The rate of the reaction :   2N₂O₅ $$ \to $$ 4NO₂ + O₂
can be written in three ways.

$${{ - d\left[ {{N_2}{O_5}} \right]} \over {dt}} = k\left[ {{N_2}{O_5}} \right]$$

$${{d\left[ {N{O_2}} \right]} \over {dt}} = k'\left[ {{N_2}{O_5}} \right];\,\,$$ $${{d\left[ {{O_2}} \right]} \over {dt}} = k''\left[ {{N_2}{O_5}} \right]$$

The relationship between k and k' and between k and k'' are

A solution contains Fe²⁺, Fe³⁺ and I^$$-$$ ions. This solution was treated with iodine at 35^oC. E^o for Fe³⁺/Fe²⁺ is + 0.77 V and E^o for I₂/2I^$$-$$ = 0.536 V.
The favourable redox reaction is

200 mL of an aqueous solution of a protein contains its 1.26 g. The osmotic pressure of this solution at 300 K is found to be 2.57 $$ \times $$ 10^$$-$$3 bar. The molar mass of protein will be (R = 0.083 L bar mol^$$-$$1 K^$$-$$1)

A 0.1 molal aqueous solution of a weak acid is 30% ionized. If K_f for water is 1.86^oC/m, the freezing point of the solution will be