Cu HNO3=Cu(NO3) NO2 H2O,how to balance this equation in algebraic method

Question

Cu HNO3=Cu(NO3) NO2 H2O,how to balance this equation in algebraic method

Answer 1

chuck norris

Answer 2

a[ Cu ] + b[ HNO3 ] = c[ Cu(NO3) ] + d[ NO2 ] + e[ H2O ]

Cu : a - c = 0   =>   a = c

H : b - 2e = 0   =>   b = 2e

N : b - c - d = 0   =>   2e - c - d = 0

O : 3b - 3c - 2d - e = 0   =>   5e - 3c - 2d = 0

5e - 3c - 2d = 0

4e - 2c - 2d = 0

e - c = 0   =>   c = e = a  =>   d = c = e = a

a = 1 , b = 2 . c = 1 , d = 1 , e = 1

Cu + 2 HNO3 = Cu(NO3) + NO2 + H2O