K2SO4 + NaOH = Na2SO4 + KOH - Chemical Equation Balancer

To balance the equation K2SO4 + NaOH = Na2SO4 + KOH 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 K₂SO₄ + b NaOH = c Na₂SO₄ + d KOH

Step 2: Create a System of Equations

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

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

Step 3: Solve For All Variables

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

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

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

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[ 2	 0	 0	-1	0]
[ 1	 0	-1	 0	0]
[ 4	 1	-4	-1	0]
[ 0	 1	-2	 0	0]
[ 0	 1	 0	-1	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 = 1 (K2SO4)
b = 2 (NaOH)
c = 1 (Na2SO4)
d = 2 (KOH)

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.

K₂SO₄ + 2 NaOH = Na₂SO₄ + 2 KOH