Sunday morning chemistry

1. Max buys a coffee at Finagle a Bagel, which comes in a cup of size 214 ml. The cup is filled with 190 ml of black coffee at 80 degrees C (container A). Max then adds 10 ml of light cream. However, when adding sugar to his coffee, the sugar container bursts open, dumping 400 g of sucrose into Max's coffee, potentially displacing some. The employees courteously give Max a new cup of coffee, with the same volumes and temperature (container B).

a. Bagged white sugar has a density of 700kg/m^3. What volume, if any, of coffee was displaced due to sugar containment failure?

b. Given your answer to a, and the temperature of the coffee, what is the current sugar-coffee solution in the first cup of coffee? You may treat black coffee as distilled water for your calculations.

c. Given your answer to b, if max fills container A to the top with coffee from container B, stirs it as to homogenize the mixture, and then pours the mixture from container B back into container A, how many times will Max have to repeat this process until the concentration of sugar in container B reaches that of container A, if ever? Remember the pile of undissolved sugar that may or may not be at the bottom of container A.