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Chapter 12: Q63 E (page 709)

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?

Short Answer

Expert verified

The energy of activation for the reaction is 178.79 kJ/mol.

Step by step solution

01

Plot of ln K vs 1/T

T (K)

1/T (K-1)

k (M-1s-1)

ln k

555

0.0018

6.23*10-7

-14.2887

575

0.00174

2.42*10-6

-12.9317

645

0.00155

1.44*10-4

-8.84570

700

0.00143

2.01*10-3

-6.20962

The plot of ln k vs 1/T gives a straight line.

02

Calculation of Activation energy

The activated energy of a reaction is the minimum energy that a reactant must possess to convert into products.

The Arrhenius equation is given as

\(\begin{align}k &= A{e^{\frac{{ - {E_a}}}{{RT}}}}\\\ln k &= \ln A + (\frac{{ - {E_a}}}{{RT}})\end{align}\)

Here k is the rate constant; A is the pre-exponential factor, Eais the activation energy, R is the universal gas constant, and T is the temperature.

The value of\({{\bf{E}}_{\bf{a}}}\)can be calculated from the slope of the plot.

\({\bf{Slope = }}\frac{{{\bf{ - }}{{\bf{E}}_{\bf{a}}}}}{{\bf{R}}}\)

Considering the second and third data points on the plot, the slope is

\(\begin{align}Slope &= \frac{{\Delta y}}{{\Delta x}}\\\frac{{ - {E_a}}}{R} &= \frac{{ - 12.9317 - \left( { - 8.8457} \right)}}{{0.00174 - 0.00155}}\\ - {E_a} &= - 21505.26 \times 8.314\\{E_a} &= 178794.7J/mol\\{E_a} &= 178.79kJ/mol\end{align}\)

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Most popular questions from this chapter

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?

A study of the rate of dimerization of \({{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{6}}}\) gave the data shown in:

\({\bf{2}}{{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{6}}} \to {{\bf{C}}_{\bf{8}}}{{\bf{H}}_{{\bf{12}}}}\)

  1. Determine the average rate of dimerization between 0 s and 1600 s, and between 1600 s and 3200 s.
  2. Estimate the instantaneous rate of dimerization at 3200 s from a graph of time versus (\({{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{6}}}\)). What are the units of this rate?

(c) Determine the average rate of formation of \({{\bf{C}}_{\bf{8}}}{{\bf{H}}_{{\bf{12}}}}\) at 1600 s and the instantaneous rate of formation at 3200 s from the rates found in parts (a) and (b).

:How does an increase in temperature affect rate of reaction? Explain this effect in terms of the collision theory of the reaction rate

In the PhET Reactions & Rates (http://openstaxcollege.org/l/16PHETreaction) interactive, on the Many Collisions tab, set up a simulation with 15 molecules of A and 10 molecules of BC. Select 鈥淪how Bonds鈥� under Options.

  1. Leave the Initial Temperature at the default setting. Observe the reaction. Is the rate of reaction fast or slow?
  2. Click 鈥淧ause鈥� and then 鈥淩eset All,鈥� and then enter 15 molecules of A and 10 molecules of BC once again. Select 鈥淪how Bonds鈥� under Options. This time, increase the initial temperature until, on the graph, the total average energy line is completely above the potential energy curve. Describe what happens to the reaction

Account for the increase in reaction rate brought about by a catalyst.
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