Word Equation

Disodium hydrogen phosphate + phosphoric acid → sodium dihydrogen phosphate

Input Interpretation

The word equation can be represented in a chemical formula as 

Na2HPO4 + H3PO4 → 2 NaH2PO4

This means that when disodium hydrogen phosphate and phosphoric acid are combined, they react to form sodium dihydrogen phosphate.

Balanced Equation

To balance the chemical equation algebraically, we need to add stoichiometric coefficients, c, to the reactants and products. The balanced equation can be represented as 

c1 Na2HPO4 + c2H3PO4 → c3 2NaH2PO4.

Next, we need to set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, and P. The balanced equation can be represented as:

H: C1 + 3c2 = 2C3

Na: 2c1 = c3

O: 4c1 + 4c2 = 4c3

P: c1 + c2 = c3

Since the coefficients are relative quantities and underdetermined, we choose a coefficient to set arbitrarily. We typically set the arbitrary value to one to keep the coefficients small. For example, we can set c1 = 1 and solve the system of equations for the remaining coefficients:

C1 = 1

C2 = 1

C3 = 2

Finally, we substitute the coefficients into the chemical reaction to obtain the balanced equation:

Na2HPO4 + H3PO4 → 2 NaH2PO4