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Chapter 12: Q12.5CYL (page 666)

Use the provided initial rate data to derive the rate law for the reaction whose equation is: \({\bf{OC}}{{\bf{l}}^ - }\)(aq) + \({{\bf{I}}^ - }\)(aq) 鉄禣I鈭�(aq) +\({\bf{C}}{{\bf{l}}^ - }\)(aq)

Trial

(\({\bf{OC}}{{\bf{l}}^ - }\)) (mol/L)

(\({{\bf{I}}^ - }\)) (mol/L)

Initial Rate (mol/L/s)

1.

0.0040

0.0020

0.00184

2.

0.0020

0.0040

0.00092

3.

0.0020

0.0020

0.00046

Determine the rate law expression and the value of the rate constant k with appropriate units for this reaction.

Short Answer

Expert verified

The rate, \(r = k\left( {{\bf{OC}}{{\bf{l}}^ - }} \right)\left( {{{\bf{l}}^ - }} \right)\) with rate constant k = 5.75 脳 104mol-2L2s-1.

Step by step solution

01

Rate of a Reaction

The rate of reaction may be defined as the speed of the reactant react to give product in a particular reaction at a particular time. The concentration of the reactant and product are represented into mole/L.

\({\bf{rate = k}}{\left( {\bf{A}} \right)^{\bf{m}}}{\left( {\bf{B}} \right)^{\bf{n}}}^{}\)

02

Value of r \(\)

\(\begin{aligned}{}\begin{aligned}{{}{}}{{\bf{rate 2 / rate 3 = 0}}{\bf{.00092 / 0}}{\bf{.00046}}}\\{{\bf{rate 2 / rate 3 = k}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{y}}}{\bf{/\;k}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{y}}}}\end{aligned}\\\begin{aligned}{{}{}}{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{2}}{\bf{.00 = 2}}{\bf{.0}}{{\bf{0}}^{\bf{y}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{y = 1}}}\end{aligned}\end{aligned}\)

\(\begin{aligned}{}\begin{aligned}{{}{}}{{\bf{rate 1 / rate 2 = 0}}{\bf{.00184 / 0}}{\bf{.00092}}}\\{{\bf{rate 1 / rate 2 = k}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{y}}}{\bf{/ k}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{y}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{2}}{\bf{.00 = }}{{\bf{2}}^{\bf{x}}}{{\bf{2}}^{\bf{y}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{2}}{\bf{.00 = }}{{\bf{2}}^{\bf{x}}}{{\bf{2}}^{\bf{1}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{4}}{\bf{.00 = }}{{\bf{2}}^{\bf{x}}}}\end{aligned}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{x = 2}}\end{aligned}\)

03

Value of k

Putting value in rate equation and we can calculate K: \(\)

\(\begin{aligned}{}\begin{aligned}{{}{}}{\,\,\,\,\,\,\,\,\,{\bf{rate = k}}{{\left( {{\bf{OC}}{{\bf{l}}^{\bf{ - }}}} \right)}^{\bf{2}}}{{\left( {{{\bf{I}}^{\bf{ - }}}} \right)}^{\bf{1}}}}\\{{\bf{0}}{\bf{.00184 = k}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{2}}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{1}}}}\end{aligned}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{k = 5}}{\bf{.75 \times 1}}{{\bf{0}}^{\bf{4}}}{\bf{mo}}{{\bf{l}}^{{\bf{ - 2}}}}{{\bf{L}}^{\bf{2}}}{{\bf{s}}^{{\bf{ - 1}}}}\end{aligned}\)

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Most popular questions from this chapter

For the past 10 years, the unsaturated hydrocarbon 1,3-butadiene \(\left( {{\bf{C}}{{\bf{H}}_{\bf{2}}}{\bf{ = CH - CH = C}}{{\bf{H}}_{\bf{2}}}} \right)\) has ranked 38th among the top 50 industrial chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene:

The isomerization of cyclobutene to butadiene is first-order, and the rate constant has been measured as \({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 4}}}}{{\bf{s}}^{{\bf{ - 1}}}}\) at 150 \({\bf{^\circ C}}\) in a 0.53-L flask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at 150 \({\bf{^\circ C}}\) with an initial pressure of 55 torr.

Use the data provided in a graphical method to determine the order and rate constant of the following reaction:\({\bf{2P}} \to {\bf{Q}} + {\bf{W}}\)

Time (s)

9.0

13.0

18.0

22.0

25.0

(P) (M)

1.077 脳 10鈭�3

1.068 脳 10鈭�3

1.055 脳 10鈭�3

1.046 脳 10鈭�3

1.039 脳 10鈭�3

Usethe data provided to graphically determine the order and rate constant of the following reaction: \({\bf{S}}{{\bf{O}}_{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}} \to {\bf{S}}{{\bf{O}}_{\bf{2}}}{\bf{ + C}}{{\bf{l}}_{\bf{2}}}\)

Time(hr)

0

5.00*\({\bf{1}}{{\bf{0}}^{\bf{3}}}\)

1.00*\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)

1.50*\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)

2.50*\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)

3.00*104

4.00*104

\({\bf{(S}}{{\bf{O}}_{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{)}}\)(M)

0.100

0.0896

0.0802

0.0719

0.0577

0.0517

0.0415

For the reaction\({\bf{Q}} \to {\bf{W + X}}\), the following data were obtained at 30 掳C

  1. What is the order of the reaction with respect to (Q), and what is the rate law?
  2. What is the rate constant?

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for \(\frac{{\bf{1}}}{{{\bf{64}}}}\) of the initial dose to remain in the athlete鈥檚 body?
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