# Work required to concentrate a dilute solution

1. Nov 23, 2008

### staceybiomed

I am not really good at using the specials characters, etc so please forgive me!

1. The problem statement, all variables and given/known data
a) Calculate the work required to concentrate a dilute sucrose solution. Assume that we begin with 10 wt % solution of sucrose in water and we want to end with a 30 wt % sucrose solution. Pick a basis of 1 kg of 10 wt % solution and express answer in Joules.

b) Compare your to answer to that which would be obtained if you assumed the sucrose-water solution to be ideal (i.e. where the activities are set equal to the mole fraction)

T of separation = 20C
MW of sucrose = 342.3 g/mol
For 10 wt% sucrose solution: molality (moles sucrose/kg H2O) = 0.3249, mole fraction H2O = 0.99419, Activity of water = 0.99393
For 30 wt% sucrose solution: molality = 1.253, mole fraction H2O = 0.99794, activity of water = 0.97596

2. Relevant equations
non-ideal:
G = $$\Sigma(xi * $$\gamma$$)$$
where $$\gamma$$ is activity coefficient

ideal:
G = $$\Sigma(xi)$$ + RT * $$\Sigma(xi*ln xi)$$

3. The attempt at a solution
I know that if we start with 1 kg of 10 wt % solution, I start with 0.100 kg of sucrose (also known as 0.292 moles) and the mass/moles of sucrose remains constant during concentration. It is just the amount of water that reduces (goes from 0.900 kg to 0.233 kg in 30 wt % solution). Also, the solution mass goes from 1 kg to 0.333 kg.

I think that if I can get Gibbs F.E. for non-ideal by just adding the (mole fraction * activity coefficients) at each concentration but not sure if that is the right way to start. Also, I'm not sure how to connect work to Gibbs free energy.

P.S. I have 2 other problems that I need help on so stay tuned... :-)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 30, 2008