# nh3 h2so4

To balance the equation NH3 + H2SO4 = (NH4)2SO4 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 NH3 + b H2SO4 = c (NH4)2SO4

### Step 2: Create a System of Equations

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

```N:	1a	+	0b	=	2c
H:	3a	+	2b	=	8c
S:	0a	+	1b	=	1c
O:	0a	+	4b	=	4c

```

### Step 3: Solve For All Variables

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

• 1a - 2c = 0
• 3a + 2b - 8c = 0
• 1b - 1c = 0
• 4b - 4c = 0

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

```[ 1	 0	-2	0]
[ 3	 2	-8	0]
[ 0	 1	-1	0]
[ 0	 4	-4	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 = 2 (NH3)
• b = 1 (H2SO4)
• c = 1 ((NH4)2SO4)

### 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 NH3 + H2SO4 = (NH4)2SO4

Reactants Products N 2 2 ✔️ 8 8 ✔️ 1 1 ✔️ 4 4 ✔️

Since there is an equal number of each element in the reactants and products of 2NH3 + H2SO4 = (NH4)2SO4, the equation is balanced.