Arrhenius Equation The variation of the rate constant with temperature can be ex

Question

Arrhenius Equation

The variation of the rate constant with temperature can be expressed by the Arrhenius Equation. The two-point form of this equation can be written as:

1

1

R

T2

T1

where k2 and k1 are the values of the rate constant at the Kelvin temperatures T2 and T1, respectively, Ea is the activation energy, and R is the ideal gas constant.

Notice that k2 is over k1, there is a minus sign preceding Ea/R, and T2 comes before T1. This is the form of the equation used in the OWL feedback.

You may see slightly different, but equivalent, forms of this equation. It's easy to confuse the different forms. They will all give the same result, but not if you mix parts of one form with parts of another!

Here are two more forms that you are likely to see. Can you spot the differences between these and the OWL form above?

1

1

R

T1

T2

1

1

R

T2

T1

Both of these are missing the minus sign preceding Ea/R.

In the first one, this is balanced by interchanging the 1/T2 and 1/T1 terms.

In the second one, this is balanced by interchanging k2 and k1.

Problem:

1

1

R

T2

T1

Explanation / Answer

1)

The activation energy for the gas phase decomposition of trichloroethane Ea = 200 kJ = 200*10^3 J

here, The rate constant at T1 = 625 K is K1 = 6.10×10-5 /s. and K2 = 5.44*10^-4

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

ln(5.44*10^-4/6.1*10^-5) = 200*10^3/8.314 (1/625 - 1/T2)

solving this we get, T2 = 1267.7 K .............. Answer

2)

the rate constant at T1 = 655 K is K1 = 3.54×10-4 /s and T2 = 689 K., K2 = ?

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

ln(K2/3.54*10^-4) = 200*1000/8.314 ( 1/655-1/689)

solving we get, K2 = 2.17 *10^-3 ............. Answer

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