# Problem: The reaction(CH3)3CBr + OH- → (CH3)3COH + Br-in a certain solvent is first order with respect to (CH3)3CBr 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 104 K and y-intercept of 33.5. Assume k has units of s-1.c. Calculate the value of k at 25°C.

###### FREE Expert Solution

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:

where:

k = rate constant

Ea = 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:

where:

m = slope

b = y-intercept

Given:

m = -1.10x104 K

b = 33.5

t = 25°C + 273.15 = 298.15 K

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###### Problem Details

The reaction

(CH3)3CBr + OH→ (CH3)3COH + Br-

in a certain solvent is first order with respect to (CH3)3CBr 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 104 K and y-intercept of 33.5. Assume k has units of s-1.

c. Calculate the value of k at 25°C.