Chemistry 2000, Fall 96
Assignment 1 Solutions

1. Take a logarithm (log or ln) or both sides of the equation and use the rule to get the out of the exponent:

   

   

2. We can get rid of the logarithm by using the fact that is the inverse function of :

   

   

   Would you believe that I didn't do it on purpose? The brain works in mysterious ways.

3. In the first solution,

   

   In the second solution,

   

   The number of moles of chloride in the mixture is the sum of the amounts in each solution so . We also need the number of moles of water. There is a total of 20mL of water. This corresponds to

   

   The mole fraction of the chloride ions is therefore

   

   

4. Sodium sulphate is Na SO . The number of moles of Na SO formula units is

   

   Multiply this last number by two to get the number of sodium ions.

5. To compute the derivative at t=1, use the data to either side of this point:

   

   We do this for each point which is bracketed by two others to obtain the table

   

   The graph has the following appearance:

   The points lie on a beautifully straight line. This is not a coincidence.