Find the solubility product of a saturated solution of Ag₂CrO₄ in water at 298 K if the emf of the cell Ag|Ag⁺ (satd. Ag₂CrO₄ soln.) || Ag⁺ (0.1 M) | Ag is 0.164 V at 298 K.

The rate constant of a reaction is 1.5 $$\times$$ 10⁷ s^-1 at 50^oC and 4.5 $$\times$$ 10⁷ s^-1 at 100^oC. Evaluate the Arrhenius parameters A and E_a.

If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals

The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1} $$, equals