Ea or k from Arrhenius Plot Information

Question

For the gas phase decomposition of chloroethane,

CH₃CH₂ClC₂H₄ + HCl

the rate constant in s^-1 has been determined at several temperatures. When ln k is plotted against the reciprocal of the Kelvin temperature, the resulting linear plot has a slope of -3.06×10⁴ K and a y-intercept of 33.6.

The value of the rate constant for the gas phase decomposition of chloroethane at 753 K is

Answer 1

The plot being described is an Arrhenius plot. The equation for this plot is that in the form of a straight line.

ln k = -Ea/R (1/T) + ln A

y = m x + b

So, the slope of the line (-3.06x10⁴) = - Ea/R where R = 8.314 J/Kmol

The y-intercept (33.6) = ln A

Solving for Ea and A, we have the following:

-3.06x10⁴ = - Ea/8.314

Ea = 2.54x10⁵ J/mol = 2.54x10² kJ/mol = 254 kJ/mol

33.6 = ln A

A = 3.91x19¹⁴

Go back to the original Arrhenius equation, and plug in the above values, and solve for k...

ln k = -Ea/R (1/T) + ln A

Solve for k

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Edited comments:

ln k = - Ea/R (1/T) = ln A

ln k = -254 / 0.008314 (1/753) + ln 3.91x10¹⁴

ln k = -30,550 (0.00133) + 33.6

ln k = -40.6 + 33.6

ln k = - 7.0

k = 9.1x10^-4

(be sure to check the math, but this seems correct). Hope this helps somewhat.