To balance the equation Fe + CuNO3 = Cu + Fe(NO3)2 using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.
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Step 1: Label Each Compound With a Variable
Label each compound (reactant or product) in the equation with a variable vĩ đại represent the unknown coefficients.
a Fe + b CuNO3 = c Cu + d Fe(NO3)2
Step 2: Create a System of Equations
Create an equation for each element (Fe, Cu, N, O) where each term represents the number of atoms of the element in each reactant or product.
Fe: 1a + 0b = 0c + 1d Cu: 0a + 1b = 1c + 0d N: 0a + 1b = 0c + 2d O: 0a + 3b = 0c + 6d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.
- 1a - 1d = 0
- 1b - 1c = 0
- 1b - 2d = 0
- 3b - 6d = 0
Use your graphing calculator's rref() function (or an online rref calculator) vĩ đại convert the following matrix into reduced row-echelon-form:
Xem thêm: p+h2so4 đặc
[ 1 0 0 -1 0] [ 0 1 -1 0 0] [ 0 1 0 -2 0] [ 0 3 0 -6 0]
The resulting matrix can be used vĩ đại determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result vĩ đại get the lowest, whole integer values.
- a = 1 (Fe)
- b = 2 (CuNO3)
- c = 2 (Cu)
- d = 1 (Fe(NO3)2)
Step 4: Substitute Coefficients and Verify Result
Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.
Fe + 2 CuNO3 = 2 Cu + Fe(NO3)2
| Fe | 1 | 1 | ✔️ |
|---|---|---|---|
| Cu | 2 | 2 | ✔️ |
| N | 2 | 2 | ✔️ |
| O | 6 | 6 | ✔️ |
Since there is an equal number of each element in the reactants and products of Fe + 2CuNO3 = 2Cu + Fe(NO3)2, the equation is balanced.
Xem thêm: fes2 ra fe2o3
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