First try to figure out how particular atoms reduce/oxidize. Make the following analysis
NH
4ClO
4 + Al = HCl + Cl
2 + NO + Al
2O
3 + HOH
2N(3-) - 10e- --> 2N(2+) – I doubled the nitrogen to make equal to total Cl – coming from the same molecule NH
4ClO
4
Cl(7+) + 7e- --> Cl(0)
Cl(7+) + 8e- --> Cl(1-)
Al(0) - 3e- --> Al(3+)
Basically, the complexity of this reaction is related to an unusual situation: it features two reducing agents and only one oxidizer. Still, the number of electrons given and accepted must stay equal. This provides a clue about basic coefficients. The total number of donated electrons is 10+3=13, and 7+8=15 accepted. The only coefficient can equalize them is 13x15=195. Nitrogen and Al must supply these electrons proportionally to their 10e- and 3e- loss, so let’s distribute these 195 electrons proportionally to demand by assigning multiplication coefficients:
2N(3-) - 10e- --> 2N(2+) x15 = 150e- = donated
Cl(7+) + 7e- --> Cl(0) x13=91e- - accepted
Cl(7+) + 8e- --> Cl(1-) x13=104e- accepted
Al(0) - 3e- --> Al(3+) x15=45e- - donated
Check: the number of donated and accepted electrons is equal and equal to the total of 195
The problem is that such coefficients will not provide equal numbers of N and Cl atoms – remember coming from the same molecule. We can only vary amount of Al.
Let’s equalize coefficients at N and Cl and let's absorb the difference by Al
2N(3-) - 10e- --> 2N(2+) x15 = 150e- = donated
Cl(7+) + 7e- --> Cl(0) x15=105e- - accepted
Cl(7+) + 8e- --> Cl(1-) x15=120e- accepted (total accepted 105+120=225; 225-150=75e- go to Al
Al(0) - 3e- --> Al(3+) x25=75e- - donated
Check again: the number of donated and accepted electrons is equal and equal to the total of 225
Now let’s put these found coefficients to play:
15x2NH
4ClO
4 + 25Al = 15HCl + 15/2Cl
2 + 30NO + 25/2Al
2O
3 + #HOH
Let’s multiply by 2 for convenience and calculate the number of protons to make water:
60NH
4ClO
4 + 50Al = 30HCl + 15Cl
2 + 60NO + 25Al
2O
3 + 105HOH
Finally oxygen check: 240 on the left and 240 on the right
Wow! That was the toughest one on this forum so far! Go collect your credit. I wonder where did you get this one?
By the way, this reaction has infinite number of solutions. That's why automatic program tells the following "Error: equation NH
4ClO
4+Al=HCl+Cl
2+NO+Al
2O
3+HOH can be balanced in an infinite number of ways: this is a combination of two different reactions"
http://www.webqc.org/balance.php