16xx3/7 P_A^0=P_A^0(7/16+27/(16xx7))` `y_A^1P_T^1=P_A^0 X_A^1 implies y_A^1 =(7/16)/(((49+27)/(16xx7)))=(7xx16xx7)/(16(49+27))=49/76` `P^(11)=49/76xxP_A^0 +27/76xx3/7 P_A^0=P_A^0((49xx7+81)/(7xx76))` `y_A^1 P_T^11=P_A^0x_A^11implies y_A^11=P_A^0(P_A^0xx79//76)/((49xx7+81)/(7xx76))=(49xx7xx76)/(76(49xx7+81))` `y_A^1=0.8089 ge0.8` There will be 3 repeated distillation to GET `X_A=0.8`