Question

# The rate constants for a first order reaction are found to be 2.76*10-5 s^-1 at 25...

The rate constants for a first order reaction are found to be 2.76*10-5 s^-1 at 25 degrees celsius and 6.65*10^-4 s^-1 at 50 degrees celsius, respectively. A) Calculate the activation energy Ea in kilojoules per mole. B) Calculate the rate constant at 75 degrees celsius

a)

Given:

T1 = 25 oC

=(25+273)K

= 298 K

T2 = 50 oC

=(50+273)K

= 323 K

K1 = 2.76*10^-5 s-1

K2 = 6.65*10^-4 s-1

use:

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

ln(6.65*10^-4/2.76*10^-5) = ( Ea/8.314)*(1/298 - 1/323)

3.182 = (Ea/8.314)*(2.597*10^-4)

Ea = 101856 J/mol

Ea = 101.8556 KJ/mol

b)

Given:

T1 = 25 oC

=(25+273)K

= 298 K

T2 = 75 oC

=(75+273)K

= 348 K

K1 = 2.76*10^-5 s-1

Ea = 101.8556 KJ/mol

= 101856 J/mol

use:

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

ln(K2/2.76*10^-5) = (101856/8.314)*(1/298 - 1/348.0)

ln(K2/2.76*10^-5) = 12251*(4.821*10^-4)

K2 = 1.014*10^-2 s-1

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