Problem 24 - Chemistry and Chemical Reactivity

Question

Balance the following equations, and then write the net ionic equation: (a) \(\mathrm{Zn}(\mathrm{s})+\mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{ZnCl}_{2}(\mathrm{aq})\) (b) \(\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)\) (c) \(\mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{CaCO}_{3}(\mathrm{s}) \longrightarrow\) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(\mathrm{g})\)

Step-by-Step Solution

Answer

(a) Balanced: Zn(s) + 2HCl(aq) → H2(g) + ZnCl2(aq); Net Ionic: Zn(s) + 2H+(aq) → H2(g) + Zn2+(aq) (b) Balanced: Mg(OH)2(s) + 2HCl(aq) → MgCl2(aq) + 2H2O(l); Net Ionic: Mg(OH)2(s) + 2H+(aq) → Mg2+(aq) + 2H2O(l) (c) Balanced: 2HNO3(aq) + CaCO3(s) → Ca(NO3)2(aq) + H2O(l) + CO2(g); Net Ionic: 2H+(aq) + CaCO3(s) → Ca2+(aq) + H2O(l) + CO2(g)

Step 1: Balance Equation (a)

The unbalanced equation is \( \mathrm{Zn}(\mathrm{s}) + \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g}) + \mathrm{ZnCl}_{2}(\mathrm{aq}) \). To balance it, observe the number of atoms of each element:- Zn: 1 on both sides- Cl: 1 on the left, 2 on the right- H: 1 on the left, 2 on the rightWe have to place a coefficient of 2 before \( \mathrm{HCl} \) to balance Cl and H:\[ \mathrm{Zn}(\mathrm{s}) + 2\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g}) + \mathrm{ZnCl}_{2}(\mathrm{aq}) \]. Now the equation is balanced.

Step 2: Write the Net Ionic Equation for (a)

Split the aqueous compounds into ions:\[ \mathrm{Zn}(\mathrm{s}) + 2\mathrm{H}^{+}(\mathrm{aq}) + 2\mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g}) + \mathrm{Zn}^{2+}(\mathrm{aq}) + 2\mathrm{Cl}^{-}(\mathrm{aq}) \].Eliminate the spectator ions, resulting in:\[ \mathrm{Zn}(\mathrm{s}) + 2\mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g}) + \mathrm{Zn}^{2+}(\mathrm{aq}) \].

Step 3: Balance Equation (b)

The unbalanced equation is \( \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s}) + \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O}(\ell) \). Balancing: - Mg: 1 on both sides- Cl: 1 on the left, 2 on the right- H: 3 on the left (1 from each \( \mathrm{HCl} \) and 2 from \( \mathrm{H}_{2}\mathrm{O} \)), 2 on the rightPlace a 2 before \( \mathrm{HCl} \):\[ \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s}) + 2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq}) + 2 \mathrm{H}_{2}\mathrm{O}(\ell) \]. Now it is balanced.

Step 4: Write the Net Ionic Equation for (b)

Split the aqueous compounds into ions:\[ \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s}) + 2\mathrm{H}^{+}(\mathrm{aq}) + 2\mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{Mg}^{2+}(\mathrm{aq}) + 2\mathrm{Cl}^{-}(\mathrm{aq}) + 2\mathrm{H}_{2}\mathrm{O}(\ell) \].Cancel the spectator ions (\(\mathrm{Cl}^{-}\)):\[ \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s}) + 2\mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{Mg}^{2+}(\mathrm{aq}) + 2\mathrm{H}_{2}\mathrm{O}(\ell) \].

Step 5: Balance Equation (c)

The unbalanced equation is \( \mathrm{HNO}_{3}(\mathrm{aq}) + \mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{Ca}(\mathrm{NO}_{3})_{2}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O}(\ell) + \mathrm{CO}_{2}(\mathrm{g}) \). Balancing:- Ca: 1 on both sides- \(\mathrm{NO}_3\): 1 on the left, 2 on the right- H: 1 on the left, 2 on the rightPlace a coefficient of 2 before \( \mathrm{HNO}_{3} \):\[ 2\mathrm{HNO}_{3}(\mathrm{aq}) + \mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{Ca}(\mathrm{NO}_{3})_{2}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O}(\ell) + \mathrm{CO}_{2}(\mathrm{g}) \]. Now the equation is balanced.

Step 6: Write the Net Ionic Equation for (c)

Split the aqueous compounds into ions:\[ 2\mathrm{H}^{+}(\mathrm{aq}) + 2\mathrm{NO}_{3}^{-}(\mathrm{aq}) + \mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{Ca}^{2+}(\mathrm{aq}) + 2\mathrm{NO}_{3}^{-}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O}(\ell) + \mathrm{CO}_{2}(\mathrm{g}) \].Cancel the spectator ions (\( \mathrm{NO}_{3}^{-} \)):\[ 2\mathrm{H}^{+}(\mathrm{aq}) + \mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{Ca}^{2+}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O}(\ell) + \mathrm{CO}_{2}(\mathrm{g}) \].

Key Concepts

Net Ionic Equations

A net ionic equation is a simplified version of a chemical equation. It shows only the species that actually participate in the chemical reaction. This means only ions and molecules directly involved in producing the reaction are included.
To find the net ionic equation, you first write the balanced molecular equation. Then, you need to dissociate all the strong electrolytes into their respective ions.
For instance, the reaction between zinc and hydrochloric acid:

• Start with the balanced equation: \( \mathrm{Zn} ( \mathrm{s} ) + 2\mathrm{HCl} ( \mathrm{aq} ) \rightarrow \mathrm{H}_2 ( \mathrm{g} ) + \mathrm{ZnCl}_2 ( \mathrm{aq} ) \).
• Write the ions for aqueous substances: \( \mathrm{Zn} ( \mathrm{s} ) + 2\mathrm{H}^{+} ( \mathrm{aq} ) + 2\mathrm{Cl}^{-} ( \mathrm{aq} ) \rightarrow \mathrm{H}_2 ( \mathrm{g} ) + \mathrm{Zn}^{2+} ( \mathrm{aq} ) + 2\mathrm{Cl}^{-} ( \mathrm{aq} ) \).
• Cancel out the spectator ions, if any, to focus on the reacting substances. Here, the spectator ion \( \mathrm{Cl}^- \) appears on both sides and is cancelled out.

The final net ionic equation is: \( \mathrm{Zn} ( \mathrm{s} ) + 2\mathrm{H}^+ ( \mathrm{aq} ) \rightarrow \mathrm{H}_2 ( \mathrm{g} ) + \mathrm{Zn}^{2+} ( \mathrm{aq} ) \).
This simplified approach helps to clearly identify which ions contribute to the chemical change.

Spectator Ions

Spectator ions are ions in a solution that do not participate in the actual chemical reaction. They are present in the reactant and as well as the product side of a chemical equation in exactly the same form.
In many chemical reactions, particularly those occurring in aqueous solutions, some ions will simply "watch" the reaction without taking part.
For instance, in the reaction of magnesium hydroxide and hydrochloric acid, before simplification:

• Start with the dissociated ions: \( \mathrm{Mg} ( \mathrm{OH} )_2 ( \mathrm{s} ) + 2\mathrm{H}^{+} ( \mathrm{aq} ) + 2\mathrm{Cl}^{-} ( \mathrm{aq} ) \rightarrow \mathrm{Mg}^{2+} ( \mathrm{aq} ) + 2\mathrm{Cl}^{-} ( \mathrm{aq} ) + 2\mathrm{H}_2 \mathrm{O} ( \ell ) \).
• Evaluate which ions are unchanged: The \( \mathrm{Cl}^- \) ion is unchanged on both sides of the equation.

These \( \mathrm{Cl}^- \) ions are the spectator ions, and hence are left out when writing the net ionic equation.
Spectator ions are crucial to know about because they provide a clearer view of the actual chemical processes happening within the reaction.

Acid-Base Reactions

Acid-base reactions involve the transfer of hydrogen ions (H^+). Specifically, an acid (proton donor) reacts with a base (proton acceptor) to produce water and often a salt.
For example, consider the reaction between nitric acid and calcium carbonate:

• Balanced molecular equation: \( 2\mathrm{HNO}_3 ( \mathrm{aq} ) + \mathrm{CaCO}_3 ( \mathrm{s} ) \rightarrow \mathrm{Ca} ( \mathrm{NO}_3 )_2 ( \mathrm{aq} ) + \mathrm{H}_2\mathrm{O} ( \ell ) + \mathrm{CO}_2 ( \mathrm{g} ) \).
• Here, \( \mathrm{HNO}_3 \) donates H^+, a typical feature of an acid, and reacts with \( \mathrm{CaCO}_3 \), resulting in the formation of water and carbon dioxide.

This reaction is characteristic of an acid reacting with a carbonate-based salt which also indicates the evolution of a gas - carbon dioxide.
Understanding these reactions provides insight into how many substances interact in various chemical environments, such as biological systems and industrial processes.

Precipitation Reactions

Precipitation reactions occur when two aqueous solutions combine to form an insoluble solid, known as a precipitate. These types of reactions are common in both laboratory and natural settings.
When two ionic compounds are dissolved in water, their ions are free to move around. Sometimes, when the two solutions are mixed, certain ions attract each other strongly enough to form a solid.
For a reaction example, we didn't have a direct one from the exercise, but imagine that when mixing aqueous sodium chloride (\( \mathrm{NaCl} \)) and silver nitrate (\( \mathrm{AgNO}_3 \)), the silver ion (\( \mathrm{Ag}^{+} \)) and chloride ion (\( \mathrm{Cl}^{-} \)) will form solid silver chloride (\( \mathrm{AgCl} \)).

• The net ionic equation: \( \mathrm{Ag}^{+} ( \mathrm{aq} ) + \mathrm{Cl}^{-} ( \mathrm{aq} ) \rightarrow \mathrm{AgCl} ( \mathrm{s} ) \).
• This highlights the process of formation of a precipitate.

Such reactions are fundamental in analytical chemistry, where detecting and quantifying ions in a solution may rely on precipitation.