Question

Write a balanced equation to describe any precipitation reaction that should occur when the following substances are mixed. (a) \(\mathrm{MgSO}_{4}(a q)\) and \(\mathrm{BaCl}_{3}(a q)\) (b) \(\mathrm{K}_{\mathrm{S}} \mathrm{SO}_{4}(a q)\) and \(\mathrm{MgCl}_{2}(a q)\) (c) \(\mathrm{MgCl}_{2}(a q)\) and \(\mathrm{Pt}\left(\mathrm{NO}_{2}\right)_{2}(\omega q)\)

Short answer

(a) \(\mathrm{MgSO}_{4}(a q) + \(\mathrm{BaCl}_{3}(a q) \rightarrow \mathrm{MgCl}_{2}(a q) + \mathrm{BaSO}_{4}(s)\), (b) \(\mathrm{K}_{\mathrm{S}} \mathrm{SO}_{4}(a q) + \mathrm{2MgCl}_{2}(a q) \rightarrow \mathrm{2KMgCl}_{2}(s) + \mathrm{K}_{2}\mathrm{SO}_{4}(a q)\), and (c) \(\mathrm{MgCl}_{2}(a q) + \mathrm{Pt}(NO_{2})_{2}(a q) \rightarrow \mathrm{Mg(NO}_{2})_{2}(a q) + \mathrm{PtCl}_{2}(s\)

Step-by-step solution

- Identify and Write the Precipitate

For each pair of substances, exchange the cations and anions and write the resultant compounds. Use the solubility rules to predict the possible precipitate. In (a), the resultants are \(\mathrm{MgCl}_{2}\) and \(\mathrm{BaSO}_{4}\). For (b), the resultants are \(\mathrm{KMgCl}_{2}\) and \(\mathrm{K}_{2}\mathrm{SO}_{4}\), and (c) gives \(\mathrm{Mg(NO}_{2})_{2}\) and \(\mathrm{PtCl}_{2}\). Using the solubility rules, \(\mathrm{BaSO}_{4}\), \(\mathrm{KMgCl}_{2}\), and \(\mathrm{PtCl}_{2}\) are insoluble and hence will precipitate.

- Write the Balanced Equations

Write balanced chemical reactions depicting the formation of the identified precipitates. For (a), the balanced equation is \(\mathrm{MgSO}_{4}(a q) + \mathrm{BaCl}_{3}(a q) \rightarrow \mathrm{MgCl}_{2}(a q) + \mathrm{BaSO}_{4}(s)\), for (b) it is: \(\mathrm{K}_{\mathrm{S}} \mathrm{SO}_{4}(a q) + \mathrm{2MgCl}_{2}(a q) \rightarrow \mathrm{2KMgCl}_{2}(s) + \mathrm{K}_{2}\mathrm{SO}_{4}(a q)\), and (c) gives: \(\mathrm{MgCl}_{2}(a q) + \mathrm{Pt}(NO_{2})_{2}(a q) \rightarrow \mathrm{Mg(NO}_{2})_{2}(a q) + \mathrm{PtCl}_{2}(s)\)

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that allows us to accurately represent chemical reactions. The law of conservation of mass dictates that the number of atoms for each element must be the same on both sides of the equation. To balance the equation, start by listing the number of atoms of each element in the reactants and products. Then, adjust the coefficients, which are the numbers in front of the chemical formulas, to ensure the same number of atoms on both sides.

For example, if we take the reaction from exercise (b) listed above, we initially write the unbalanced chemical equation as \(\mathrm{K}_{\mathrm{S}}\mathrm{SO}_{4}(aq) + \mathrm{MgCl}_{2}(aq)\rightarrow\mathrm{KMgCl}_{2}(s) + \mathrm{K}_{2}\mathrm{SO}_{4}(aq)\). We notice that the equation is not balanced: there are two chloride ions in \(\mathrm{MgCl}_{2}(aq)\) on the reactant side, but only one chloride ion in \(\mathrm{KMgCl}_{2}(s)\) on the product side. Therefore, we adjust the coefficient in front of \(\mathrm{KMgCl}_{2}(s)\) to 2, balancing the chlorides. We also adjust the potassium and sulfate accordingly, resulting in a balanced equation. This process ensures that our chemical equation follows the law of conservation of mass, an essential principle in chemistry.

Predicting Precipitates

Predicting whether a precipitate will form in a chemical reaction involves understanding how different ions in solution might react with one another. When two aqueous solutions are mixed, the ions can recombine to form new compounds. If any of these new compounds are insoluble, they will form a solid precipitate that separates from the solution.

To predict a precipitate, exchange the cations and anions of the reacting compounds, as shown in the textbook exercise. Then, refer to the solubility rules to determine if any of the new combinations are likely to precipitate. In exercise (a), when \(\mathrm{MgSO}_{4}(aq)\) and \(\mathrm{BaCl}_{3}(aq)\) are mixed, the barium and sulfate ions can combine to form \(\mathrm{BaSO}_{4}\), which the solubility rules tell us is insoluble and will therefore precipitate. By following a systematic approach to exchange the ions and then applying the solubility rules, we can predict the formation of precipitates in chemical reactions.

Solubility Rules

Solubility rules are guidelines that help us predict whether a compound will be soluble in water. These rules are based on empirical data and can be memorized to quickly determine the solubility of ionic compounds in aqueous solutions. Generally, compounds containing alkali metal ions and the ammonium ion \(\mathrm{NH}_{4}^{+}\) are soluble, as are nitrates \(\mathrm{NO}_{3}^{-}\), bicarbonates \(\mathrm{HCO}_{3}^{-}\), and chlorates \(\mathrm{ClO}_{3}^{-}\).

However, there are exceptions. For example, carbonates \(\mathrm{CO}_{3}^{2-}\), phosphates \(\mathrm{PO}_{4}^{3-}\), sulfides \(\mathrm{S}^{2-}\), and hydroxides \(\mathrm{OH}^{-}\) are typically insoluble, except when paired with the aforementioned soluble cations. In our exercise example (a), \(\mathrm{BaSO}_{4}\) is insoluble according to these rules, leading to its precipitation. It's important to get familiar with these rules, as they are critical for not only predicting precipitates but also for understanding the behavior of compounds in aqueous solutions.