Problem 110 - Chemistry: The Central Science in SI Units, Global Edition

Question

Ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl}\), is a very soluble salt in water. (a) Draw the Lewis structures of the ammonium and chloride ions. (b) Is there an \(\mathrm{N}-\mathrm{Cl}\) bond in solid ammonium chloride? (c) If you dissolve \(14 \mathrm{~g}\) of ammonium chloride in \(500.0 \mathrm{~mL}\) of water, what is the molar concentration of the solution? (d) How many grams of silver nitrate do you need to add to the solution in part (c) to precipitate all of the chloride as silver chloride?

Step-by-Step Solution

Answer

(a) Ammonium ion: \(\mathrm{H} - \mathrm{N}^{+} - \mathrm{H}\) | \(\mathrm{H}\) and Chloride ion: \(\mathrm{Cl}^{-} : \hspace{2mm} \ominus \) (b) No, there is no direct N-Cl bond in solid ammonium chloride. (c) The molar concentration is approximately 0.524 M. (d) 44.5 grams of silver nitrate are needed to precipitate all chloride as silver chloride.

Step 1: Drawing Lewis structures of ammonium and chloride ions

For the ammonium ion (NH₄⁺), nitrogen (N) has 5 valence electrons and each hydrogen (H) has 1 valence electron. In the ammonium ion, nitrogen forms four covalent bonds with hydrogen atoms and has a positive charge: \[ \mathrm{H} - \mathrm{N}^{+} - \mathrm{H} \] | \(\mathrm{H}\) For the chloride ion (Cl⁻), chlorine (Cl) has 7 valence electrons. It gains 1 electron to complete its octet and becomes negatively charged: \[\mathrm{Cl}^{-} : \hspace{2mm} \ominus \]

Step 2: N-Cl bond in solid ammonium chloride

In solid ammonium chloride (NH₄Cl), there is no direct N-Cl bond. Instead, the compound exists as an ionic lattice structure where the positively charged ammonium ions (NH₄⁺) are attracted to the negatively charged chloride ions (Cl⁻).

Step 3: Calculating the molar concentration of the solution

To calculate the molar concentration of the solution, first find the moles of ammonium chloride dissolved. The molar mass of NH₄Cl is 53.49 g/mol (14.01 for N, 4 x 1.01 for each H, and 35.45 for Cl): Moles of ammonium chloride = mass / molar mass = 14 g / 53.49 g/mol ≈ 0.262 mol The volume of the solution is 500.0 mL, which is equal to 0.500 L. To calculate the molar concentration, divide the moles of solute by the volume of the solution: Molar concentration = 0.262 mol / 0.500 L ≈ 0.524 M

Step 4: Determining the mass of silver nitrate needed to precipitate all chloride

When silver nitrate (AgNO₃) reacts with ammonium chloride (NH₄Cl), it forms silver chloride (AgCl) and ammonium nitrate (NH₄NO₃): \[ \mathrm{AgNO}_{3} (aq) + \mathrm{NH}_{4}\mathrm{Cl} (aq) \to \mathrm{AgCl}(s) + \mathrm{NH}_{4}\mathrm{NO}_{3} (aq) \] Notice that the reaction has a one-to-one stoichiometry for AgNO₃ and NH₄Cl. Since we know the moles of NH₄Cl in the solution (0.262 mol), we can find the moles of AgNO₃ needed: Moles of AgNO₃ = 0.262 mol The molar mass of AgNO₃ is 169.87 g/mol (107.87 for Ag, 14.01 for N, and 48.00 for O₃). Therefore, the mass of AgNO₃ needed: Mass of AgNO₃ = moles x molar mass = 0.262 mol x 169.87 g/mol ≈ 44.5 g So, 44.5 grams of silver nitrate is needed to precipitate all chloride as silver chloride.

Key Concepts

Lewis Structures

Lewis structures are diagrams that show the bonding between atoms of a molecule. This visual representation helps in understanding how electrons are shared between atoms. For the ammonium ion, NH₄⁺, nitrogen begins with five valence electrons. Each hydrogen contributes one electron for bonding. Thus, nitrogen forms four single covalent bonds with four hydrogen atoms. The NH₄ molecule carries a positive charge because it has one less electron than the combined total of electrons from nitrogen and the hydrogens. In a Lewis structure, this can be depicted as:

• The central nitrogen atom bonded to four hydrogen atoms in a tetrahedral shape.
• The charge is indicated by a superscript plus sign (+) outside the brackets of the structure.

For the chloride ion, Cl⁻, chlorine has seven valence electrons. By gaining an electron, it achieves a stable octet. Thus, Cl becomes a chloride ion with a negative charge, shown as Cl⁻ with an extra electron represented alongside the symbol. The overall complete octet for chlorine is achieved with eight electrons around it: seven original from chlorine and the additional one gained electron.

Molar Concentration

Molar concentration (also called molarity) is a measure of the concentration of a solute in a solution. It is expressed in moles per liter ( ext{mol/L}"). To calculate it, first determine the number of moles of solute in the solution. For instance, if there are 14 grams of ammonium chloride (NH₄Cl) dissolved, and the molar mass of NH₄Cl is 53.49 g/mol, then:

• Number of moles = mass / molar mass = 14 g / 53.49 g/mol ≈ 0.262 mol

Then, you measure the volume of the solution in liters. For 500.0 mL of water, convert it to liters: 500.0 mL is equivalent to 0.500 L.

• Molarity (M) = moles of solute / volume of solution in liters = 0.262 mol / 0.500 L ≈ 0.524 M

This calculation indicates that the solution of ammonium chloride has a concentration of 0.524 mol/L.

Ionic Lattice Structure

An ionic lattice structure is a highly ordered, repeating pattern in which ions are arranged. In a solid ammonium chloride sample, the NH₄⁺ and Cl⁻ ions do not form a direct nitrogen-chlorine bond. Instead, they align to create a crystal lattice. Here, each positively charged ammonium ion is surrounded by negatively charged chloride ions. The key characteristics of an ionic lattice structure include:

• The arrangement is maintained by strong electrostatic forces of attraction between oppositely charged ions.
• The structure is usually very stable and solid at room temperature.
• It leads to distinct properties such as high melting and boiling points.

This orderly structure explains why solid ammonium chloride has no specific N-Cl bond, but rather exists as an ionic compound.

Precipitation Reaction

A precipitation reaction involves mixing two solutions that result in the formation of an insoluble solid, known as the precipitate. In the context of ammonium chloride, if silver nitrate (AgNO₃) is added to the NH₄Cl solution, silver chloride (AgCl) precipitates out. The detailed reaction is:

• AgNO₃(aq) + NH₄Cl(aq) → AgCl(s) + NH₄NO₃(aq)

In this reaction:

• Silver ions (Ag⁺) from silver nitrate react with chloride ions (Cl⁻) from ammonium chloride to form AgCl, which is insoluble in water.
• AgCl appears as a whitish solid that settles out of the solution.
• The remaining ions, NH₄⁺ and NO₃⁻, stay dissolved in water as ammonium nitrate.

The stoichiometry of the reaction is one-to-one: one mole of silver nitrate reacts with one mole of ammonium chloride to produce one mole of silver chloride, making it crucial to calculate the correct mass of silver nitrate needed for complete precipitation based on the initial moles of chloride ions present.