Predict the products of the following reactions and balance the equations.
(a) $\mathrm{Zn}$ is added to a solution of $\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}$ in acid.
(b) $\mathrm{FeCl}_{2}$ is added to a solution containing an excess of $\mathrm{Cr}_{2} \mathrm{O}_{7}{^2}{^-}$ in hydrochloric acid.
(c) $\mathrm{Cr}^{2+}$ is added to $\mathrm{Cr}_{2} \mathrm{O}_{7}{^3}{^-}$ in acid solution.
(d) Mn is heated with CrO $_{3}$
(e) CrO is added to $2 \mathrm{HNO}_{3}$ in water.
(f) $\mathrm{FeCl}_{3}$ is added to an aqueous solution of $\mathrm{NaOH}$.