Question

Balance the equation by oxidation number method
Cu+HNO³=Cu(No³)2+No²+H²O

Answer 1

Answer:

3Cu + 8HNO₃ → 4H₂O + 2NO ↑ + 3Cu (NO₃) ₂

Explanation:

Algebraic method:

To begin, we apply an unknown coefficient to each term:

x₁Cu + x₂HNO₃ → x₃H₂O + x₄NO + x₅Cu (NO₃) ₂

Now atom by atom we are going to adjust the coefficients by establishing equations:

Copper is affected by the coefficients x₁ and x₅

Cu {x₁ = x₅} Equation 1

Hydrogen is affected by the coefficients x₂ and x₃

H {x₂ = 2x₃} Equation 2

Nitrogen is affected by the coefficients x₂, x₄ and x₅

N {x₂ = x₄ + 2x₅} Equation 3

Oxygen is affected by the coefficients x₂, x₃, x₄ and x₅

O {3x₂ = x₃ + x₄ + 6x₅} Equation 4

We have 4 equations with 5 unknowns, then we can put 4 unknowns based on the fifth:

{x₂ = 2x₃} Equation 2

{x₂ = x₄ + 2x₅} Equation 3

Substituting the value of x₂ from equation 2, into equation 3:

2x₃ = x₄ + 2x₅

And now, from here we can solve for x₄

x₄ = 2x₃ - 2x₅

{x₂ = 2x₃} Equation 2

{3x₂ = x₃ + x₄ + 6x₅} Equation 4

Substituting the value of x₂ from equation 2, into equation 4:

3 2x₃ = x₃ + x₄ + 6x₅

6x₃ - x₃ = x₄ + 6x₅

5x₃ = x₄ + 6x₅

And now, from here we can also solve for x₄

x₄ = 5x₃ - 6x₅

We set the two expressions equal to x₄

2x₃ - 2x₅ = 5x₃ - 6x₅

- 2x₅ + 6x₅ = 5x₃ -2x₃

4x₅ = 3x₃

We can now put x₃ in function of x₅

x₃ = 4x₅ / 3

And now, we can put all the variables as a function of x₅

{ x₁ = x₅ } Equation 1

{x₂ = 2x₃} Equation 2

And substituting the value of x₃ in function of x₅:

x₂ = 2 4x₅ / 3 = 8x₅ / 3

x₃ = 4x₅ / 3

x₄ = 2x₃ - 2x₅

and substituting the value of x₃ in function of x₅:

x₄ = 2 4x₅ / 3 - 2x₅ = 8x₅ / 3 - 2x₅ = (8x₅-3 2x₅) / 3 = (8x₅-6x₅) / 3 = 2x₅ / 3

x₅ = x₅

We already have the 5 coefficients of the reaction as a function of x₅

x₁ = x₅, x₂ = 8x₅ / 3, x₃ = 4x₅ / 3, x₄ = 2x₅ / 3, x₅ = x₅

We are going to give the value 3 to x₅ so that the denominators disappear:

x₁ = 3, x₂ = 8, x₃ = 4, x₄ = 2, x₅ = 3

We can now apply these coefficients to the reaction and verify them

x₁Cu + x₂HNO₃ → x₃H₂O + x₄NO₂ + x₅Cu (NO₃) ₂

3Cu + 8HNO₃ → 4H₂O + 2NO + 3Cu (NO₃) ₂

Answer: 3Cu + 8HNO₃ → 4H₂O + 2NO ↑ + 3Cu (NO₃) ₂✔️

Note: NO is a gas, which is given off, indicated by the arrow ↑

check

We check that the total of each atom is equal to both sides of the reaction:

Cu = 3 · 1 = 3 → 3 · 1 = 3✔️correct

H = 8 · 1 = 8 → 4 · 2 = 8✔️correct

N = 8 · 1 = 8 → 2 · 1 + 3 · 2 = 2 + 6 = 8✔️correct

O = 8 3 = 24 → 4 1 + 2 1 + 3 6 = 4 + 2 + 18 = 24✔️correct

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