The first order rate constant for the decomposition of CaCO₃ at 700 K is 6.36 $$\times$$ 10^$$-$$3s^$$-$$1 and activation energy is 209 kJ mol^$$-$$1. Its rate constant (in s^$$-$$1) at 600 K is x $$\times$$ 10^$$-$$6. The value of x is ___________. (Nearest integer)

[Given R = 8.31 J K^$$-$$ mol^$$-$$1; log 6.36 $$\times$$ 10^$$-$$3 = $$-$$2.19, 10^$$-$$4.79 = 1.62 $$\times$$ 10^$$-$$5]

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is

$$2{K_2}C{r_2}{O_7} + 8{H_2}S{O_4} + 3{C_2}{H_6}O \to 2C{r_2}{(S{O_4})_3} + 3{C_2}{H_4}{O_2} + 2{K_2}S{O_4} + 11{H_2}O$$

If the rate of appearance of Cr₂(SO₄)₃ is 2.67 mol min^$$-$$1 at a particular time, the rate of disappearance of C₂H₆O at the same time is _____________ mol min^$$-$$1. (Nearest integer)

The overall stability constant of the complex ion [Cu(NH₃)₄]²⁺ is 2.1 $$\times$$ 10¹³. The overall dissociations constant is y $$\times$$ 10^$$-$$14. Then y is __________. (Nearest integer)

The reaction rate for the reaction

[PtCl₄]^2$$-$$ + H₂O $$\rightleftharpoons$$ [Pt(H₂O)Cl₃]^$$-$$ + Cl^$$-$$

was measured as a function of concentrations of different species. It was observed that $${{ - d\left[ {{{\left[ {PtC{l_4}} \right]}^{2 - }}} \right]} \over {dt}} = 4.8 \times {10^{ - 5}}\left[ {{{\left[ {PtC{l_4}} \right]}^{2 - }}} \right] - 2.4 \times {10^{ - 3}}\left[ {{{\left[ {Pt({H_2}O)C{l_3}} \right]}^ - }} \right]\left[ {C{l^ - }} \right]$$.

where square brackets are used to denote molar concentrations. The equilibrium constant K_c = ____________ . (Nearest integer)