Write a balanced chemical reaction for the condensation reaction between \(\mathrm{H}_{3} \mathrm{PO}_{4}\), molecules to form $\mathrm{H}_{6} \mathrm{P}_{4} \mathrm{O}_{13}$.

In this condensation reaction, the reactant is phosphoric acid (H₃PO₄) and the product is condensed phosphoric acid (H₆P₄O₁₃).

An unbalanced chemical equation is the one in which both sides of the equation have different numbers of atoms for each element. Write the unbalanced equation as follows: \(H_{3}PO_{4} \rightarrow H_{6}P_{4}O_{13}\)

To balance the equation, we need to adjust the coefficients for the reactants and products until the number of atoms for each element is the same on both sides of the equation. First, balance the phosphorus (P) atoms. There are 4 P atoms in the product molecule and only 1 in the reactant molecule. Add a coefficient of 4 in front of the reactant to balance the P atoms: \(4H_{3}PO_{4} \rightarrow H_{6}P_{4}O_{13}\) Now, balance the hydrogen (H) atoms. There are 12 H atoms on the reactant side and 6 H atoms on the product side. Since the number of hydrogen atoms on the product side is already balanced, we do not need to make any changes in this case. Next, balance the oxygen (O) atoms. There are 16 O atoms on the reactant side and 13 O atoms on the product side. Add a coefficient of .5 or 1/2, in front of the product to balance the O atoms: \(4H_{3}PO_{4} \rightarrow 1/2H_{6}P_{4}O_{13}\) However, having fractional coefficients is not ideal in a balanced chemical equation. Therefore, to eliminate the fractional coefficient, we can multiply the entire equation by 2: \(2(4H_{3}PO_{4} \rightarrow 1/2H_{6}P_{4}O_{13})\) This results in the final balanced chemical equation: \(8H_{3}PO_{4} \rightarrow H_{6}P_{4}O_{13}\)