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