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Chapter 12: Q59 E (page 708)

The rate constant at 325掳C for the decomposition reaction \({{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{8}}} \to {\bf{2}}{{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}\)is 6.1 脳 10鈭�8 s鈭�1, and the activation energy is 261 kJ per mole of\({{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{8}}}\). Determine the frequency factor for the reaction.

Short Answer

Expert verified

The frequency factor for the reaction is\({\bf{3}}{\bf{.84*1}}{{\bf{0}}^{{\bf{15}}}}{{\bf{s}}^{{\bf{ - 1}}}}\).

Step by step solution

01

Using Arrhenius Equation

The Arrhenius equation is given as\({\bf{k = A}}{{\bf{e}}^{\frac{{{\bf{ - }}{{\bf{E}}_{\bf{a}}}}}{{{\bf{RT}}}}}}\),where A is the frequency factor, k is the rate constant,\({{\bf{E}}_{\bf{a}}}\)is the activation energy, R is the gas constant and T is the temperature in Kelvin.

02

Calculation of Activation energy

Replacing the values in the reaction,

\(6.1*{10^{ - 8}} = A{e^{\frac{{ - 261000}}{{8.314*598}}}}\)

\( \Rightarrow 6.1*{10^{ - 8}} = A{e^{ - 52.5}}\)

\( \Rightarrow A = \frac{{6.1*{{10}^{ - 8}}}}{{1.589*{{10}^{ - 23}}}}\)

\( \Rightarrow A = 3.84*{10^{15}}{s^{ - 1}}\)

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Most popular questions from this chapter

From the given data, use a graphical method to determine the order and rate constant of the following reaction: 2X鉄禮 + Z

Time(s)

5.0

10.0

15.0

20.0

25.0

30.0

35.0.

40.0

(X)(M)

0.0990

0.0497

0.0332

0.0249

0.0200

0.0166

0.0143

0.0125

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?

Doubling the concentration of a reactant increases the rate of a reaction four times. With this knowledge, answer the following questions:

  1. What is the order of the reaction with respect to that reactant?
  2. Tripling the concentration of a different reactant increases the rate of a reaction three times. What is the order of the reaction with respect to that reactant?

In an experiment, a sample of NaClO3 was 90% decomposed in 48 min. Approximately how long would this decomposition have taken if the sample had been heated 20掳C higher?

Determine which of the two diagrams here (both for the same reaction) involves a catalyst, and identify the activation energy for the catalyzed reaction:
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