Chemistry 2720, Fall 96, Assignment 1 Solutions

1. To get work in Joules (the SI unit of energy), we must transform the external pressure to Pascals and to cubic meters:

   

   

2. We need to calculate the amount of heat required to raise the water's temperature from 20 to C. 1.5L is . Using the density of water at C, we find

   

   The heat required to bring the water to its boiling point is therefore

   

   This heat is supplied by a 1500W heating element. A Watt is a Joule per second so

   

   

3. To make each lead sphere:
   1. You have to solidify the molten lead. This requires the removal of of heat, i.e. the water gains this much heat.
   2. The spheres cool from C to C. Relative to the lead spheres, this process yields of heat. Thus the water gains .
   Overall, the water gains . The heat gained by the water in going from 20 to C is

   

   Therefore

   

   

4. The work done on each box is . There are 24 boxes so the total work done is 3.5kJ. Relative to the person doing the lifting, . To compensate for this energy use, the person must take in at least 3.5kJ of usable (catabolizable) energy in the form of food. Carbohydrates provide 4.0kcal/g which is 16.7kJ/g. Therefore

   

   Note that this calculation assumes 100% efficiency of all the processes involved (muscle work, extraction of nutrients from food, etc.). Nevertheless, it's safe to conclude that it won't be necessary to eat double portions.

   

5. 1. First, balance the reaction:

      

      For this reaction,

      

      

   2. By definition, . Therefore For ideal gases, PV=nRT while for solids and liquids, the product PV is insignificantly small. Accordingly,

      

      where is the change in the number of moles of gas during the reaction. For this reaction (as written), there are reactant molecules and 2 product molecules so . That gives