Question

Balance each of the following equations that describe precipitation reactions. a. \(\mathrm{CaCl}_{2}(a q)+\mathrm{AgNO}_{3}(a q) \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{AgCl}(s)\) b. \(\mathrm{AgNO}_{3}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{CrO}_{4}(s)+\mathrm{KNO}_{3}(a q)\) c. \(\mathrm{BaCl}_{2}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{BaSO}_{4}(s)+\mathrm{KCl}(a q)\)

Short answer

The balanced chemical equations for the given precipitation reactions are: a. \(\mathrm{CaCl}_{2}(a q)+2\mathrm{AgNO}_{3}(a q) \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2\mathrm{AgCl}(s)\) b. \(2\mathrm{AgNO}_{3}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{CrO}_{4}(s)+2\mathrm{KNO}_{3}(a q)\) c. \(\mathrm{BaCl}_{2}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{BaSO}_{4}(s)+2\mathrm{KCl}(a q)\)

Step-by-step solution

a. Balancing \(\mathrm{CaCl}_{2}(a q)+\mathrm{AgNO}_{3}(a q) \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{AgCl}(s)\)

1. Identify elements: In this equation, we have 4 elements - Ca, Cl, Ag, and N. 2. Count the number of each atom on both sides of the equation: Reactants: 1 Ca, 2 Cl, 1 Ag, 1 N, 3 O Products: 1 Ca, 2 N, 6 O, 1 Ag, 2 Cl 3. Adjust coefficients to balance atoms: The number of N is not balanced. We can balance N by placing a coefficient of 2 in front of \(\mathrm{AgNO}_{3}(a q)\) on the reactants side. Now the equation is: \(\mathrm{CaCl}_{2}(a q)+2\mathrm{AgNO}_{3}(a q) \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{AgCl}(s)\). All the elements are now balanced (1 Ca, 2 Cl, 2 Ag, 2 N, 6 O). This is our balanced equation.

b. Balancing \(\mathrm{AgNO}_{3}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{CrO}_{4}(s)+\mathrm{KNO}_{3}(a q)\)

1. Identify elements: In this equation, we have 5 elements - Ag, N, K, Cr, and O. 2. Count the number of each atom on both sides of the equation: Reactants: 1 Ag, 1 N, 2 K, 1 Cr, 7 O Products: 2 Ag, 1 N, 1 K, 1 Cr, 7 O 3. Adjust coefficients to balance atoms: The number of Ag and K is not balanced. We can balance Ag by placing a coefficient of 2 in front of \(\mathrm{AgNO}_{3}(a q)\) on the reactants side, and balance K by placing a coefficient of 2 in front of \(\mathrm{KNO}_{3}(a q)\) on the products side. Now the equation is: \(2\mathrm{AgNO}_{3}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{CrO}_{4}(s)+2\mathrm{KNO}_{3}(a q)\). All the elements are now balanced (2 Ag, 2 N, 2 K, 1 Cr, 7 O). This is our balanced equation.

c. Balancing \(\mathrm{BaCl}_{2}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{BaSO}_{4}(s)+\mathrm{KCl}(a q)\)

1. Identify elements: In this equation, we have 5 elements - Ba, Cl, K, S, and O. 2. Count the number of each atom on both sides of the equation: Reactants: 1 Ba, 2 Cl, 2 K, 1 S, 4 O Products: 1 Ba, 1 Cl, 1 K, 1 S, 4 O 3. Adjust coefficients to balance atoms: The number of Cl and K is not balanced. We can balance Cl and K by placing a coefficient of 2 in front of \(\mathrm{KCl}(a q)\) on the products side. Now the equation is: \(\mathrm{BaCl}_{2}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{BaSO}_{4}(s)+2\mathrm{KCl}(a q)\). All the elements are now balanced (1 Ba, 2 Cl, 2 K, 1 S, 4 O). This is our balanced equation.

Key concepts

Precipitation Reactions

In chemistry, a precipitation reaction occurs when two soluble salts in aqueous solution combine and form an insoluble solid known as a precipitate. Precipitation reactions are a type of double displacement reaction where two reactant compounds swap components. These reactions are useful for identifying the presence of various ions in a solution.

For instance, in the reactions given in the exercise, precipitates such as

• AgCl in example (a)
• Ag₂CrO₄ in example (b)
• BaSO₄ in example (c)

are formed. Understanding precipitation is crucial in fields like analytical chemistry where it's used to purify or separate ions. Identifying the precipitate (color and formation) helps confirm the occurrence of a specific chemical reaction.

When writing equations for precipitation reactions, always include the state symbols to show which compounds are aqueous and which are solid precipitates.

Stoichiometry

Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It involves using balanced chemical equations to determine the relative amounts of each substance involved in the reaction. The coefficients in a balanced equation reveal the molar ratios of the compounds, which can be used to calculate how much of each reactant is needed or how much product will be produced.

In our exercises, stoichiometry helps determine how much of each reactant like CaCl₂ and AgNO₃ or product like AgCl or Ca(NO₃)₂ is present during the reactions. Balancing the equation ensures that no atoms are lost or gained in the reaction, obeying the Law of Conservation of Mass. It's essential for accurately predicting yields in chemical manufacturing and laboratory settings, where precise calculations are critical to success.

Chemical Formulas

Chemical formulas are shorthand ways of denoting the number and types of atoms present in a compound. They are a vital part of writing and balancing chemical equations, which describe chemical reactions. There are different types of chemical formulas including molecular, empirical, and structural. The molecular formula shows the number of each type of atom in a molecule, like

• \( \text{CaCl}_2 \) for calcium chloride, meaning one calcium atom and two chlorine atoms.
• \( \text{AgNO}_3 \) for silver nitrate, showing one silver, one nitrogen, and three oxygen atoms.

When balancing chemical equations, understanding these formulas helps in predicting the outcomes of chemical reactions by showing the exact number of atoms that must balance on both sides of the equation. Chemical formulas provide the basics needed for calculating molar masses, which are crucial in stoichiometric calculations.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances through breaking and forming chemical bonds. They're represented by chemical equations which must be balanced to preserve mass and comply with the Law of Conservation of Mass. This means that the same number of each type of atom must appear on both sides of the equation.

In the examples provided:

• In (a), calcium chloride reacts with silver nitrate to produce calcium nitrate and silver chloride.
• In (b), silver nitrate and potassium chromate form silver chromate and potassium nitrate.
• In (c), barium chloride reacts with potassium sulfate to yield barium sulfate and potassium chloride.

Every chemical equation shows the reactants (starting materials) to the left of the arrow and the products (end materials) to the right. Understanding chemical reactions is fundamental for fields like chemistry and biology, where reactions form the basis of studying and developing new materials and processes.