The Gibbs activation function for a chemical reaction ΔG^† follows from the rate constant k acco

Step 1: u000ATo find the uncertainty in u005C(u005CDelta G^{u005Cdagger}u005C) due to the uncertainty in the rate co

The Gibbs activation function for a chemical reaction ΔG^†...

The Gibbs activation function for a chemical reaction $\Delta G^{\dagger}$ follows from the rate constant $k$ according to Eyring's equation $$ k=\left(k_B T / h\right) \exp \left(-\Delta G^{\ddagger} / R T\right) $$ Here $k_B$ is Boltzmann's constant, $h$ is Planck's constant and $R$ the gas constant (see the data sheet PHYSICAL CONSTANTS on page 209, or use the Python module physcon.py). (a) If the rate constant $k$ has an uncertainty of $10 \%$, what is the resulting uncertainty in $\Delta G^{\dagger}$ ? (b) Discuss how an uncertainty in the temperature propagates into $\Delta G^{\ddagger}$. (c) If $\Delta G^\psi=30 \mathrm{~kJ} / \mathrm{mol}$ and $T=300 \mathrm{~K}$, how large is the uncertainty in $\Delta G^t$ as a result of an uncertainty of $5^{\circ} \mathrm{C}$ in the temperature?

The Gibbs activation function for a chemical reaction $\Delta G^{\dagger}$ follows from the rate constant $k$ according to Eyring's equation
$$
k=\left(k_B T / h\right) \exp \left(-\Delta G^{\ddagger} / R T\right)
$$
Here $k_B$ is Boltzmann's constant, $h$ is Planck's constant and $R$ the gas constant (see the data sheet PHYSICAL CONSTANTS on page 209, or use the Python module physcon.py).
(a) If the rate constant $k$ has an uncertainty of $10 \%$, what is the resulting uncertainty in $\Delta G^{\dagger}$ ?
(b) Discuss how an uncertainty in the temperature propagates into $\Delta G^{\ddagger}$.
(c) If $\Delta G^\psi=30 \mathrm{~kJ} / \mathrm{mol}$ and $T=300 \mathrm{~K}$, how large is the uncertainty in $\Delta G^t$ as a result of an uncertainty of $5^{\circ} \mathrm{C}$ in the temperature?

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