1. a) Look up the composition of air. Estimate its average molecular weight.
b) Qualitatively describe whether the density of air should be large or small compared to the density of water.
c) Qualitatively describe whether the mass density of air should be large or small compared to that of oxygen if the same number of moles of the two gasses are contained in identical containers.
d) If the density of air under certain conditions is 1.06 g/m^3, how much does a gallon of air weigh?
2. a) Using both of the formulas for average density, calculate estimates for the density of a 50% by mass solution of toluene and benzene. Comment on the results.
b) Repeat this calculation for varying concentrations of toluene. When does it make the most difference which formula you use? When does it make the least? Show the results graphically. Would the trend be the same for any binary solution?
c) Suppose that a 50% mixture of toluene and benzene is to be separated by crystallization. The solution is cooled until one of the components completely freezes and only the other is left as a liquid. The liquid is then removed. What will the majority of the solid be? What will the liquid be? What temperature should be used to achieve this? (give an estimate)
d) In the crystallization process in part c, suppose that the after separation, the solid crystals contained all of the benzene and 1% of the toluene from the original mixture. Suppose also that after melting the solid, the resulting liquid weighed 1435 g. Calculate the mass of the original solution.
3.. Consider a publishing company in which books are to be bound, printed, and shipped. At 5 a.m. every morning, a shipment of 10,000 reams of paper comes in, as well as enough materials to make 150,000 books, and 30000 pounds of ink. In this particular plant, the average size of a book is 250 pages and each uses about 0.2 pounds of ink.
a) How many books can be printed for each shipment? (Hint: What is the limiting factor?)
b) Suppose that, on average, 4% of all books printed are misprints and must be destroyed. The remaining books are to be distributed to each of 6 continents in the following proportions:
North America 15%
South America 10%
Each book that is printed (including those that are destroyed) costs the company US$0.50 to print. Those that are shipped cost the following prices to ship from the US:
North America $0.05
South America $0.08
If each book sells for an equivalent of US$1.00, what is the maximum profit that the company can make per day?
c) Challenge What is the minimum number of books that the company can sell (from any continent) in order to return a profit? (Hint: what is the total cost of this scheme? Does it matter where the books are sold once they are distributed?)
d) How many pounds of ink per day end up in each continent under the scheme in part b? How many pages of paper?
e) Can you think of any ways you can improve this process? What may be some ways to improve the profit margin? How can inventory be reduced? What are some possible problems with your proposed solutions?