**The following problems are taken from T. L. Brown, H.
E. Lemay, B. E. Bursten, & J. R. Burdge, Chemistry: The Central Science,
Ninth ^{} Edition, Chapter 14. To see the solution to a problem or to
return from the solution, click on the number of the problem.**

**12)** ** (a) Consider the combustion of ethylene, C _{2}H_{4}(g) + 3O_{2}(g) 2CO_{2}(g) + 2H_{2}O(g). If the concentration of C_{2}H_{4} is decreasing at the rate of 0.23 M/s, what are the rates of change in the concentration of CO_{2} and H_{2}O? **

** (b) The rate of decrease in N _{2}H_{4} partial pressure in a closed reaction vessel from the reaction, N_{2}H_{4}(g) + H_{2}(g) 2NH_{3}(g), is 45 torr/hr. What are the rates of change of NH_{3} partial pressure and total pressure in the vessel? **

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22**)** ** The reaction 2ClO _{2}(aq) + 2OH^{-}(aq) ClO_{3}^{-}(aq) + ClO_{2}^{-}(aq) + H_{2}O(l) was studied with the following results: **

** Experiment [ClO _{2}], M [OH^{-}], M Rate, M/s **

** 1 0.060 0.030 0.0248
2 0.020 0.030 0.00276
3 0.020 0.090 0.00828**

** (a) Determine the rate law for the reaction. **

** (b) Calculate the rate constant.**

** (c) Calculate the rate when [ClO _{2}] = 0.010 M and [OH^{-}] = 0.015 M. **

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32**)** ** The first-order rate constant for the decomposition of N _{2}O_{5}, N_{2}O_{5}(g) 2NO_{2}(g) + O_{2}(g) at 70°C is 6.82 x 10^{-3}s^{-1}. Suppose we start with 0.0250 mol of N_{2}O_{5}(g) in a volume of 2.0 L. **

** (a) How many moles of N _{2}O_{5} will remain after 2.5 min? **

** (b) How many minutes will it take for the quantity of N _{2}O_{5} to drop to 0.010 mol? **

** (c) What is the half-life of N _{2}O_{5} at 70°C?**

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42**)** ** (a) The activation energy for the isomerization of methyl isonitrile is 160 kJ/mol. Calculate the fraction of methyl isonitrile molecules that have an energy of 160.0 kJ or greater at 500 K. **

** (b) Calculate this fraction for a temperature of 510 K. What is the ratio of the fraction at 510 K to that of 500 K? **

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60**)** ** The following mechanism has been proposed for the reaction of NO with H _{2} to form N_{2}O and H_{2}O:**

** NO(g) + NO(g) N _{2}O_{2}(g)**

** N _{2}O_{2}(g) + H_{2}(g) N_{2}O(g) + H_{2}O(g) **

** (a) Show that the elementary steps of the proposed mechanism add to provide a balanced equation for the reaction. **

** (b) Write a rate law for each elementary step in the mechanism.**

** (c) Identify any intermediates in the mechansim.**

** (d) The observed rate law is rate = k[NO] ^{2}[H_{2}]. If the proposed mechanism is correct, what can we conclude about the relative speeds of the first and second steps? **

**76) The reaction 2NO(g) + O _{2}(g) 2NO_{2}(g) is second order in NO and first order in O_{2}. When [NO] = 0.040 M and [O_{2}] = 0.035 M, the observed rate of disappearance of NO is 9.3 x 10^{-5} M/s. **

** (a) What is the rate of disappearance of O _{2} at this moment? **

** (b) What is the value of the rate constant? **

** (c) What are the units of the rate constant?**

** (d) What would happen to the rate if the concentration of NO were increased by a factor of 1.8? **