# p2o5+h2

To balance the equation P2O5 + H2 = PH3 + H2O 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 P2O5 + b H2 = c PH3 + d H2O

### Step 2: Create a System of Equations

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

```P:	2a	+	0b	=	1c	+	0d
O:	5a	+	0b	=	0c	+	1d
H:	0a	+	2b	=	3c	+	2d

```

### Step 3: Solve For All Variables

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

• 2a - 1c = 0
• 5a - 1d = 0
• 2b - 3c - 2d = 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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```[ 2	 0	-1	 0	0]
[ 5	 0	 0	-1	0]
[ 0	 2	-3	-2	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 = 1 (P2O5)
• b = 8 (H2)
• c = 2 (PH3)
• d = 5 (H2O)

### 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.

P2O5 + 8 H2 = 2 PH3 + 5 H2O

Reactants Products P 2 2 ✔️ 5 5 ✔️ 16 16 ✔️

Since there is an equal number of each element in the reactants and products of P2O5 + 8H2 = 2PH3 + 5H2O, the equation is balanced.