The following equations are balanced in following manner:
a)
\(Zn(s) + C{r_2}{\left( {S{O_4}} \right)_3}(aq) + {H_3}{O^ + }(aq) \to ZnS{O_4}(aq) + CrS{O_4}(aq) + {H_2}(g)\)
After balancing the oxidation number and reduction number we have:
\(\begin{aligned}{l}O:Zn \to Z{n^{2 + }} + 2{e^ - }\\O:2C{r^{3 + }} \to 2C{r^{6 + }} + 6{e^ - }\\R:2{S^{6 + }} + 8{e^ - } \to 2{S^{2 + }}\\\overline {Zn + 2C{r^{3 + }} + 2{S^{6 + }} \to Z{n^{2 + }} + 2C{r^{6 + }} + 2{S^{2 + }}} \end{aligned}\)
From, that we have,
\(Zn(s) + C{r_2}{\left( {S{O_4}} \right)_3}(aq) + 2{H_3}{O^ + }(aq) \to ZnS{O_4}(aq) + 2CrS{O_4}(aq) + {H_2}(g) + 2{H_2}O(l)\)
b)
\(FeC{l_2}(s) + C{r_2}O_7^{2 - }(aq) + HCl(aq) \to FeC{l_3}(aq) + CrC{l_3}(aq) + C{l^ - }(aq) + {H_2}O(l)\)
After balancing the oxidation number and reduction number we have:
\(\begin{aligned}{l}O:6F{e^{2 + }} \to 6F{e^{3 + }} + 6{e^ - }\\R:C{r_2}O_7^{2 - } + 6{e^ - } + 14{H^ + } \to 2C{r^{3 + }} + 7{H_2}O\\\overline {6F{e^{2 + }} + C{r_2}O_7^{2 - } + 14{H^ + } \to 6F{e^{3 + }} + 2C{r^{3 + }} + 7{H_2}O} \end{aligned}\)
From, that we have,
\(6FeC{l_2}(s) + C{r_2}O_7^{2 - }(aq) + 14HCl(aq) \to 6FeC{l_3}(aq) + 2CrC{l_3}(aq) + 2C{l^ - }(aq) + 7{H_2}O(l)\)
c)
\(C{r^{2 + }}(aq) + C{r_2}O_7^{2 - }(aq) + {H^ + }(aq) \to C{r^{3 + }}(aq) + {H_2}O(l)\)
After balancing the oxidation number and reduction number we have:
\(\begin{aligned}{l}O:6C{r^{2 + }} \to 6C{r^{3 + }} + 6{e^ - }\\R:C{r_2}O_7^{2 - } + 6{e^ - } + 14{H^ + } \to 2C{r^{3 + }} + 7{H_2}O\\\overline {6C{r^{2 + }} + C{r_2}O_7^{2 - } + 14{H^ + } \to 8C{r^{3 + }} + 7{H_2}O}\end{aligned}\)
From, that we have,
\(6C{r^{2 + }} + C{r_2}O_7^{2 - } + 14{H^ + } \to 8C{r^{3 + }} + 7{H_2}O\)
d)
\(Mn(s) + Cr{O_3}(s) \to M{n_3}{O_4}(s) + C{r_2}{O_3}(s)\)
After balancing the oxidation number and reduction number we have:
\(\begin{aligned}{l}O:9Mn \to 9M{n^{\frac{8}{3} + }} + 24{e^ - }\\R:8C{r_2}{O_3} + 24{e^ - } \to 4C{r_2}{O_3}\\\overline {9Mn + 8C{r_2}{O_3} \to 9M{n^{3 + }} + 4C{r_2}{O_3}} \end{aligned}\)
From, that we have,
\(9Mn(s) + 8Cr{O_3}(s) \to 9M{n_3}{O_4}(s) + 4C{r_2}{O_3}(s)\)
e)
\(CrO(s) + 2NO_3^ - (aq) + {H_3}{O^ + }(aq) \to C{r^{2 + }}(aq) + 2NO_3^ - (aq) + {H_2}O(l)\)
After balancing the oxidation number and reduction number we have:
\(CrO(s) + 2NO_3^ - (aq) + 3{H_3}{O^ + }(aq) \to C{r^{2 + }}(aq) + 2NO_3^ - (aq) + 2{H_2}O(l)\)
f)
\(FeC{l_3}(s) + NaOH(aq) \to Fe{(OH)_3}(s) + N{a^ + }(aq) + C{l^ - }(aq)\)
After balancing the oxidation number and reduction number we have:
\(\begin{aligned}{l}O:3Cl \to 3Cl + 3{e^ - }\\R:3N{a^ + } + 3{e^ - } \to 3Na\\\overline {6F{e^{2 + }} + C{r_2}O_7^{2 - } + 14{H^ + } \to 6F{e^{3 + }} + 2C{r^{3 + }} + 7{H_2}O} \end{aligned}\)
From, that we have,
\(FeC{l_3}(s) + 3NaOH(aq) \to Fe{(OH)_3}(s) + 3N{a^ + }(aq) + 3C{l^ - }(aq)\)
Hence, the final answer is,
The balanced reactions are as follow:
a)\(Zn(s) + C{r_2}{\left( {S{O_4}} \right)_3}(aq) + 2{H_3}{O^ + }(aq) \to ZnS{O_4}(aq) + 2CrS{O_4}(aq) + {H_2}(g) + 2{H_2}O(l)\)
b)\(6FeC{l_2}(s) + C{r_2}O_7^{2 - }(aq) + 14HCl(aq) \to 6FeC{l_3}(aq) + 2CrC{l_3}(aq) + 2C{l^ - }(aq) + 7{H_2}O(l)\)
c)\(6C{r^{2 + }} + C{r_2}O_7^{2 - } + 14{H^ + } \to 8C{r^{3 + }} + 7{H_2}O\)
d)\(9Mn(s) + 8Cr{O_3}(s) \to 9M{n_3}{O_4}(s) + 4C{r_2}{O_3}(s)\)
e)\(CrO(s) + 2NO_3^ - (aq) + 3{H_3}{O^ + }(aq) \to C{r^{2 + }}(aq) + 2NO_3^ - (aq) + 2{H_2}O(l)\)
f)\(FeC{l_3}(s) + 3NaOH(aq) \to Fe{(OH)_3}(s) + 3N{a^ + }(aq) + 3C{l^ - }(aq)\)
