College Chemistry
posted by Christian Gillard .
A student placed 14.0g of glucose (C6H1206) in a volumetric flask, added enough water to dissolve the glucose by swirling, then carefully added additional water until the 100.mL mark on the neck of the flask was reached. The flask was then shaken until the solution was uniform. A 35.0mL sample of this glucose solution was diluted to 0.500mL . How many grams of glucose are in 100mL. of the final solution?

SURELY you have a typo. I don't know how you can dilute a 35.0 mL sample to 0.500 mL. You might dilute it to 0.500 L but not mL. I will assume you intended to write "A 35.0 mL sample of this glucose solution was diluted to 0.500 L. How many grams of glucose are in 100 mL of the final solution?"
These dilution problem really are simple if you just reason through them.
We have 14.0 g glucose in 100 mL. So that is 14.0/100 = 0.140 g/mL. Now we take a 35.0 mL sample of that solution. How much did we take? We have 0.14 g/mL x 35.0 mL = 4.90 g. We place that in a 0.500 L (500 mL) flask so now we have 4.90 g in 500 mL. How much is that per mL? 4.90/500 = 0.00980 g/mL. So how much is in 100 mL of that solution.
0.00980 x 100 = 0.980 grams/100 mL.
Check my thinking. Check my arithmetic. 
correct answer is 0.700 grams