We’re being asked to determine the value of k at 30°C. We’re given the activation energy and the rates at two different temperatures.

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

$\overline{){\mathbf{ln}}{\mathbf{}}\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}{\mathbf{[}}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}{\mathbf{-}}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}{\mathbf{]}}}$

where:

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

For the reaction

2N_{2}O_{5}(g) → 4NO_{2}(g) + O_{2}(g)

The activation energy is 1.0 × 10^{5} J/mol and the value of k at 20◦C is 2.0 × 10^{−5} s^{-1 }. What is the value of k at 30^{◦}C?

A. 2.0 × 10^{−5} s^{-1}

B. 2.0 × 10^{−6 } s^{-1}

C. 8.4 × 10^{−13 } s^{-1}

D. 9.3 × 10^{−4} s^{-1}

E. 7.3 × 10^{−5} s^{-1}

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