The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 $$\times$$ 10^$$-$$3 s^$$-$$1 and the activation energy E_a = 11.488 kJ mol^$$-$$1, the rate constant at 200 K is ____________ $$\times$$ 10^$$-$$5 s^$$-$$1. (Round off to the Nearest Integer). (Given : R = 8.314 J mol^$$-$$1 K^$$-$$1)

If the activation energy of a reaction is 80.9 kJ mol^$$-$$1, the fraction of molecules at 700 K, having enough energy to react to form
products is e^$$-$$x. The value of x is __________. (Rounded off to the nearest integer) [Use R = 8.31 J K^$$-$$1 mol^$$-$$1]

The rate constant of a reaction increases by five times on increase in temperature from 27$$^\circ$$C to 52$$^\circ$$C. The value of activation energy in kJ mol^$$-$$1 is _________. (Rounded off to the nearest integer)

[R = 8.314 J K^$$-$$1mol^$$-$$1]

For the reaction, aA + bB $$ \to $$ cC + dD, the plot of log k vs $${1 \over T}$$ is given below :


The temperature at which the rate constant of the reaction is 10^-4 s^-1 is _________ K. (Rounded off to the nearest integer)

[Given : The rate constant of the reaction is 10^-5 s^-1 at 500 K.]