Oxidation number method:
The oxidation number of P decreases from 0 to -3 and increases from 0 to +2. Hence,
P4 is oxidizing as well as reducing agent.
During reduction, the total decrease in the oxidation number for 4 P atoms is 12.
During oxidation, total increase in the oxidation number for 4 P atoms is 4.
The increase in the oxidation number is balanced with decrease in the oxidation number by multiplying H2PO−2 with 3.
P4(s)+OH−(aq)→PH3(g)+3H2PO−2(aq)
To balance O atoms, multiply OH− ions by 6.
P4(s)+6OH−(aq)→PH3(g)+3H2PO−2(aq)
To balance H atoms, 3 water molecules are added to L.H.S and 3 hydroxide ions on R.H.S.
P4(s)+6OH−(aq)+3H2O(l)→PH3(g)+3H2PO−2(aq)+3OH−(aq)
Subtract 3 hydroxide ions from both sides.
P4(s)+3OH−(aq)+3H2O(l)→PH3(g)+3H2PO−2(aq)
Ion electron method:
The oxidation half reaction is P4(s)→H2PO−2(aq).
The P atom is balanced.
P4(s)→4H2PO−2(aq)
The oxidation number is balanced by adding 4 electrons on RHS.
P4(s)→4H2PO−2(aq)+4e−
The charge is balanced by adding 8 hydroxide ions on LHS.
P4(s)+8OH−(aq)→4H2PO−2(aq)
The O and H atoms are balanced.
The reduction half reaction is P4(s)→PH3(g).
The oxidation number is balanced by adding 12 eelctrons on LHS.
P4(s)+12e−→PH3(g)
The charge is balanced by adding 12 hydroxide ions on RHS.
P4(s)+12e−→PH3(g)+12OH−
The oxidation half reaction is multiplied by 3 and the reduction half reaction is multiplied by 2.
The half reactions are then added to obtain balanced chemical equation.
P4(s)+3OH−(aq)+3H2O(l)→PH3(g)+3H2PO−2(aq)