An excess of liquid mercury is added to an acidified solution of 1.0 $$\times$$ 10^-3 M Fe³⁺. It is found that 5% of Fe³⁺ remains at equilibrium at 25^oC. Calculate $$E_{Hg_2^{2 + }|\,Hg}^o$$, assuming that only reaction that occurs is
2Hg + 2Fe³⁺ $$\to$$ $$Hg_2^{2+}$$ + 2Fe²⁺
(Given $$E_{F{e^{3 + }}|\,F{e^{2 + }}}^o$$ = 0.77 V)

At 380^oC, the half-life period for the first order decomposition of H₂O₂ is 360 min. Calculate the time required for 75% decomposition at 450^oC.

The minimum value of the expression $$\sin \,\alpha + \sin \,\beta \, + \sin \,\gamma ,\,$$ where $$\alpha ,\,\beta ,\,\gamma $$ are real numbers satisfying $$\alpha + \beta + \gamma = \pi $$ is

If $$i{z^3} + {z^2} - z + i = 0$$ , then show that $$\left| z \right| = 1$$.