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The activation energy for the gas phase isomerization of dimethyl citraconate is 105 kJ.

cis-(CH3OOC)(CH3)C=CHCOOCH3trans-(CH3OOC)(CH3)C=CHCOOCH3
The rate constant at 641 K is 2.77×10-4 /s. The rate constant will be
/s at 682 K.

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Answer:

[tex]k_2=9.06x10^{-4}/s[/tex]

Explanation:

Hello there!

In this case, since the activation energy, rate law and temperature, when variable, are related to each other as shown below:

[tex]ln(\frac{k_2}{k_1} )=\frac{-Ea}{R}(\frac{1}{T_2} -\frac{1}{T_1} )[/tex]

Thus, when solving for the rate constant at 682 K, we will obtain:

[tex]ln(\frac{k_2}{2.77x10^{-4}/s} )=\frac{-105000J/mol}{8.3145\frac{J}{mol*K}}(\frac{1}{682K} -\frac{1}{641K} ) \\\\ln(\frac{k_2}{2.77x10^{-4}/s} )=1.184\\\\\frac{k_2}{2.77x10^{-4}/s}=exp(1.184)\\\\k_2=2.77x10^{-4}/s*3.269\\\\k_2=9.06x10^{-4}/s[/tex]

Best regards!

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