The equilibrium constant for the reaction

N₂(g) + O₂(g) $$\rightleftharpoons$$ 2NO(g) is 4 $$\times$$ 10^$$-$$4 at 2000 K. In presence of a catalyst the equilibrium is attained 10 times faster. Therefore, the equilibrium constant, in presence of the catalyst at 2000 K is

Under the same reaction conditions, initial concentration of 1.386 mol dm^$$-$$3 of a substance becomes half in 40 s and 20 s through first-order and zero-order kinetics respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} \right)$$ of the rate constants for first-order (k₁) and zero-order (k₀) of the reactions is

2.5 mL 0.4 M weak monoacidic base (K_b = 1 $$\times$$ 10^$$-$$12 at 25$$^\circ$$C) is titrated with 2/15 M HCl in water at 25$$^\circ$$C. The concentration of H⁺ at equivalence point is (K_w = 1 $$\times$$ 10^$$-$$14, at 25$$^\circ$$C)

For a reaction 2A + B $$ \to $$ P, when concentration of B alone is doubled, t_1/2 does not change and when concentrations of both A and B is doubled, rate increases by a factor of 4. The unit of rate constant is,