To balance the equation C2H4(OH)2 + Cu(OH)2 = (C2H4(OHO))2Cu + H2O 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.
Step 1: Label Each Compound With a Variable
Label each compound (reactant or product) in the equation with a variable to tát represent the unknown coefficients.
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a C2H4(OH)2 + b Cu(OH)2 = c (C2H4(OHO))2Cu + d H2O
Step 2: Create a System of Equations
Create an equation for each element (C, H, O, Cu) where each term represents the number of atoms of the element in each reactant or product.
C: 2a + 0b = 4c + 0d H: 6a + 2b = 10c + 2d O: 2a + 2b = 4c + 1d Cu: 0a + 1b = 1c + 0d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator to tát solve for each variable.
- 2a - 4c = 0
- 6a + 2b - 10c - 2d = 0
- 2a + 2b - 4c - 1d = 0
- 1b - 1c = 0
Use your graphing calculator's rref() function (or an online rref calculator) to tát convert the following matrix into reduced row-echelon-form:
[ 2 0 -4 0 0] [ 6 2 -10 -2 0] [ 2 2 -4 -1 0] [ 0 1 -1 0 0]
The resulting matrix can be used to tát determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result to tát get the lowest, whole integer values.
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- a = 2 (C2H4(OH)2)
- b = 1 (Cu(OH)2)
- c = 1 ((C2H4(OHO))2Cu)
- d = 2 (H2O)
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.
2 C2H4(OH)2 + Cu(OH)2 = (C2H4(OHO))2Cu + 2 H2O
Since there is an equal number of each element in the reactants and products of 2C2H4(OH)2 + Cu(OH)2 = (C2H4(OHO))2Cu + 2H2O, the equation is balanced.