Ammonium nitrate is a chemical compound with the formula NH4NO3. When it reacts with lead (IV) nitrate (Pb(NO3)4), it forms lead (IV) phosphate (Pb3(PO4)4) and ammonium nitrate (NH4NO3).

## Input interpretation:

(NH4)3PO4 + Pb(NO3)4 → Pb3(PO4)4 + NH4NO3

## Balanced equation:

The balanced equation for this reaction can be found by following these steps:

Write the unbalanced equation:

(NH4)3PO4 + Pb(NO3)4 → Pb3(PO4)4 + NH4NO3

Add stoichiometric coefficients to the reactants and products:

c1(NH4)3PO4 + c2Pb(NO3)4 → c3Pb3(PO4)4 + c4NH4NO3

Set the number of atoms in the reactants equal to the number of atoms in the products for N, H, P, O, and Pb:

N: 3c1 = 2c4

H: 12c1 = 4c4

P: c1 = 4c3

O: 4c + 12c2 = 16c3 + 3c4

Pb: c2 = 3c3

Choose an arbitrary coefficient to set, and solve the system of equations for the remaining coefficients. For this example, let's set c3 = 1:

c1 = 4

c2 = 3

c3 = 1

c4 = 12

Substitute the coefficients into the chemical equation to obtain the balanced equation:

4(NH4)3PO4 + 3Pb(NO3)4 → Pb3(PO4)4 + 12NH4NO3

In conclusion, the balanced chemical equation for the reaction between ammonium nitrate and lead (IV) nitrate is 4(NH4)3PO4 + 3Pb(NO3)4 → Pb3(PO4)4 + 12NH4NO3. This equation represents the conservation of atoms in the reaction and provides useful information for understanding and predicting the behavior of these chemicals.