Problem 47 - Chemistry The Science in Context

Question

Which of the following solutions has the greatest number of particles (atoms or ions) of solute per liter? (a) \(1 M \mathrm{NaCl} ;\) (b) \(1 M \mathrm{CaCl}_{2} ;\) (c) \(1 M\) ethanol; (d) \(1 M\) acetic acid

Step-by-Step Solution

Answer

(a) 1 M sodium chloride (NaCl) (b) 1 M calcium chloride (CaCl2) (c) 1 M ethanol (C2H5OH) (d) 1 M acetic acid (CH3COOH) Answer: (b) 1 M calcium chloride (CaCl2)

Step 1: Analyze the solutes

First, let's analyze each solute and determine their chemical formulas: (a) Sodium chloride, NaCl (b) Calcium chloride, CaCl2 (c) Ethanol, C2H5OH (d) Acetic acid, CH3COOH

Step 2: Calculate the number of particles generated by each solute in water

When each solute is dissolved in water, they will generate a specific number of particles: (a) NaCl: \(1 \ Na^+\) ion and \(1 \ Cl^-\) ion per molecule; total of \(2\) particles (b) CaCl2: \(1 \ Ca^{2+}\) ion and \(2 \ Cl^-\) ions per molecule; total of \(3\) particles (c) Ethanol (C2H5OH): does not dissociate in water, \(1\) particle (d) Acetic acid (CH3COOH): weak acid, primarily in undissociated form, approximately \(1\) particle

Step 3: Compare the number of particles generated

Comparing the number of particles generated by each solute per molecule when dissolved in water, we find that: NaCl generates 2 particles CaCl2 generates 3 particles Ethanol generates 1 particle Acetic acid generates approximately 1 particle

Step 4: Determine the solute with the greatest number of particles

Based on the comparison made in Step 3, we can conclude that the solution with the greatest number of particles of solute per liter is a 1 M solution of calcium chloride (CaCl2), with each molecule generating 3 particles when dissolved in water. Therefore, the solution (b) has the greatest number of particles (atoms or ions) of solute per liter.

Key Concepts

Dissociation of Ionic Compounds

Understanding the concept of dissociation is pivotal when analyzing ionic compounds like sodium chloride (NaCl) and calcium chloride (CaCl2) in solution.

Dissociation refers to the process by which an ionic compound separates into its individual ions when it dissolves in water. This is because water is a polar solvent, and the positive and negative parts of the water molecule can stabilize the positive and negative ions, respectively.

Example: Sodium Chloride (NaCl)

When NaCl dissolves in water, it splits into one sodium ion (Na+) and one chloride ion (Cl-), resulting in a total of two particles per formula unit.

Example: Calcium Chloride (CaCl2)

In the case of CaCl2, the compound separates into one calcium ion (Ca2+) and two chloride ions (Cl-), producing three particles per formula unit.
Due to these dissociations, when comparing molar solutions of NaCl and CaCl2, CaCl2 will yield more particles in solution, making it crucial in calculations where particle concentration is significant.

Molecular Solutes in Solution

Molecular solutes such as ethanol (C2H5OH) behave differently in solution compared to ionic compounds. A molecular solute does not dissociate into ions; instead, it dissolves as whole molecules.

This distinction stems from the nature of the bonding in molecular substances, which is covalent as opposed to the ionic bonds in salts. In water, ethanol molecules will interact with water molecules via hydrogen bonding and other intermolecular forces but will remain as individual, intact ethanol molecules. As a result, a 1 M solution of a molecular solute like ethanol will only produce one particle per molecule in the solution, making it less likely to have the highest particle concentration compared to ionic solutes.

Stoichiometry of Solutes

Stoichiometry of solutes is essential when comparing concentrations to ascertain which solution contains more particles. It involves looking at the molar ratios and the quantities of each substance involved in chemical reactions or when dissolved in solution.

For a solution with a given molarity, we must consider the stoichiometry of the solute to understand how many particles will be present in the solution.

Stoichiometric Calculation

For instance, in a 1 M solution of CaCl2, stoichiometry tells us that for every mole of CaCl2, there will be 3 moles of ions produced (1 mole of Ca2+ ions and 2 moles of Cl- ions). Therefore, in terms of particle count, a 1 M solution of an ionic compound that dissociates into multiple ions will have a notably higher concentration of particles than a 1 M solution of a molecular compound that does not dissociate, as seen in the example exercise involving NaCl, CaCl2, ethanol, and acetic acid.