Chemistry 2720 assignment 1

Due: Friday, January 23, noon.

Most of the data you need is right in the assignment, but some of it is not and can be found in any textbook.

1. The ideal gas law is only valid for most gases at very low temperatures. Real gases are more accurately described by the van der Waals equation:

   

   where a and b are constants specific to a particular gas, R is the ideal gas constant, P is the pressure, V the volume and n the number of moles.

   1. Derive an equation for the work done during a reversible, isothermal expansion of a van der Waals gas. [8 marks]
   2. For nitrogen, and . Calculate the work done when 1kmol of nitrogen is expanded reversibly and isothermally at a temperature of 300K from 1 to . [2 marks]
2. The constant pressure heat capacity of the metal indium is given by the equation

   

   where T is in Kelvin and is in .

   1. Calculate the amount of heat required to raise the temperature of a 12g piece of indium from 50 to . [6 marks]
   2. How large an error would result from using a (constant) average value of ? [4 marks]
3. 5.2g of potassium bromide is dissolved in 100g of water initially at in an insulated container held at constant pressure. Assume that the heat capacity of the solution is approximately equal to the heat capacity of the water alone (usually a reasonable approximation) and calculate the final temperature. [10 marks]
4. Lead melts at 600.6K. The enthalpy of melting is 4.774kJ/mol. Suppose that a company has an electrical furnace (a device that converts electrical work completely into heat) that melts 100kg of lead per hour. The lead enters the furnace at a temperature of . Assuming that no heat is lost, how much electrical power is required to operate the furnace? [10 marks]

   Hints:

   1. Power is measured in Watts. A Watt is a Joule per second.
   2. Lead has a constant-pressure heat capacity of .