Help with a chemical engineering question
 

Someone please help me, been struggling for a bit: It's a material balances question from chemical engineering:

Strawberries contain about 15% solids and 85% water. To make strawberry jam, crushed strawberries and sugar are mixed in a 45:55 ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass. Draw and label a flowchart of this process, and use it too calculate how many pounds of strawberries are needed to make a pound of jam.

Now, I can set up the flowchart, but do I assume that initially I have 100 pounds, giving me 55 pounds of sugar, and 45 pounds of strawberries. And, of those 45 pounds of strawberries, 15% are solid, and 85% are water ?

My problem is the output. It has to also be 100 pounds right, but I cannot understand how to balance the sugar, water and solids, and how to determine how man pounds of strawberries are needed for 1 pound of jam. Please help!

If you start with 100 pounds of ingredients and then evaporate off about 5 percent of the water, you're not going to still have 100 pounds of product.

But, yeah, you seem to be on basically the right track. Mostly these problems are about helping you figure out that, if you set up your flow correctly, you can just reverse the math and figure out how much stock you need to order.

100 lbm of pre-jam will be 0.45*0.85=38.25 lbm of water. So you need to evaporate about 4.917 lbm of water to give you the 33% water by mass. So you get 95.083 lbm of jam for 45 lbm of strawberries. At that point it's a straight proportionality.

45/95.083 = X/1
or about 0.473 lbm of strawberries for a lbm of jam.

I see what u are saying, but I do not see how you would draw the flow chart for that, or do the degree of freedom analysis.

I'm not a chemical engineer, but I'll give it a shot:

There are three degrees of freedom: mass of strawberries, mass of sugar, quantity of water evaporated. (Assuming that the 45:55 ratio and 1/3% water aren't constraints.) Nothing else in the procedure can be changed, right?

Flow: strawberries (85% solid, 15% water) + sugar into the vat, evaporated water + jam out of the vat.

Again, I'm no ChemE--(I'm an Env. Engineer) so I'd double check with someone else with my analysis.

danny, perhaps i'm missing something here, but why are you looking to find 100 lbs. the problem is for 1lb? regardless, if you're trying to calculate how many lbs of strawberries you need, i would suggest not worrying about water. as i understand it, adopt 1 lb of finished product as your basis.

I think the only facts you need to worry about are:

1. you know that 2/3 of the jam will be solids from the strawberries + sugar.

2. you know the mixing ratio of strawberries to sugar

3. you know how much of the strawberries are solids.

If that doesn't help, then post back.