Answer:
(a)
Given equation is :
\[{{P}_{4}}+O{{H}^{-}}\to P{{H}_{3}}+HPO_{2}^{-}\]
half equations are :
\[{{P}_{4}}\to P{{H}_{3}}\]
\[{{P}_{4}}\to HPO_{2}^{-}\]
These half equations can be balanced as
\[[{{P}_{4}}+12{{H}^{+}}+12{{e}^{-}}\to 4P{{H}_{3}}]\times
2\]
\[On\,addition\frac{\frac{[{{P}_{4}}+8{{H}_{2}}O\to 4HPO_{2}^{-}+12{{H}^{+}}+8{{e}^{-}}]\times
3}{5{{P}_{4}}+24{{H}_{2}}O\to 8P{{H}_{3}}+12HPO_{2}^{-}+12{{H}^{+}}}}{{}}\]converting
above equation into basic medium we get
\[5{{P}_{4}}+12{{H}_{2}}O+12O{{H}^{-}}\to
8P{{H}_{3}}+12HPO_{2}^{-}\]
(b) Given equation is :
\[{{N}_{2}}{{H}_{4}}(l)+ClO_{3}^{-}(aq)\to
NO(q)+C{{l}^{-}}(aq)\]
Half equations are:
\[{{N}_{2}}{{H}_{4}}(l)\to
NO(q)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.......(i)\]
\[{{N}_{2}}{{H}_{4}}(l)\to NO(q)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.......(i)\]
These half equations can be balanced as
\[[{{N}_{2}}{{H}_{4}}(l)]+2{{H}_{2}}O\to
2NO+8{{H}^{+}}+8{{e}^{-}}]\times 3\]
On \[ONaddition\frac{[ClO_{3}^{-}(aq)]+6{{H}^{+}}+6{{e}^{-}}\to
C{{l}^{-}}(aq)+3{{H}_{2}}O]\times 4}{\frac{3{{N}_{2}}{{H}_{4}}(l)+4ClO_{3}^{-}(aq)\to
6NO+4C{{l}^{-}}(aq)+6{{H}_{2}}O}{{}}}\](c) \[C{{l}_{2}}{{O}_{7}}(g)+{{H}_{2}}{{O}_{2}}(aq)\to
ClO_{2}^{-}(aq)\]
\[+{{O}_{2}}(g)+{{H}^{+}}(aq)\]
Step I: Splitting the
equation into two half equations:
\[C{{l}_{2}}{{O}_{7}}(g)\to ClO_{2}^{-};\]
\[{{H}_{2}}{{O}_{2}}(aq)\to
{{O}_{2}}(g)+{{H}^{+}}(aq)\]
Step II: Balancing the
element other than hydrogen and oxygen:
\[C{{l}_{2}}{{O}_{7}}(g)\to ClO_{2}^{-};\]
\[{{H}_{2}}{{O}_{2}}(aq)\to
{{O}_{2}}(g)+{{H}^{+}}(aq)\]
Step III: Balancing
oxygen by adding water molecules:
\[C{{l}_{2}}{{O}_{7}}(g)\to
ClO_{2}^{-}+3{{H}_{2}}O\]
\[{{H}_{2}}{{O}_{2}}(aq)\to
{{O}_{2}}(g)+{{H}^{+}}(aq)\]
Step IV: Balancing
hydrogen by adding \[{{H}^{+}}\] ions.
\[C{{l}_{2}}{{O}_{7}}+6{{H}^{+}}+8{{e}^{-}}\to
2ClO_{2}^{-}+3{{H}_{2}}O\]
\[{{H}_{2}}{{O}_{2}}(aq)\to {{O}_{2}}(g)+2{{H}^{+}}\]
Step V: Balancing
charge by adding electron, we get
\[C{{l}_{2}}{{O}_{7}}(g)+6{{H}^{+}}+8{{e}^{-}}\to
2ClO_{2}^{-}+3{{H}_{2}}O\]
\[[{{H}_{2}}O(aq)\to
{{O}_{2}}(g)+2{{H}^{+}}+2{{e}^{-}}]\times 4\]
Step VI: Adding above
equations, we get
\[C{{l}_{2}}{{O}_{7}}(g)+4{{H}_{2}}{{O}_{2}}(aq)\to
2ClO_{2}^{-}+3{{H}_{2}}O+2{{H}^{+}}\]
This equation can be balanced in basic medium by adding two
\[O{{H}^{-}}\] ions on both sides:
\[C{{l}_{2}}{{O}_{7}}(g)+4{{H}_{2}}{{O}_{2}}(aq)2O{{H}^{-}}\to
2ClO_{2}^{-}+\]
\[3{{H}_{2}}O+2{{H}^{+}}+2O{{H}^{-}}\]
OR
\[C{{l}_{2}}{{O}_{7}}(g)+4{{H}_{2}}{{O}_{2}}(aq)2O{{H}^{-}}(aq)\to
2ClO_{2}^{-}+5{{H}_{2}}O\]
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