How do you balance #NO_2 + H_2O → HNO_3 + NO#?

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Answer 1 · 2017-11-25T13:38:13

#3NO_2+H_2O -> 2HNO_3+NO#

Given:

#NO_2 + H_2O -> HNO_3 + NO#

We are looking for something like:

#aNO_2 + bH_2O -> cHNO_3 + d NO#

for some integers #a, b, c, d#.

Equating the amounts of #N#, #O# and #H#, we find:

#{ (a = c + d), (2a+b = 3c+d), (2b = c) :}#

Subtracting the first equation from the second to eliminate #d#, we find:

#a+b = 2c#

Then subtracting twice the third equation, we find:

#a-3b = 0#

So let's put #b=1#, #a=3#, #c=2# and #d=1# to find:

#3NO_2+H_2O -> 2HNO_3+NO#