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Chapter 12: Q60 E (page 708)

The rate constant for the decomposition of acetaldehyde, \({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{CHO}}\), to methane, \({\bf{C}}{{\bf{H}}_{\bf{4}}}\), and carbon monoxide, CO, in the gas phase is 1.1 × 10−2 L/mol/s at 703 K and 4.95 L/mol/s at 865 K. Determine the activation energy for this decomposition.

Short Answer

Expert verified

The energy of activation for the reaction is 96.769 kJ/mol

Step by step solution

01

Step 1: Using Arrhenius Equation

From the Arrhenius Equation, the rate of reaction at two different temperatures is given as

\(\log \frac{{{k_2}}}{{{k_1}}} = \frac{{{E_a}}}{{2.303*R}}\left( {\frac{1}{{{T_1}}} - \frac{1}{{{T_2}}}} \right)\)

where k1and k2are the rate constants at \({{\bf{T}}_{\bf{1}}}\) and \({{\bf{T}}_{\bf{2}}}\) where \({{\bf{T}}_{\bf{1}}}{\bf{ < }}{{\bf{T}}_{\bf{2}}}\). \({{\bf{E}}_{\bf{a}}}\)is the activation energy (in J) and R is the gas constant

02

Calculation

Replacing the values,

\(\log \frac{{4.95}}{{1.1*{{10}^{ - 2}}}} = \frac{{{E_a}}}{{2.303*8.314}}\left( {\frac{1}{{703}} - \frac{1}{{865}}} \right)\)

\({E_a} = 190691.9J/mol\)

\({E_a} = 190.69kJ/mol\)

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Most popular questions from this chapter

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

The element Co exists in two oxidation states, Co(II) and Co(III), and the ions form many complexes. The rate at which one of the complexes of Co(III) was reduced by Fe(II) in water was measured. Determine the activation energy of the reaction from the following data:

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k(s-1)

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Trial

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

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

Initial Rate (mol/L/s)

1.

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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.

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