# mgso4 koh

To balance the equation KOH + MgSO4 = Mg(OH)2 + K2SO4 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 tướng represent the unknown coefficients.

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a KOH + b MgSO4 = c Mg(OH)2 + d K2SO4

### Step 2: Create a System of Equations

Create an equation for each element (K, O, H, Mg, S) where each term represents the number of atoms of the element in each reactant or product.

```K:	1a	+	0b	=	0c	+	2d
O:	1a	+	4b	=	2c	+	4d
H:	1a	+	0b	=	2c	+	0d
Mg:	0a	+	1b	=	1c	+	0d
S:	0a	+	1b	=	0c	+	1d

```

### Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator to tướng solve for each variable.

• 1a - 2d = 0
• 1a + 4b - 2c - 4d = 0
• 1a - 2c = 0
• 1b - 1c = 0
• 1b - 1d = 0

Use your graphing calculator's rref() function (or an online rref calculator) to tướng convert the following matrix into reduced row-echelon-form:

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```[ 1	 0	 0	-2	0]
[ 1	 4	-2	-4	0]
[ 1	 0	-2	 0	0]
[ 0	 1	-1	 0	0]
[ 0	 1	 0	-1	0]
```

The resulting matrix can be used to tướng determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

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

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• a = 2 (KOH)
• b = 1 (MgSO4)
• c = 1 (Mg(OH)2)
• d = 1 (K2SO4)

### 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 KOH + MgSO4 = Mg(OH)2 + K2SO4

Reactants Products K 2 2 ✔️ 6 6 ✔️ 2 2 ✔️ 1 1 ✔️ 1 1 ✔️

Since there is an equal number of each element in the reactants and products of 2KOH + MgSO4 = Mg(OH)2 + K2SO4, the equation is balanced.