Chapter 5: Problem 143
\(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is \(50 \%\) ionized in aqueous solution. Find the value of \(i\).
Short Answer
Expert verified
The van't Hoff factor \(i\) is 2.
Step by step solution
01
Identify Initial Problem
We are given that \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is 50\% ionized in an aqueous solution, and we need to find the value of the van't Hoff factor \(i\). For an ionic compound like this, the van't Hoff factor represents the total number of particles in the solution after ionization.
02
Understand the Ionization Process
\(\mathrm{K}_{2} \mathrm{HgI}_{4} \) ionizes in water to form 2 \(\mathrm{K}^+\) ions and 1 \(\mathrm{HgI}_{4}^{2-}\) ions. The total number of ions produced from complete ionization of 1 unit is 3.
03
Determine the Degree of Ionization
Since 50\% of \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is ionized, this means that only half of the compound undergoes ionization to form ions. Therefore, the degree of ionization, \(\alpha\), is 0.5.
04
Calculate the Effective Van't Hoff Factor
The formula to calculate the van't Hoff factor \(i\) when the degree of ionization is known is: \[i = 1 + (n - 1) \times \alpha\]where \(n\) is the number of ions formed from one formula unit upon complete ionization. Substitute \(n = 3\) and \(\alpha = 0.5\) into the equation:\[i = 1 + (3 - 1) \times 0.5 = 1 + 2 \times 0.5 = 1 + 1 = 2\]
05
Final Calculation and Result
Based on the calculation, the van't Hoff factor \(i\) for \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is 2. This means the effective number of ions formed in the solution is equivalent to that produced by 2 unit particles.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ionization Process
When a compound like \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) dissolves in water, it undergoes the ionization process. This is a crucial chemical transformation where a neutral molecule splits into positive and negative ions.
During ionization, each molecule of \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) splits into two \(\mathrm{K}^+\) ions and one \(\mathrm{HgI}_{4}^{2-}\) ion. This increment in the number of particles plays a significant role in assessing properties like boiling point elevation and freezing point depression in solutions.
Understanding this process helps explain how the number of ions contributes to a solution's colligative properties, demonstrating how an ionic compound affects its surrounding environment.
When referring to the ionization process in the context of a chemical equation, it is essential to balance the charges and matter to ensure that mass and electric charge are conserved. In simple terms, if you started with a certain number of atoms and charges, you must end with the same number distributed among ions. This conservation is a fundamental principle of chemistry.
During ionization, each molecule of \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) splits into two \(\mathrm{K}^+\) ions and one \(\mathrm{HgI}_{4}^{2-}\) ion. This increment in the number of particles plays a significant role in assessing properties like boiling point elevation and freezing point depression in solutions.
Understanding this process helps explain how the number of ions contributes to a solution's colligative properties, demonstrating how an ionic compound affects its surrounding environment.
When referring to the ionization process in the context of a chemical equation, it is essential to balance the charges and matter to ensure that mass and electric charge are conserved. In simple terms, if you started with a certain number of atoms and charges, you must end with the same number distributed among ions. This conservation is a fundamental principle of chemistry.
Degree of Ionization
The term 'degree of ionization' refers to what fraction of a solute dissociates into ions in a solution.
In the case of \(\mathrm{K}_{2} \mathrm{HgI}_{4}\), the exercise stated it's 50% ionized, meaning only half the solution's molecules break apart to form ions.
Degree of ionization is symbolized by \(\alpha\) and calculated as the ratio of the ionized solute to the total solute. It is represented as: \[\alpha = \frac{\text{number of ionized molecules}}{\text{total number of molecules}}\]
In our exercise, \(\alpha = 0.5\) indicates half of the \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) units have ionized in the solution. Factors affecting this degree include concentration, temperature, and the nature of the solute and solvent.
Understanding the degree of ionization is essential for calculating factors like the van’t Hoff factor, which in turn helps predict solution behaviors.
In the case of \(\mathrm{K}_{2} \mathrm{HgI}_{4}\), the exercise stated it's 50% ionized, meaning only half the solution's molecules break apart to form ions.
Degree of ionization is symbolized by \(\alpha\) and calculated as the ratio of the ionized solute to the total solute. It is represented as: \[\alpha = \frac{\text{number of ionized molecules}}{\text{total number of molecules}}\]
In our exercise, \(\alpha = 0.5\) indicates half of the \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) units have ionized in the solution. Factors affecting this degree include concentration, temperature, and the nature of the solute and solvent.
- Concentration: Typically, the higher the concentration, the less degree of ionization occurs.
- Temperature: Ionization can increase with rising temperature as molecules move more vigorously.
- Nature of solute and solvent: Some substances ionize better in specific solvents; water, being polar, aids ionization of ionic compounds.
Understanding the degree of ionization is essential for calculating factors like the van’t Hoff factor, which in turn helps predict solution behaviors.
Aqueous Solution Chemistry
Aqueous solution chemistry is the study of substances dissolved in water, a common solvent in chemical reactions.
When \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is dissolved in water, it forms ions through the ionization process, illustrating the fundamental characteristics of aqueous solutions: conductive behavior due to the presence of ions.
Another crucial aspect is the understanding of solubility. Ionic compounds must be soluble in water to dissociate into ions.
Aqueous chemistry involves principles like:
Through investigating these areas, students gain insight into behavior of ionic compounds in water, the role of the solvent, and the factors influencing solubility and reactions, providing a foundation for more complex chemical analysis.
When \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is dissolved in water, it forms ions through the ionization process, illustrating the fundamental characteristics of aqueous solutions: conductive behavior due to the presence of ions.
Another crucial aspect is the understanding of solubility. Ionic compounds must be soluble in water to dissociate into ions.
Aqueous chemistry involves principles like:
- Electrolyte classification: Substances like \(\mathrm{K}_{2} \mathrm{HgI}_{4}\) are considered strong electrolytes because they ionize completely or to a significant degree in water.
- Colligative properties: These depend on the number of solute particles in the solution rather than their nature, affecting properties such as boiling point elevation or freezing point depression.
Through investigating these areas, students gain insight into behavior of ionic compounds in water, the role of the solvent, and the factors influencing solubility and reactions, providing a foundation for more complex chemical analysis.
