Question

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.

Answer 1

`k_2=9.06x10^(-4)/s`

Step-by-step explanation:

Hello there!

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

`ln((k_2)/(k_1) )=(-Ea)/(R)((1)/(T_2) -(1)/(T_1) )`

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

`ln((k_2)/(2.77x10^(-4)/s) )=(-105000J/mol)/(8.3145(J)/(mol*K))((1)/(682K) -(1)/(641K) ) \\\\ln((k_2)/(2.77x10^(-4)/s) )=1.184\\\\(k_2)/(2.77x10^(-4)/s)=exp(1.184)\\\\k_2=2.77x10^(-4)/s*3.269\\\\k_2=9.06x10^(-4)/s`

Best regards!