A certain first order reaction has a rate constant at .0001 at 30 degrees Celsius and an activation energy of 120 kJ/mol. What is the rate constant for this reaction at 64 degrees celsius?

1 Answer
Truong-Son N.
May 26, 2018

#k_2 = 4.80#

What are the units on #k_2# and #k_1#? Why?

The Arrhenius equation relates rate constants to the temperature...

#ln(k_2/k_1) = -E_a/R[1/T_2 - 1/T_1]#

where #E_a# is the activation energy in #"kJ/mol"#, #R# is the universal gas constant, and #T# is the temperature in... no, not #""^@ "C"#, but #"K"#.

We choose

  • #k_2# to be at temperature #T_2 = 64+273.15 = "337.15 K"#
  • #k_1 = 0.0001# at #T_1 = 30 + 273.15 = "303.15 K"#.

We algebraically solve to get:

#k_2 = k_1"exp"(-E_a/R[1/T_2 - 1/T_1])#

where #"exp"(x) = e^x#.

Therefore:

#color(blue)(k_2) = 0.0001 cdot "exp"(-("120 kJ/mol")/("0.008314472 kJ/mol"cdot"K")[1/"337.15 K" - 1/"303.15 K"])#

#= color(blue)("4.80 s"^(-1))#

How did I know what the units of #k_2# are, and what are the units of #k_1#?

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