We’re being asked to **determine the rate constant** at 25°C of the reaction when k = 8.54 x 10^{-4} s ^{-1} at 45°C with a EA = 90.8 kJ

This means we need to use the ** two-point form of the Arrhenius Equation**:

$\overline{){\mathbf{ln}}\left(\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}\right){\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}\frac{\mathbf{Ea}}{\mathbf{R}}\left[\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\right]}$

where:

**k _{1}** = rate constant at T

**k _{2}** = rate constant at T

**E _{a}** = activation energy (in J/mol)

**R** = gas constant (8.314 J/mol•K)

**T _{1} and T_{2}** = temperature (in K).

A certain first-order reaction has a rate constant of 2.75 x 10^{-2} s^{-1} at 25°C. What is the value of K at 90.0 °C if E_{a} = 275 kJ/mol?

a. 1.16x10^{7 }s^{-1}

b. 2.71x10^{10 }s^{-1}

c. 2.43x10^{11 }s^{-1}

d. 9.11x10^{10}^{ }s^{-1}

e. 2.31x10^{9 }s^{-1}

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