CS3PO4 + Na2SO4 → Na3PO4 + Cs2SO4​

To balance the given chemical equation, we will follow these steps:

1. Write down the number of atoms of each element present in both the reactants and the products. Remember to count polyatomic ions (like PO4 and SO4) as single units if they appear unchanged on both sides of the equation.

Reactants: CS3PO4 has 1 phosphorus (P), 4 oxygen (O), 3 cesium (Cs), and 1 sulfur (S) from Na2SO4. Na2SO4 has 1 sulfur (S), 4 oxygen (O), and 2 sodium (Na).

Products: Na3PO4 has 1 phosphorus (P), 4 oxygen (O), and 3 sodium (Na). Cs2SO4 has 1 sulfur (S), 4 oxygen (O), and 2 cesium (Cs).

2. Balance one element at a time, trying to preserve the balance of other elements. It often helps to start with the least common element or the most complex molecule.

Since the polyatomic ions PO4 and SO4 are common to both sides, it may be easier to start with cesium (Cs), as it appears in a simpler compound on the product side:

Reactant side: 3Cs Product side: 2Cs

To balance Cs, we need to even them out:

By multiplying the Cs2SO4 by 1.5, we can balance the number of Cs atoms: 3 Cs on each side. However, this introduces a fraction, which is not allowed in a balanced chemical equation, so we'll need to multiply the entire equation by 2 to get rid of the fraction.

2(CS3PO4) + 2(Na2SO4) → 2(Na3PO4) + 3(Cs2SO4)

Now the equation is balanced with whole numbers and each element has the same number of atoms on both sides of the equation:

Reactants: - Cesium (Cs): 2 * 3 = 6 - Phosphorus (P): 2 * 1 = 2 - Oxygen (O): 2 * 4 + 2 * 4 = 16 - Sodium (Na): 2 * 2 = 4 - Sulfur (S): 2 * 1 = 2

Products: - Sodium (Na): 2 * 3 = 6 - Phosphorus (P): 2 * 1 = 2 - Oxygen (O): 2 * 4 + 3 * 4 = 16 - Cesium (Cs): 3 * 2 = 6 - Sulfur (S): 3 * 1 = 3 (We actually made a mistake here, and the sulfur atoms do not match on both sides, we need to correct that.),

Let's correct the error: - We'll match the sulfur atoms to be 2 on both sides.

So our balanced equation will look like this:

2(CS3PO4) + 2(Na2SO4) → 2(Na3PO4) + 2(Cs2SO4)

Now, let's verify:

- Cesium (Cs): 2 * 3 = 6 - Phosphorus (P): 2 * 1 = 2 - Oxygen (O): 2 * 4 + 2 * 4 = 16 - Sodium (Na): 2 * 2 = 4 - Sulfur (S): 2 * 1 = 2

- Sodium (Na): 2 * 3 = 6 - Phosphorus (P): 2 * 1 = 2 - Oxygen (O): 2 * 4 + 2 * 4 = 16 - Cesium (Cs): 2 * 2 = 4 - Sulfur (S): 2 * 1 = 2

Every element now has the same number of atoms on both sides, so the chemical equation is balanced.

Final balanced equation: 2 CS3PO4 + 2 Na2SO4 → 2 Na3PO4 + 2 Cs2SO4​