Question

Two streams flow into a 500-gallon tank. The first stream is 10wt% ethanol and 90wt% hexane (mixture density=0.68g/cm^3) and the second is 90wt% ethanol and 10wt% hexane (mixture density=0.78g/cm^3). After the tank has been filled, which takes 22 minutes, an analysis of its contents determines the mixture is 60wt% ethanol and 40wt% hexane. Determine the density of the final mixture and the volumetric flow rates of the two feed streams.

Answer 1

let F1= Mass flow rate of stream1 and F2= mass flow rate of stream 2

Moles of Ethanol (E) : Stream 1 : 0.1F1 and stream 2 : 0.9F2

Balance of E can be written as = 0.1F1+0.9F2= (F1+F2)*0.4

0.1F1+0.9F2= F1*0.4+0.4F2

0.3F1= 0.5F2

F2= 0.6F1 (1)

Volume of Ethanol in F1= F1/0.68 cc=1.471F1 and volume of ethanol in stream 2= F2/0.78= F2*1.282

1.47F1+1.282F2= 500*3.78/22 l/min =85.91 L/min= 85.91*1000 cc/min =85910 cc/min (2)

but F2= 0.6F1 (from 1)

Eq.2 becomes 1.47F1+1.28*0.6F1= 85901 =2.238 F1= 85901

F1= 85901/2.238 g/min =38382.93 g/min =38382.93/0.68 cc /min =56445cc/min= 56.445 L/min

and that of second stream F2=0.6*38382.93 g/min =23030 g/min = 23030/0.78= 29525.33 cc/min= 29.525 L/min

Total mass entering the tank=F1+F2= 38382.93+23030=61412 gm/min

Total volumetrif flow rate= 85910 cc/min

Density of mixture = 61412/85910 gm/cc =0.7148 g/cc