P2O5 + H2O = H3PO4 - Chemical Equation Balancer

To balance the equation P2O5 + H2O = H3PO4 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.

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Step 1: Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable lớn represent the unknown coefficients.

a P₂O₅ + b H₂O = c H₃PO₄

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 O: 5a + 1b = 4c H: 0a + 2b = 3c

Step 3: Solve For All Variables

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

2a - 1c = 0
5a + 1b - 4c = 0
2b - 3c = 0

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

Xem thêm: vận tốc góc

[ 2 0 -1 0] [ 5 1 -4 0] [ 0 2 -3 0]

The resulting matrix can be used lớn determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result lớn get the lowest, whole integer values.

a = 1 (P2O5)
b = 3 (H2O)
c = 2 (H3PO4)

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 + 3 H₂O = 2 H₃PO₄