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Chapter 12: Q40 E (page 706)

What is the half-life for the decomposition of \({{\bf{O}}_{\bf{3}}}\) when the concentration of \({{\bf{O}}_{\bf{3}}}\)is \({\bf{2}}{\bf{.35 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)M? The rate constant for this second-order reaction is 50.4 L/mol/h.

Short Answer

Expert verified

Half-life periods may be defined as the time period at which half the concentration of reactant converts into the product. The half-life period of the second-order decomposition of the O3 is \(2.33 \times {10^{ - 8}}\)hours which has a rate constant of 50.4L/mole/h.

Step by step solution

01

Reaction Rate

The reaction involved the effective collision of two reactants to produce the desired products. Reactions can be natural, which occur in the surrounding environment, whereas it can be artificially done in the laboratory to form a desired required product.

The reaction rate can be defined as the reaction speed to produce the products. The reaction rate can be slow, fast or moderate. The reaction can take less than a millisecond to produce products, or it can take years to produce the desired product.

The half-life period can be defined as the time period at which half the concentration of the reactants gets converted into a product.

02

Explanation

The half-life period of the second-order decomposition of the O3 is:

\({\bf{Half - life period = }}\frac{{\left( {\bf{A}} \right){\bf{^\circ }}}}{{{\bf{2k}}}}\)

Where \(\left( {\bf{A}} \right){\bf{^\circ }}\) = initial concentration of reactant

K = Rate constant

Initial concentration of reactant, (A)掳 =\({\bf{2}}{\bf{.35 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)M

Rate constant for the decomposition of O3 = 50.4L/mol/h

\(\begin{align}{\bf{Half - life period = }}\frac{{{\bf{2}}{\bf{.35 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{mole/L}}}}{{{\bf{2 \times }}\left( {{\bf{50}}{\bf{.4L/mole/h}}} \right)}}\\{\bf{Half - life period = }}\frac{{{\bf{2}}{\bf{.35 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{mole/L}}}}{{{\bf{100}}{\bf{.8L/mole/h}}}}\\{\bf{Half - life period = 2}}{\bf{.33 \times 1}}{{\bf{0}}^{{\bf{ - 8}}}}{\bf{hour}}\end{align}\)

Half-life period = \(2.33 \times {10^{ - 8}}\) hour.

Hence, the half-life period of the second-order decomposition of the O3 is \(2.33 \times {10^{ - 8}}\) hours which has rate constant is 50.4 L/mol/h.

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Most popular questions from this chapter

Regular flights of supersonic aircraft in the stratosphere are of concern because such aircraft produce nitric oxide, NO, as a by-product in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction \({\bf{NO + }}{{\bf{O}}_{\bf{3}}} \to {\bf{N}}{{\bf{O}}_{\bf{2}}}{\bf{ + }}{{\bf{O}}_{\bf{2}}}\) is first order with respect to both NO and \({{\bf{O}}_{\bf{3}}}\) with a rate constant of \({\bf{2}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{7}}}{\bf{mol}}{{\bf{L}}^{{\bf{ - 1}}}}{{\bf{s}}^{{\bf{ - 1}}}}\). What is the instantaneous rate of disappearance of NO when \(\left( {{\bf{NO}}} \right){\bf{ = 3}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{ M}}\) and \({\bf{(}}{{\bf{O}}_{\bf{3}}}{\bf{) = 5}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 7}}}}{\bf{ M}}\)?

In the PhET Reactions & Rates (http://openstaxcollege.org/l/16PHETreaction) interactive, use the 鈥淢any Collisions鈥� tab to observe how multiple atoms and molecules interact under varying conditions. Select a molecule to pump into the chamber. Set the initial temperature and select the current amounts of each reactant. Select 鈥淪how bonds鈥� under Options. How is the rate of the reaction affected by concentration and temperature?

Why are elementary reactions involving three or more reactants very uncommon?

How much and in what direction will each of the following effect the rate of the reaction:

CO(g) + \({\bf{NO}}{}_{\bf{2}}\) (g)鉄� \({\bf{CO}}{}_{\bf{2}}\) (g) + NO(g) if the rate law for the reaction is rate =\({\bf{k(NO}}{}_{\bf{2}}{{\bf{)}}^{\bf{2}}}{\bf{a}}\)?

  1. Decreasing the pressure of \({\bf{NO}}{}_{\bf{2}}\) from 0.50 atm to 0.250 atm.
  2. Increasing the concentration of CO from 0.01 M to 0.03 M.

The rate law for the reaction: \({{\bf{H}}_{\bf{2}}}\) (g) + 2\({\bf{NO}}\) (g) 鉄禱({\bf{N}}2{\bf{O}}\) (g) + \({{\bf{H}}_{\bf{2}}}\)O(g) has been determined to be rate = k(\({\bf{NO}}\))2 (\({{\bf{H}}_{\bf{2}}}\)). What are the orders with respect to each reactant, and what is the overall order of the reaction?
See all solutions

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