The rate constant for a first order reaction is given by the following equation:

$$\ln k = 33.24 - {{2.0 \times {{10}^4}\,K} \over T}$$

The activation energy for the reaction is given by ____________ kJ mol^$$-$$1. (In nearest integer) (Given : R = 8.3 J K^$$-$$1 mol^$$-$$1)

Catalyst A reduces the activation energy for a reaction by 10 kJ mol^$$-$$1 at 300 K. The ratio of rate constants, $${{{}^kT,\,Catalysed} \over {{}^kT,\,Uncatalysed}}$$ is e^x. The value of x is ___________. [nearest integer]

[Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 J K^$$-$$1 mol^$$-$$1]

A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is ___________ s.

(Given : ln 2 = 0.693)

At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ____________. [integer answer]