To solve, determine the formulas for the possible products using the general double-displacement equation, AB + CD
→ AD + CB: Chromium(III) chloride and sodium phosphate yields chromium(III) phosphate and sodium chloride. Now, we convert the names to formulas. Chromium(III) chloride is an ionic compound, so we write the name of the cation followed by the name of the anion. The charge of the cation, Cr, is +3, and the charge of the anion, Cl, is
−1. Thus, the formula for chromium(III) chloride is:
CrCl3. Sodium phosphate is an ionic compound. The charge of the cation, Na, is +1, and the charge of the anion, PO
4, is
−3. Thus, the formula for sodium phosphate is:
Na3PO4. Chromium phosphate is also an ionic compound. The charge of the cation, Cr, is +3, and the charge of the anion, PO
4, is
−3. Thus, the formula for chromium phosphate is:
CrPO4. Sodium chloride is an ionic compound with the formula:
NaCl. The unbalanced equation then is:
CrCl3 + Na3PO4 → CrPO4 + NaCl.
Next, add in the state-of-matter for each formula. The reactants are followed by (
aq). The first product is CrPO
4. By definition, compounds containing phosphate ions are insoluble in water except with group 1 metallic ions and ammonium ions. Chromium is not a group 1 metallic ion. Thus, this product is
insoluble and is followed by (
s). The second product is NaCl. By definition, compounds containing chloride ions are water-soluble except with silver ions and lead(II) ions. Thus, this product is
soluble and is followed by (
aq). The unbalanced equation with states-of-matter is:
CrCl3(aq) + Na3PO4(aq) → CrPO4(s) + NaCl(aq).
Finally, balance the equation with the lowest possible whole number coefficients. Cr is the first element in the first formula. The moles of Cr appear to be balanced at this stage. The next element in the formula is Cl. There are 3 moles of Cl listed on the reactant side of the unbalanced equation, but there is only 1 mole of Cl listed on the product side. We can balance them with
3 moles of NaCl, which corresponds to 3
✕ 1 = 3 moles of Cl.
CrCl3(aq) + Na3PO4(aq) → CrPO4(s) + 3 NaCl(aq)
The next element in the equation is Na, which appears to be balanced at this stage with 3 moles of Na on each side of the unbalanced equation. Since PO
4 appears in the same form on both sides of the chemical equation, it can be balanced as though it was a single atom. The moles of PO
4 appear to be balanced at this stage with 1 mole of PO
4 on both sides of the unbalanced equation. The complete equation, then, is:
CrCl3(aq) + Na3PO4(aq) → CrPO4(s) + 3 NaCl(aq).