To balance the equation K2HPO4 + H3PO4 = KH2PO4 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 lớn represent the unknown coefficients.
Bạn đang xem: h3po4+k2hpo4
a K2HPO4 + b H3PO4 = c KH2PO4
Step 2: Create a System of Equations
Create an equation for each element (K, H, Phường, O) where each term represents the number of atoms of the element in each reactant or product.
K: 2a + 0b = 1c H: 1a + 3b = 2c P: 1a + 1b = 1c O: 4a + 4b = 4c
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator lớn solve for each variable.
- 2a - 1c = 0
- 1a + 3b - 2c = 0
- 1a + 1b - 1c = 0
- 4a + 4b - 4c = 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: so sánh hai phân số khác mẫu số
[ 2 0 -1 0] [ 1 3 -2 0] [ 1 1 -1 0] [ 4 4 -4 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 (K2HPO4)
- b = 1 (H3PO4)
- c = 2 (KH2PO4)
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.
K2HPO4 + H3PO4 = 2 KH2PO4
Since there is an equal number of each element in the reactants and products of K2HPO4 + H3PO4 = 2KH2PO4, the equation is balanced.