Material balance help, chemical engineering

[simon.23]

Homework Statement

Toluene is recovered from a mixture of toluene and nitrogen (containing 52 mol% toluene) by cooling the mixture at constant pressure of 1.2 bar to condense out some of the toluene. If the flow rate of the mixture into the condenser is 179 kmol h-1, determine the flowrate of the condensed toluene if the mixture is cooled to a temperature of 25ºC in the condenser. Give your answer in kmol h-1 to an accuracy of one decimal place.

Data: The saturated vapour pressure of toluene in kPa (p*) at TºC is given by:

$$log_{10} (p*) = 6.0758-\frac{1342.31}{T +219.19}$$

I have tired this question so many times, and I can't get the right answer, can anyone check my working and guide me as to where I am going wrong?

Thank you.

I know I need to use daltons law to work out the mole fraction first;

$$y_{v} = \frac{P^{o}_{v}}{P_{T}}$$

where

$$y_{v}$$ = mole fraction.
$$P^{o}_{v}$$ = saturated vapour pressure

$$P_{T}$$ = total pressure1.2 bar = 120 Kpa

from the temperature given I can work out the sturated vapour pressure of tolunene, after being condensed, and hence the mole fraction.

$$log_{10} (p*) = 6.0758-\frac{1342.31}{25 +219.19}$$

$$log_{10} (p*) = 0.56$$

$$p = 10^{0.56} = 3.79 kpa$$

so mole fraction of condensed toluene;
$$y_{v} = \frac{3.79}{120} \times 100 = 3.16 mol \%$$

so now I have to do a material balance to work out the flowrate of the liquid stream,

I will use a basis of 100 kmol h^{-1} ,ans scale up to 179kmol ^{-1} after the answer.

This is where I am stuck. My material balance just cancels out, I can't seem to make any equations out of it;

I have attached the material balance diagram, please can someone check it and let me know if it is correct?

Thank you.

 

[Valkarie]

F_{m} = F_{in} = F_{L} + F_{V} 179 kmol h^{-1} = F_{L} + F_{V} Homework EquationsDaltons law of partial pressuresy_{v} = \frac{P^{o}_{v}}{P_{T}} The Attempt at a SolutionI have attached the material balance diagram, please can someone check it and let me know if it is correct? Thank you.