Question

Hi, I need help with this Chemistry problem, much like General Chemistry but I am really confused when I look at the solution. I will provide you the solution of the problem together with the problem. What I need you to do is to walk me through all the reasonings, logical steps that lead to the solution provided. I appreciate your help and I will give you feedback as to how clear your answer is.

Problem 6 (A little harder-20 points): An ice cube made of frozen pure water floats in a glass of sweet tea. Because it has a lot of dissolved sugar in it, the specific gravity of the sweet tea is greater than that of pure water. The ice melts, and the resulting tea is stirred well. a) Express the change in liquid level in the glass as a function of the initial volume of the sweet tea, the initial volume of the ice cube, the specific gravity of the sweet tea, the specific gravity of the ice cube, and the area of the base of the glass (A). b) Express the specific gravity of the final mixture in terms of the variables stated in part a). Note that your final equation may not necessarily include all of these variables. Assume the specific gravity of water is equal to one.

And here is the solution to this problem:

Thanks a lot!

Answer 1

This problem is based on Archimedes principle.

Volume = area of tube X height of level

Height of level before - Height of level after = Volume before - Volume after / Area

Volume before = Volume of tea + volume of ice = Mass of tea / Density of tea + Mass of ice / Density of ice

volume after = Volume of tea + volume of water = Mass of tea / Density of tea + Mass of water / Density of water

B-A =   Mass of tea X density of ice + mass of ice X density of tea - Mass of tea Xdensity of water - Mass of water X density of tea /Density of tea X density of ice

mass of ice X density of tea = Mass of water X density of tea

B-A = Mass of tea X density of ice - Mass of tea X density of water / Density of tea X density of ice

B-A = (Mass of tea X density of ice / Density of tea X density of ice) - (Mass of tea X density of water / Density of tea X density of ice )

on simplification

B-A = (volume of ice X density of ice / Density of water) (Density of water / Density of tea - 1)