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Chapter 12: Q5E (page 702)

A study of the rate of the reaction represented as 2A⟶ B gave the following data:

  1. Determine the average rate of disappearance of A between 0.0 s and 10.0 s, and between 10.0 s and 20.0 s.
  2. Estimate the instantaneous rate of disappearance of A at 15.0 s from a graph of time versus (A). What are the units of this rate?
  3. Use the rates found in parts (a) and (b) to determine the average rate of formation of B between 0.00 s and 10.0 s, and the instantaneous rate of formation of B at 15.0 s.

Short Answer

Expert verified

1.The average rate of disappearance of A between 0.0 s and 10.0 s is 0.0374 M/s and Average rate of disappearance of A between 10.0 s and 20.0 s is 0.0255M/s.

2.The instantaneous rate of disappearance of A at 15.0 s from a graph of time versus (A) is 0.05M/s and the units of this rate is \({\bf{mol \times }}{{\bf{L}}^{{\bf{ - 1}}}}{\bf{ \times }}{{\bf{s}}^{{\bf{ - 1}}}}\).

3.The average rate of formation of B between 0.00 s and 10.0 s is get 0.0188M/s and the instantaneous rate of formation of B at 15.0 s is 0.025.

Step by step solution

01

Determine average rate of disappearance

\(\frac{{{\bf{ - \Delta A}}}}{{{\bf{2\Delta t}}}}{\bf{ = }}\frac{{{\bf{\Delta B}}}}{{{\bf{\Delta t}}}}\)

Average rate of disappearance from 0s to 10s

\(\begin{aligned}{}{\bf{ = }}\frac{{{\bf{ - \Delta A}}}}{{{\bf{\Delta t}}}}\\{\bf{ = }}\frac{{{\bf{0}}{\bf{.370 - 0}}{\bf{.625}}}}{{{\bf{20 - 10}}}}\\{\bf{ = 0}}{\bf{.0255M/s}}\end{aligned}\)

Average rate of disappearance from 10s to 20s

\(\begin{aligned}{}{\bf{ = }}\frac{{{\bf{ - \Delta A}}}}{{{\bf{\Delta t}}}}\\{\bf{ = }}\frac{{{\bf{0}}{\bf{.370 - 0}}{\bf{.625}}}}{{{\bf{20 - 10}}}}\\{\bf{ = 0}}{\bf{.0255M/s}}\end{aligned}\)

02

Determine the instantaneous rate of disappearance

Linear from of each order to plot point A y-axis, ln A y-axis and 1/A y-axis

First order:

\(\begin{aligned}{}\left( {\bf{A}} \right){\bf{ = - kt + (}}{{\bf{A}}_{\bf{0}}}{\bf{)}}\\{\bf{In}}\,\,\left( {\bf{A}} \right){\bf{ = - kt + In(}}{{\bf{A}}_{\bf{0}}}{\bf{)}}\\\frac{{\bf{1}}}{{{\bf{(A)}}}}{\bf{ = kt + }}\frac{{\bf{1}}}{{{\bf{(}}{{\bf{A}}_{\bf{0}}}{\bf{)}}}}\end{aligned}\)

Here notice that second order is most linear

Rate = \(\frac{{{\bf{ - d(A)}}}}{{{\bf{2dt}}}}{\bf{ = k(A}}{{\bf{)}}^{\bf{2}}}\,\,\,\,\,\,\,\,\,\, - - - - {\bf{(1)}}\)

we find k is 0.116 from slope of graph and at 15s (A)=0.465 to put all value in equation (1)

rate of disappearance of A is 0.05M/s

03

Determine average rate of formation

\(\frac{{{\bf{ - \Delta A}}}}{{{\bf{2\Delta t}}}}{\bf{ = }}\frac{{{\bf{\Delta B}}}}{{{\bf{\Delta t}}}}\,\,\,\,\,...{\rm{ }}\left( {\bf{2}} \right)\)

We divided the rate in part (a) and (b) by 2 to get 0.0188M/s and 0.25M/s respectively.

The average rate of formation of B between 0.00 s and 10.0 s is get 0.0188M/s and the instantaneous rate of formation of B at 15.0 s is 0.025.

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Most popular questions from this chapter

In the nuclear industry, chlorine trifluoride is used to prepare uranium hexafluoride, a volatile compound of uranium used in the separation of uranium isotopes. Chlorine trifluoride is prepared by the reaction \({\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{(g) + 3}}{{\bf{F}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2Cl}}{{\bf{F}}_{\bf{3}}}{\bf{(g)}}\). Write the equation that relates the rate expressions for this reaction in terms of the disappearance of \({\bf{C}}{{\bf{l}}_{\bf{2}}}\) and \({{\bf{F}}_{\bf{2}}}\) and the formation of \({\bf{Cl}}{{\bf{F}}_{\bf{3}}}\).

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.

Graph the following data to determine whether the reaction A⟶B + C is first order.

Trial

Time(s)

(A)

1

4.0

0.220

2

8.0

0.144

3

12.0

0.110

4

16.0

0.088

5

20.0

0.074

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of \({\bf{3 \times 1}}{{\bf{0}}^{\bf{4}}}\)g/mole that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalysed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 µg (\({\bf{0}}{\bf{.15 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.

(Penicillin) (M)

Rate (mole/L/min)

\({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\) \(\)

\({\bf{1}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\)

\({\bf{3}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)

\({\bf{1}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\)

\({\bf{4}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)

\({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\)

When every collision between reactants leads to a reaction, what determines the rate at which the reaction occurs?
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