Chemistry 2710 Review Problems

1. A kineticist is studying a proton-generating reaction . Solutions of A and B are rapidly mixed and the is measured as a function of time until it has changed by several tenths of a unit.
   1. Argue that, if the initial concentrations of A and B are a significant fraction of 1mol/L and the initial is not too acidic, the slope of a graph of vs t will give the initial rate for this reaction.
   2. In one run, the following data were obtained:

      

      
      

      

      Calculate the initial rate.

2. For the decomposition of dinitrogen pentoxide in tetrachloromethane ( ), the following initial rate data has been obtained:

   

   1. Determine the empirical rate law (order of reaction and rate constant).
   2. The structure of is

      .

      Do you think that this reaction is elementary? Briefly explain your reasoning.

3. For the bromination of acetone ( ), the following initial rate data were obtained:

   

   1. Determine the rate law (orders and rate constant).
   2. Do you think that this reaction is elementary? Briefly explain your reasoning.
4. 1. Write down a complete set of rate equations for the mechanism

      

   2. What is the overall reaction?
   3. The empirical rate law for this reaction is . What does this tell us about the elementary reactions? How is k related to the rate constants of the two steps?
5. Proflavin is a large aromatic ion used to stain DNA:

   

   Like many other planar aromatic species, proflavin dimerizes in water:

   

   where P is a proflavin ion and D is the dimer. The rate constants have been measured by a technique which we shall discuss later. They are

   

   Calculate the equilibrium constant for the dimerization reaction.

6. Suppose that the reaction has an empirical rate law v = ka when studied in water. Is it possible that the rate-determining step of the reaction involves water? How could you test this experimentally?
7. has a half-life of 28.1y. This radioisotope is particularly hazardous because it becomes incorporated in bones so that it remains in the body and is never excreted. If a person accidentally ingests of , how much will remain after 40y?
8. The reaction of ethyl acetate with hydroxide to form acetate ions and ethanol has a rate law with a rate constant of . If the initial concentrations are , what would the concentration of ethanol be after 10min?
9. Suppose that the reaction has a rate law v = kab. Write down an integral which relates the concentration of P to time if , and p(0)=0. Do not solve the integral.
10. Why can't the rate of a reaction with the stoichiometry be studied by monitoring the total pressure?
11. In an autocatalytic reaction, the rate depends on the concentration of a product so that the reaction actually accelerates as it goes along. This is commonly seen in reactions which have protons as products since protons catalyze many reactions. Consider a reaction with rate v = kab and arbitrary initial concentrations , .
    1. Obtain a differential equation involving only a for this reaction.
    2. Verify that

       

       is a solution to your differential equation.

    3. The above solution can be rewritten in the form

       

       Obtain an expression for the half-life.

    4. Suppose that . Compare the half-life when the its value when
       1. and ;
       2. and .
       Which has the larger effect on the half-life, the initial concentration of A or of B?
12. The progress of the gas-phase reaction carried out in a sealed flask of fixed volume was followed by measuring the total pressure. The results were as follows:

    

    The reaction is either of the first or second order with respect to A and shows no dependence on the partial pressure of B. Determine the order and rate constant.

13. Explain how you could determine the rate constant of a simple third-order reaction. What data would you need? How would you treat it?
14. Over a period of several days, a sample of 1g of osmium displays an average of 47 decays per day. These decays are due to the very long-lived radioisotope . The natural abundance of this isotope is 1.58%. What is the half-life? Express your answer in years.
15. The following table gives the population of Finland in the past two centuries:

    

    1. Doubling times are computed on the assumption that the population is growing exponentially. What is the doubling time for the population of Finland?
    2. In what year would you predict that the population will reach six million?
    3. Is the population really growing exponentially?