Question

Write a balanced equation to describe any precipitation reaction that might occur when the following substances are mixed. (a) \(\mathrm{ZnSO}_{4}(a q)\) and \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) (b) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) and \(\mathrm{K}_{2} \mathrm{PO}_{4}(a q)\) (c) \(\mathrm{ZnSO}_{4}\) (aqu) and \(\mathrm{BaCl}_{2}\) ( \(a q\) ) (d) \(\mathrm{KOH}(a q)\) and \(\mathrm{Mg} \mathrm{Cl}_{2}(a q)\) (c) \(\mathrm{CuSO}_{4}\) (aq) and \(\mathrm{BaS}\) (aq)

Short answer

The balanced equations for the precipitation reactions are: (a) \( ZnSO_{4}(aq) + Ba(NO_{3})_{2}(aq) \to Zn(NO_{3})_{2}(aq) + BaSO_{4}(s) \), (b) \(3 Ca(NO_{3})_{2}(aq) + 2 K_{2}PO_{4}(aq) \to Ca_{3}(PO_{4})_{2}(s) + 6 KNO_{3}(aq) \), (c) \(ZnSO_{4}(aq) + BaCl_{2}(aq) \to ZnCl_{2}(aq) + BaSO_{4}(s) \), (d) \(2 KOH(aq) + MgCl_{2}(aq) \to Mg(OH)_{2}(s) + 2 KCl(aq) \), (e) \(CuSO_{4}(aq) + BaS(aq) \to CuS(s) + BaSO_{4}(s) \).

Step-by-step solution

Identify Precipitate for ZnSO4(aq) and Ba(NO3)2(aq)

In reaction (a), ZnSO4 and Ba(NO3)2 are combined. By swapping ions, we get Zn(NO3)2 and BaSO4. BaSO4 is insoluble and will precipitate, so the reaction is \( ZnSO_{4}(aq) + Ba(NO_{3})_{2}(aq) \to Zn(NO_{3})_{2}(aq) + BaSO_{4}(s) \)

Identify Precipitate for Ca(NO3)2(aq) and K2PO4(aq)

In reaction (b), Ca(NO3)2 and K2PO4 are combined. By swapping ions, we get Ca3(PO4)2 and KNO3. Ca3(PO4)2 is insoluble and will precipitate, so the reaction is: \(3 Ca(NO_{3})_{2}(aq) + 2 K_{2}PO_{4}(aq) \to Ca_{3}(PO_{4})_{2}(s) + 6 KNO_{3}(aq) \)

Identify Precipitate for ZnSO4(aq) and BaCl2(aq)

In reaction (c), ZnSO4 and BaCl2 are combined. By swapping ions, we get ZnCl2 and BaSO4. BaSO4 is insoluble and will precipitate, so the reaction is: \(ZnSO_{4}(aq) + BaCl_{2}(aq) \to ZnCl_{2}(aq) + BaSO_{4}(s) \)

Identify Precipitate for KOH(aq) and MgCl2(aq)

In reaction (d), KOH and MgCl2 are combined. By swapping ions, we get Mg(OH)2 and KCl. Mg(OH)2 is insoluble and will precipitate, so the reaction is: \(2 KOH(aq) + MgCl_{2}(aq) \to Mg(OH)_{2}(s) + 2 KCl(aq) \)

Identify Precipitate for CuSO4(aq) and BaS(aq)

In reaction (e), CuSO4 and BaS are combined. By swapping ions, we get CuS and BaSO4. CuS and BaSO4 are insoluble and will precipitate, so the reaction is: \(CuSO_{4}(aq) + BaS(aq) \to CuS(s) + BaSO_{4}(s) \)

Key concepts

Chemical Equation Balancing

Understanding how to balance chemical equations is fundamental in the study of chemistry and a crucial step in solving precipitation reaction problems. When balancing an equation, the goal is to ensure that the number of atoms for each element is equal on both sides of the reaction. This obeys the Law of Conservation of Mass, stating that matter cannot be created or destroyed. For example, in the reaction between ZnSO₄ and Ba(NO₃)₂, after predicting the products, we need to check that zinc (Zn), sulfur (S), oxygen (O), barium (Ba), and nitrogen (N) have the same atom count on both sides. In this case, it's already balanced. It's helpful to start with singular elements and leave hydrogen and oxygen for last since they are often found in multiple compounds. Also, polyatomic ions that appear on both sides can be balanced as a unit for convenience.

When you encounter more complex reactions, like the one between Ca(NO₃)₂ and K₂PO₄, you may need to adjust coefficients to achieve balance. Remember, coefficients are the numbers placed in front of compounds in a reaction and are used to scale the number of molecules or formula units to balance the equation. In this exercise, we determine coefficients by the least common multiple of the ions' subscripts in the products which are 3 for Ca(NO₃)₂ and 2 for K₂PO₄, resulting in the balanced equation provided.

Solubility Rules

Solubility rules allow us to predict whether a substance will dissolve in water and are particularly useful in identifying precipitation reactions where a solid product (precipitate) forms in a solution. These rules are guidelines based on empirical evidence and frequently used to foresee which ionic compounds are soluble or insoluble in water. For example, most nitrates (NO₃^-) are soluble, which is why Zn(NO₃)₂ remains in solution in reaction (a).

In contrast, certain compounds containing sulfate (SO₄^2-) are insoluble, with exceptions like those containing alkali metals or ammonium. However, sulfates paired with ions like barium (Ba²⁺), lead (Pb²⁺), or calcium (Ca²⁺) are generally insoluble, resulting in a precipitate. That's the reason BaSO₄ forms a solid in reaction (a). Rule of thumb: if you remember key solubility rules, you can quickly identify which product will precipitate without needing to memorize every possible ionic compound's solubility.

Double Displacement Reactions

Double displacement reactions, also known as metathesis reactions, involve the exchange of ions between two compounds to form two new compounds. These reactions are commonly observed when mixing aqueous solutions of ionic compounds, leading to the formation of a precipitate, a gas, or a weak electrolyte when certain pairs of ions react.

In the exercise provided, each reaction is a type of double displacement reaction where the anions and cations of the reactants switch partners. For example, when mixing solutions of ZnSO₄ and Ba(NO₃)₂, zinc pairs with nitrate and barium pairs with sulfate, resulting in Zn(NO₃)₂ and BaSO₄. To determine the outcome of such reactions, solubility rules are applied to find out which of the products is insoluble and will form a precipitate. Improved conceptual understanding of these reactions includes recognizing patterns, such as the fact that reactions involving an alkali metal and a nitrate will rarely form a precipitate due to their solubility. Being familiar with double displacement reactions can also help predict products in real-world applications, such as water treatment and pharmaceutical formulation.