Question

How to balance this equation using algebraic method Cu + HNO3 = Cu(NO3)2 + NO2 +H2O

Answer 1

1) Write the chemical equation.

`Cu+HNO_3\rightarrow Cu(NO_3)_2+NO_2+H_2O`

Step 1: assign letters to stoichiometric coefficients.

`ACu_{}+BHNO_3\rightarrow CCu(NO_3)_2+DNO_2+EH_2O_{}`

Step 2: list the elements involved in the reaction.

Cu: 1A = 1C

H: 1B = 2E

N: 1B = 2C + 1D

O: 3B = 6C + 2D + 1E

Step 3: assign an arbitrary number to one of the letters. Let's try C = 1.

Cu: 1A = 1C

1*A = 1*(1)

A = 1

Let's try E = 2.

H: 1B = 2E

1*B = 2*(2)

B = 4

Replace C and B in 1B = 2C + 1D

N: 1B = 2C + 1D

1*(4) = 2*(1) + 1D

4 = 2+ 1*D

D = 4-2 = 2

Step 4: replace the letter in the chemical equation and check.

`Cu+4HNO_3\rightarrow Cu(NO_3)_2+2NO_2+2H_2O`

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