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From the Eyring equation, we can simply calculate the $k$ value for it.

\begin{align} k &= \frac{k_\mathrm{b} T}{h}\exp\left(\frac{-\Delta G}{RT}\right)\\ k_\mathrm{b} &= \pu{1.38E-9 J K^-1}\\ T &= \pu{355 K}\\ h &= \pu{6.626E-34 J s}\\ R &= \pu{8.3145 J K^-1 mol^-1} \end{align}

Here, I am assuming the average of $\pu{29 kcal/mol}$ and $\pu{39 kcal/mol}$ to be $\Delta G = \pu{34 kcal mol^-1} = \pu{142256 J mol^-1}$

If we plug in the values into the equation, we get a $k$ value equal to about $\pu{8.64 x 10^-9 s^-1}$ which is quite small.

If we take for example a Gibbs free energy of activation of $\pu{23 kcal mol^-1}$, that would equate to a half-life of 2 hours at room temperature based on $t_{1/2} = \frac{\ln2}{k}$ for first-ordered reactions. If we use the same formula for the $k$ we calculated at $\pu{355 K}$, we get a half-life of $\pu{8.02 x 10^7 s}$ which is about $2.54$ years. Therefore, the reaction is likely not going to preceded quickly at $\Delta G = \pu{34 kcal mol^-1}$ and can be considered unfeasible as the reaction proceeds extremely slowly.

In terms of what temperature is required to make the reactions feasible for your given Gibbs free activation energies, after a bit of algebra, I came up with some theoretical values: at $\Delta G \pu{= 29 kcal mol^-1}$, the half-life is less than a day at $\pu{355 K}$ which is reasonable.

For the conditions, $\Delta G = \pu{34 kcal mol^-1}$ and $\Delta G = \pu{39 kcal mol^-1}$, both reactions will theoretically proceed with a half-life under one day at at a little over $\pu{412 K}$ and $\pu{471 K}$, respectively.

From the Eyring equation, we can simply calculate the $k$ value for it.

\begin{align} k &= \frac{k_\mathrm{b} T}{h}\exp\left(\frac{-\Delta G^\ddagger}{RT}\right)\\ k_\mathrm{b} &= \pu{1.38E-9 J K^-1}\\ T &= \pu{355 K}\\ h &= \pu{6.626E-34 J s}\\ R &= \pu{8.3145 J K^-1 mol^-1} \end{align}

Here, I am assuming the average of $\pu{29 kcal/mol}$ and $\pu{39 kcal/mol}$ to be $\Delta G^\ddagger = \pu{34 kcal mol^-1} = \pu{142256 J mol^-1}$

If we plug in the values into the equation, we get a $k$ value equal to about $\pu{8.64 x 10^-9 s^-1}$ which is quite small.

If we take for example a Gibbs free energy of activation of $\pu{23 kcal mol^-1}$, that would equate to a half-life of 2 hours at room temperature based on $t_{1/2} = \frac{\ln2}{k}$ for first-ordered reactions. If we use the same formula for the $k$ we calculated at $\pu{355 K}$ for $\Delta G^\ddagger = \pu{34 kcal mol^-1}$, we get a half-life of $\pu{8.02 x 10^7 s}$ which is about $2.54$ years. Therefore, the reaction is likely not going to proceed quickly at $\Delta G^\ddagger = \pu{34 kcal mol^-1}$ and can be considered unfeasible as the reaction goes extremely slowly.

If we instead take the lower end with $\Delta G^\ddagger \pu{= 29 kcal mol^-1}$, the half-life is less than a day at $\pu{355 K}$ which is reasonable. However, anything after $\Delta G^\ddagger = \pu{30 kcal mol^-1}$ are essentially unfeasible at $\pu{355 K}$. Even with $\Delta G^\ddagger = \pu{30 kcal mol^-1}$ at $\pu{355 K}$, the half-life is over 3 days and it will only increase exponentially as $\Delta G^\ddagger$ increases.

Note that $\Delta G^\ddagger$ is temperature dependant and the calculations above are done assuming that $\Delta G^\ddagger$ is constant at the given temperatures. Therefore, the theoretical values I calculated may not perfectly match the experimental results of the reaction pathway you are studying. However, it should hopefully give a general idea of the rate and the feasibility of reactions for the range of $\Delta G^\ddagger$ values you derived.

From the Eyring equation, we can simply calculate the $k$ value for it.

\begin{align} k &= \frac{k_\mathrm{b} T}{h}\exp\left(\frac{-G}{RT}\right)\\ k_\mathrm{b} &= \pu{1.38E-9 J K^-1}\\ T &= \pu{355 K}\\ h &= \pu{6.626E-34 J s}\\ R &= \pu{8.3145 J K^-1 mol^-1} \end{align}

Here, I am assuming the average of $\pu{29 kcal/mol}$ and $\pu{39 kcal/mol}$ to be $G = \pu{34 kcal mol^-1} = \pu{142256 J mol^-1}$

If we plug in the values into the equation, we get a $k$ value equal to about $\pu{8.64 x 10^-9 s^-1}$ which is quite small.

If we take for example a Gibbs free energy of activation of $\pu{23 kcal mol^-1}$, that would equate to a half-life of 2 hours at room temperature based on $t_{1/2} = \frac{\ln2}{k}$ for first-ordered reactions. If we use the same formula for the $k$ we calculated at $\pu{355 K}$, we get a half-life of $\pu{8.02 x 10^7 s}$ which is about $2.54$ years. Therefore, the reaction is likely not going to preceded quickly at $G = \pu{34 kcal mol^-1}$ and can be considered unfeasible as the reaction proceeds extremely slowly.

In terms of what temperature is required to make the reactions feasible for your given Gibbs free activation energies, after a bit of algebra, I came up with some theoretical values: at $\pu{G = 29 kcal mol^-1}$, the half-life is less than a day at $\pu{355 K}$ which is reasonable.

For the conditions, $G = \pu{34 kcal mol^-1}$ and $G = \pu{39 kcal mol^-1}$, both reactions will theoretically proceed with a half-life under one day at at a little over $\pu{412 K}$ and $\pu{471 K}$, respectively.

From the Eyring equation, we can simply calculate the $k$ value for it.

\begin{align} k &= \frac{k_\mathrm{b} T}{h}\exp\left(\frac{-\Delta G}{RT}\right)\\ k_\mathrm{b} &= \pu{1.38E-9 J K^-1}\\ T &= \pu{355 K}\\ h &= \pu{6.626E-34 J s}\\ R &= \pu{8.3145 J K^-1 mol^-1} \end{align}

Here, I am assuming the average of $\pu{29 kcal/mol}$ and $\pu{39 kcal/mol}$ to be $\Delta G = \pu{34 kcal mol^-1} = \pu{142256 J mol^-1}$

If we plug in the values into the equation, we get a $k$ value equal to about $\pu{8.64 x 10^-9 s^-1}$ which is quite small.

If we take for example a Gibbs free energy of activation of $\pu{23 kcal mol^-1}$, that would equate to a half-life of 2 hours at room temperature based on $t_{1/2} = \frac{\ln2}{k}$ for first-ordered reactions. If we use the same formula for the $k$ we calculated at $\pu{355 K}$, we get a half-life of $\pu{8.02 x 10^7 s}$ which is about $2.54$ years. Therefore, the reaction is likely not going to preceded quickly at $\Delta G = \pu{34 kcal mol^-1}$ and can be considered unfeasible as the reaction proceeds extremely slowly.

In terms of what temperature is required to make the reactions feasible for your given Gibbs free activation energies, after a bit of algebra, I came up with some theoretical values: at $\Delta G \pu{= 29 kcal mol^-1}$, the half-life is less than a day at $\pu{355 K}$ which is reasonable.

For the conditions, $\Delta G = \pu{34 kcal mol^-1}$ and $\Delta G = \pu{39 kcal mol^-1}$, both reactions will theoretically proceed with a half-life under one day at at a little over $\pu{412 K}$ and $\pu{471 K}$, respectively.

From the Eyring equation, we can simply calculate the k value for it.

$k = \frac{k_b T}{h}e^{\frac{-G}{RT}}$

$k_b = \pu{1.38 x 10^-9 J K^-1}$

$T = 355 K$

$h = \pu{6.626 x 10^-34 J s} $

$R = \pu{8.3145 J K^-1 mol^-1}$

Here, I am assuming the average of 29 and 39 to be $G = \pu{34 kcal mol^-1} = \pu{142256 J mol^-1}$

If we plug in the values into the equation, we get a k value equal to about $\pu{8.64 x 10^-9 s^-1}$ which is quite small.

If we take for example a Gibbs free energy of activation of $\pu{23 kcal mol^-1}$, that would equate to a half-life of 2 hours at room temperature based on $t_{1/2} = \frac{\ln2}{k}$ for first-ordered reactions. If we use the same formula for the k we calculated at 355 K, we get a half-life of $\pu{8.02 x 10^7 s}$ which is about 2.54 years. Therefore, the reaction is likely not going to preceded quickly at $G = \pu{34 kcal mol^-1}$ and can be considered unfeasible as the reaction proceeds extremely slowly.

In terms of what temperature is required to make the reactions feasible for your given Gibbs free activation energies, after a bit of algebra, I came up with some theoretical values: at $\pu{G = 29 kcal mol^-1}$, the half-life is less than a day at 355 K which is reasonable.

For the conditions, $G = \pu{34 kcal mol^-1}$ and $G = \pu{39 kcal mol^-1}$, both reactions will theoretically proceed with a half-life under one day at at a little over 412 K and 471 K respectively.

From the Eyring equation, we can simply calculate the $k$ value for it.

\begin{align} k &= \frac{k_\mathrm{b} T}{h}\exp\left(\frac{-G}{RT}\right)\\ k_\mathrm{b} &= \pu{1.38E-9 J K^-1}\\ T &= \pu{355 K}\\ h &= \pu{6.626E-34 J s}\\ R &= \pu{8.3145 J K^-1 mol^-1} \end{align}

Here, I am assuming the average of $\pu{29 kcal/mol}$ and $\pu{39 kcal/mol}$ to be $G = \pu{34 kcal mol^-1} = \pu{142256 J mol^-1}$

If we plug in the values into the equation, we get a $k$ value equal to about $\pu{8.64 x 10^-9 s^-1}$ which is quite small.

If we take for example a Gibbs free energy of activation of $\pu{23 kcal mol^-1}$, that would equate to a half-life of 2 hours at room temperature based on $t_{1/2} = \frac{\ln2}{k}$ for first-ordered reactions. If we use the same formula for the $k$ we calculated at $\pu{355 K}$, we get a half-life of $\pu{8.02 x 10^7 s}$ which is about $2.54$ years. Therefore, the reaction is likely not going to preceded quickly at $G = \pu{34 kcal mol^-1}$ and can be considered unfeasible as the reaction proceeds extremely slowly.

In terms of what temperature is required to make the reactions feasible for your given Gibbs free activation energies, after a bit of algebra, I came up with some theoretical values: at $\pu{G = 29 kcal mol^-1}$, the half-life is less than a day at $\pu{355 K}$ which is reasonable.

For the conditions, $G = \pu{34 kcal mol^-1}$ and $G = \pu{39 kcal mol^-1}$, both reactions will theoretically proceed with a half-life under one day at at a little over $\pu{412 K}$ and $\pu{471 K}$, respectively.