🤓 Based on our data, we think this question is relevant for Professor Hamann's class at HUNTER.

We’re given the plot of ln k (y) vs. 1/T (x).

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

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{k}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}{\mathbf{}}\left(\frac{\mathbf{1}}{\mathbf{T}}\right){\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{}}{\mathbf{A}}}$

where:

**k** = rate constant

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

**R** = gas constant (8.314 J/mol • K)

**T** = temperature (in K)

**A** = Arrhenius constant or frequency factor

This is also in the form of:

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{k}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}{\mathbf{}}\left(\frac{\mathbf{1}}{\mathbf{T}}\right){\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{}}{\mathbf{A}}}\phantom{\rule{0ex}{0ex}}{\mathbf{y}}{\mathbf{}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{}}{\mathbf{}}{\mathbf{}}{\mathbf{}}{\mathbf{m}}{\mathbf{}}{\mathbf{}}{\mathbf{}}{\mathbf{}}\left(\mathbf{x}\right){\mathbf{}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{}}{\mathbf{}}{\mathbf{b}}$

where:

**m** = slope

**b** = y-intercept

**Given:**

**m** = -1.10x10^{4} K

**b** = 33.5

**t** = 25°C + 273.15 = 298.15 K

The reaction

(CH_{3})_{3}CBr + OH^{- }→ (CH_{3})_{3}COH + Br^{-}

in a certain solvent is first order with respect to (CH_{3})_{3}CBr and zero order with respect to OH^{-}. In several experiments, the rate constant k was determined at different temperatures. A plot of ln(k) versus 1/T was constructed resulting in a straight line with a slope value of -1.10 x 10^{4} K and y-intercept of 33.5. Assume k has units of s^{-1}.

c. Calculate the value of k at 25°C.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Arrhenius Equation concept. You can view video lessons to learn Arrhenius Equation. Or if you need more Arrhenius Equation practice, you can also practice Arrhenius Equation practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Hamann's class at HUNTER.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Chemistry: An Atoms First Approach - Zumdahl 2nd Edition. You can also practice Chemistry: An Atoms First Approach - Zumdahl 2nd Edition practice problems.