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Chapter 12: Q71 E (page 710)

What is the rate equation for the elementary termolecular reaction A + 2B鉄秔roducts? For 3A鉄秔roducts?

Short Answer

Expert verified

For any reaction, the rate is given by the product of the concentration of the reactant, where each reactant concentration is raised to the power of the stoichiometric ratio.

Step by step solution

01

Termolecular reaction

For elementary termolecular reaction \({\bf{A + 2B}} \to {\bf{products}}\).

\({\bf{Rate = }}\left( {\bf{A}} \right){\left( {\bf{B}} \right)^{\bf{2}}}\).

Each concentration term in the rate equation is raised to the power equivalent to the stoichiometry of the particular reactant.

02

Rate of Termolecular reaction involving same reactants

For elementary reaction \({\bf{3A}} \to {\bf{products}}\), the rate of reaction is given by

\({\bf{Rate = }}{\left( {\bf{A}} \right)^{\bf{3}}}\)

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Most popular questions from this chapter

The rate constant for the rate of decomposition of \({{\bf{N}}_{\bf{2}}}{{\bf{O}}_{\bf{5}}}\)to\({\bf{NO}}\) and \({{\bf{O}}_{\bf{2}}}\)in the gas phase is 1.66 L/mol/s at 650 K and 7.39 L/mol/s at 700 K:

\({\bf{2}}{{\bf{N}}_{\bf{2}}}{{\bf{O}}_{\bf{5}}}{\bf{(g) - - - 4NO(g) + 3}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

Assuming the kinetics of this reaction are consistent with the Arrhenius equation, calculate the activation energy for this decomposition.

Account for the relationship between the rate of a reaction and its activation energy.

In a transesterification reaction, a triglyceride reacts with an alcohol to form an ester and glycerol. Many students learn about the reaction between methanol (\({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH}}\)) and ethyl acetate (\({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{C}}{{\bf{H}}_{\bf{2}}}{\bf{OCOC}}{{\bf{H}}_{\bf{3}}}\)) as a sample reaction before studying the chemical reactions that produce biodiesel:

\({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH + C}}{{\bf{H}}_{\bf{3}}}{\bf{C}}{{\bf{H}}_{\bf{2}}}{\bf{OCOC}}{{\bf{H}}_{\bf{3}}}{\bf{ - - - C}}{{\bf{H}}_{\bf{3}}}{\bf{OCOC}}{{\bf{H}}_{\bf{3}}}{\bf{ + C}}{{\bf{H}}_{\bf{3}}}{\bf{C}}{{\bf{H}}_{\bf{2}}}{\bf{OH}}\).The rate law for the reaction between methanol and ethyl acetate is, under certain conditions, determined to be: rate =\(k\left( {{\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH }}} \right)\). What is the order of reaction with respect to methanol and ethyl acetate, and what is the overall order of reaction?

Hydrogen iodide, HI, decomposes in the gas phase to produce hydrogen, H2, and iodine, I2. The value of the rate constant, k, for the reaction was measured at several different temperatures, and the data are shown here:

Temperature(K)

k(M-1s-1)

555

6.23*10-7

575

2.42*10-6

645

1.44*10-4

700

2.01*10-3

What is the value of the activation energy (in kJ/mol) for this reaction?

Experiments were conducted to study the rate of the reaction represented by this equation.(2)\({\rm{2NO(g) + 2}}{{\rm{H}}_{\rm{2}}}{\rm{(g) }} \to {\rm{ }}{{\rm{N}}_{\rm{2}}}{\rm{(g) + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O(g)}}\)Initial concentrations and rates of reaction are given here.

Experiment Initial Concentration

\(\left( {{\bf{NO}}} \right){\rm{ }}\left( {{\bf{mol}}/{\bf{L}}} \right)\)

Initial Concentration, \(\left( {{{\bf{H}}_{\bf{2}}}} \right){\rm{ }}\left( {{\bf{mol}}/{\bf{L}}} \right)\)Initial Rate of Formation of \({{\bf{N}}_{\bf{2}}}{\rm{ }}\left( {{\bf{mol}}/{\bf{L}}{\rm{ }}{\bf{min}}} \right)\)
1\({\bf{0}}.{\bf{0060}}\)\({\bf{0}}.{\bf{00}}1{\bf{0}}\)\({\bf{1}}.{\bf{8}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{4}}}}\)
2\({\bf{0}}.{\bf{0060}}\)\({\bf{0}}.{\bf{00}}2{\bf{0}}\)\({\bf{3}}.{\bf{6}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{4}}}}\)
3\({\bf{0}}.{\bf{00}}1{\bf{0}}\)\({\bf{0}}.{\bf{0060}}\)\({\bf{0}}.{\bf{30}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{4}}}}\)
4\({\bf{0}}.{\bf{00}}2{\bf{0}}\)\({\bf{0}}.{\bf{0060}}\)\({\bf{1}}.{\bf{2}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{4}}}}\)

Consider the following questions:(a) Determine the order for each of the reactants, \({\bf{NO}}\) and \({{\bf{H}}_{\bf{2}}}\), from the data given and show your reasoning.(b) Write the overall rate law for the reaction.(c) Calculate the value of the rate constant, k, for the reaction. Include units.(d) For experiment 2, calculate the concentration of \({\bf{NO}}\)remaining when exactly one-half of the original amount of \({{\bf{H}}_{\bf{2}}}\) had been consumed.(e) The following sequence of elementary steps is a proposed mechanism for the reaction.Step 1:Step 2:Step 3:Based on the data presented, which of these is the rate determining step? Show that the mechanism is consistent with the observed rate law for the reaction and the overall stoichiometry of the reaction.
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