Question

In: Chemistry

22. The rate constant for a reaction is 4.62 x 10-3 s -1 at 300°C. The...

22. The rate constant for a reaction is 4.62 x 10-3 s -1 at 300°C. The activation energy for the reaction is 46 kJ/mol. What is the rate constant at 600°C?

A. 1.28 x 10-1 s -1 <-Answer

B. 4.66 x 101 s -1

C. 9.37 x 10-1 s -1

D. 4.72 x 103 s -1

E. 9.37 x 103 s -1

Please explain the process in many details.

Solutions

Expert Solution

From Ahrrenius equation;

K1 = A*exp(-Ea/(RT1))

K2 = A*exp(-Ea/(RT2))

Note that A and Ea are the same, they do not depend on Temperature ( in the range fo temperature given)

Then

Divide 2 and 1

K2/K1 = A/A*exp(-Ea/(RT2)) / exp(-Ea/(RT1))

Linearize:

ln(K2/K1) = -Ea/R*(1/T2-1/T1)

get rid of negative sign

ln(K2/K1) = Ea/R*(1/T1-1/T2)

for a generic value:

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

where:

x-axis = 1/T ; inverse value of absolute temperature

y-axis = ln(K) , natural log of the rate constant

slope = -E/R or Acitvation Energy divided by Ideal Gas Constant

y-intercept = ln(A) ; natural log of the Frequency Factor

Substitute

ln(K2/(4.62*10^-3) = (46000/8.314)*(1/(300+273) - 1/(600+273))

K2 = (4.62*10^-3)*exp(3.31818)

K2 = 0.1275

K = 1.275*10^-1

choose A

queen_honey_blossom answered 1 year ago
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