znno32 + naoh

To balance the equation Zn(NO3)2 + NaOH = Zn(OH)2 + NaNO3 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 Zn(NO3)2 + b NaOH = c Zn(OH)2 + d NaNO3

Step 2: Create a System of Equations

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

```Zn:	1a	+	0b	=	1c	+	0d
N:	2a	+	0b	=	0c	+	1d
O:	6a	+	1b	=	2c	+	3d
Na:	0a	+	1b	=	0c	+	1d
H:	0a	+	1b	=	2c	+	0d

```

Step 3: Solve For All Variables

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

• 1a - 1c = 0
• 2a - 1d = 0
• 6a + 1b - 2c - 3d = 0
• 1b - 1d = 0
• 1b - 2c = 0

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

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```[ 1	 0	-1	 0	0]
[ 2	 0	 0	-1	0]
[ 6	 1	-2	-3	0]
[ 0	 1	 0	-1	0]
[ 0	 1	-2	 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 = 1 (Zn(NO3)2)
• b = 2 (NaOH)
• c = 1 (Zn(OH)2)
• d = 2 (NaNO3)

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.

Zn(NO3)2 + 2 NaOH = Zn(OH)2 + 2 NaNO3

Reactants Products Zn 1 1 ✔️ 2 2 ✔️ 8 8 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of Zn(NO3)2 + 2NaOH = Zn(OH)2 + 2NaNO3, the equation is balanced.