NaHSO4 + CaCO3 = Na2SO4 + CaSO4 + H2O + CO2 - Chemical Equation Balancer

To balance the equation NaHSO4 + CaCO3 = Na2SO4 + CaSO4 + H2O + CO2 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 NaHSO₄ + b CaCO₃ = c Na₂SO₄ + d CaSO₄ + f H₂O + g CO₂

Step 2: Create a System of Equations

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

Na:	1a	+	0b	=	2c	+	0d	+	0f	+	0g
H:	1a	+	0b	=	0c	+	0d	+	2f	+	0g
S:	1a	+	0b	=	1c	+	1d	+	0f	+	0g
O:	4a	+	3b	=	4c	+	4d	+	1f	+	2g
Ca:	0a	+	1b	=	0c	+	1d	+	0f	+	0g
C:	0a	+	1b	=	0c	+	0d	+	0f	+	1g

Step 3: Solve For All Variables

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

1a - 2c = 0
1a - 2f = 0
1a - 1c - 1d = 0
4a + 3b - 4c - 4d - 1f - 2g = 0
1b - 1d = 0
1b - 1g = 0

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

[ 1	 0	-2	 0	 0	 0	0]
[ 1	 0	 0	 0	-2	 0	0]
[ 1	 0	-1	-1	 0	 0	0]
[ 4	 3	-4	-4	-1	-2	0]
[ 0	 1	 0	-1	 0	 0	0]
[ 0	 1	 0	 0	 0	-1	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.

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a = 2 (NaHSO4)
b = 1 (CaCO3)
c = 1 (Na2SO4)
d = 1 (CaSO4)
f = 1 (H2O)
g = 1 (CO2)

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 NaHSO₄ + CaCO₃ = Na₂SO₄ + CaSO₄ + H₂O + CO₂

	Reactants	Products
Na	2	2	✔️
H	2	2	✔️
S	2	2	✔️
O	11	11	✔️
Ca	1	1	✔️
C	1	1	✔️

Since there is an equal number of each element in the reactants and products of 2NaHSO4 + CaCO3 = Na2SO4 + CaSO4 + H2O + CO2, the equation is balanced.

The law of conservation of mass states that matter cannot be created or destroyed, which means there must be the same number atoms at the over of a chemical reaction as at the beginning. To be balanced, every element in NaHSO4 + CaCO3 = Na2SO4 + CaSO4 + H2O + CO2 must have the same number of atoms on each side of the equation. When using the inspection method (also known as the trial-and-error method), this principle is used to lớn balance one element at a time until both sides are equal and the chemical equation is balanced.

Step 1: Count the number of each element on the left and right hand sides

	Reactants (Left Hand Side)			Products (Right Hand Side)
	Reactants	Products
	NaHSO₄	CaCO₃	Total	Na₂SO₄	CaSO₄	H₂O	CO₂	Total
Na	1		1	2				2	❌
H	1		1			2		2	❌
S	1		1	1	1			2	❌
O	4	3	7	4	4	1	2	11	❌
Ca		1	1		1			1	✔️
C		1	1				1	1	✔️

Step 2: Multiply coefficients for compounds to lớn balance out each element

For each element that is not equal, try to lớn balance it by adding more of it to lớn the side with less. Sometimes there may be multiple compounds with that element on one side, sánh you'll need to lớn use your best judgement and be prepared to lớn go back and try the other options.

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Na is not balanced. Add 1 molecule of NaHSO₄ to lớn the reactant (left-hand) side to lớn balance Sodium:
2NaHSO₄ + CaCO₃ = Na₂SO₄ + CaSO₄ + H₂O + CO₂
Reactants Products
Na 2 2 ✔️
H 2 2 ✔️
S 2 2 ✔️
O 11 11 ✔️
Ca 1 1 ✔️
C 1 1 ✔️