The rate constant for the decomposition of N2O5 at various temperatures is given below: Draw a graph between ln k and 1/T and calculate the values of A and Ea. Predict the rate constant at 30º and 50ºC

Question 4.22:  The rate constant for the decomposition of N₂O₅ at various temperatures is given below:

Draw a graph between ln k and 1/T and calculate the values of A and E_a. Predict the rate constant at 30º and 50ºC.
Answer


Take antilog both side we get
A = 2.91 x 10⁶
At 30º C temperature in Kelvin T = 30 + 273 = 303 K
Value of 1/ T = 1/ 303 = 3.3 x 10 ^{– 3} K^-1
Plug the values in formula now we get
ln k = -2.8
make value positive to take antilog
add and subtract 3 both side we get
ln k = -2.8 + 3 -3
ln k = 0.2 - 3

Take anti ln both side we get
k =6.06 x 10^-2 sec ^-1
Similarly calculate for 50ºC
At 50º C, K 50 + 273 = 323 K
1/T = 1/323 = 3.1 x 10 ^-3 K^-1
Plug the values we get \
ln k = -0.5
take antiln both side we get
k = 0.607 sec ^-1