# c2h4(oh)2 + cu(oh)2

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 lớn 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 lớn 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 lớn 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 lớn determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result to lớn get the lowest, whole integer values.

• 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

Reactants Products C 4 4 ✔️ 14 14 ✔️ 6 6 ✔️ 1 1 ✔️

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.