$${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + {1 \over 2}{O_{2(g)}}$$

In the above first order reaction the initial concentration of N₂O₅ is 2.40 $$\times$$ 10^$$-$$2 mol L^$$-$$1 at 318 K. The concentration of N₂O₅ after 1 hour was 1.60 $$\times$$ 10^$$-$$2 mol L^$$-$$1. The rate constant of the reaction at 318 K is ______________ $$\times$$ 10^$$-$$3 min^$$-$$1. (Nearest integer)

[Given : log 3 = 0.477, log 5 = 0.699]

$$PC{l_5}(g) \to PC{l_3}(g) + C{l_2}(g)$$

In the above first order reaction the concentration of PCl₅ reduces from initial concentration 50 mol L^$$-$$1 to 10 mol L^$$-$$1 in 120 minutes at 300 K. The rate constant for the reaction at 300 K is x $$\times$$ 10^$$-$$2 min^$$-$$1. The value of x is __________. [Given log5 = 0.6989]

The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation, 10% of the virus is inactivated. The rate constant for viral inactivation is ___________ $$\times$$ 10^$$-$$3 min^$$-$$1. (Nearest integer)

[Use : ln 10 = 2.303; log₁₀ 3 = 0.477; property
of logarithm : log x^y = y log x]

A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _________ min. (Round off to the Nearest Integer). [Use : ln 2 = 0.69; ln 10 = 2.3]