Using the data below determine the E a and A (i.e. Arrhenius equation parameters

Question

Using the data below determine the Ea and A (i.e. Arrhenius equation parameters) for the decomposition of Malonic acid

CH2(COOH)2(g) ---> CH3COOH(g) + CO2(g)

Here's the graph I made but confused on what to do now, please show work, thanks

T C) 1T k (SA-1) In k 153.6 0.002343 1083 6.98749 153.2 0.002345 1045 6.951772 143.5 0.0024 410 6.016157 142.3 0.002407 367 5.905362 208 5.337538 136.4 0.002442 134.2 0.002455 169 5.129899 y 16715x 46.15 RE 0.9998 0.00232 0.00234 0.00236 0.00238 0.0024 0.00242 0.00244 0.00246 0.00248 1/T (1/K)

Explanation / Answer

Lets use given plot and Arrhenius equation to determine Ea and A.

Ea is activation enegy and A is frequency factor.

Arrhenius equation is

Ln k = - ( Ea/RT) + ln A

Ea is activation energy, k is rate constant , T is temperature in K and A is frequency factor, R is gas constant and its value is 8.314 J per (mol K)

Lets sort the term in the form of y = mx +c

y = ln K

m =- Ea/R

x = 1/T

ln A = C

m = slope = -Ea/R

Lets use equation on the graph

y = - 16715 x + 46.15

slope of this equation, m = -16715

Lets plug in the value of slope

-16715 = - Ea/R

-16715 = - Ea/ 8.314

Ea = 16715 * 8.314 = 139018.7

Ea = 139019.0 J /mol

Calculation of A

Ln A = 46.15

Lets take exp of both side

Exp ( ln A) = exp ( 46.15)

A = exp ( 46.15)

A = 1.10 E20

Frequency factor A = 1.10 E 20

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