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Chapter 12: Problem 68

What is the van't Hoff factor? What information does it provide?

Short Answer

Expert verified
The van't Hoff factor ('i') provides insight into the number of particles a substance can produce in a solution, telling us about its potential to alter a solution's colligative properties like boiling point, freezing point, and osmotic pressure. Essentially, it serves as an indicator of a substance's behavior in a solution.

Step by step solution

01

Definition

The van't Hoff factor, or 'i', is a dimensionless factor used in physical chemistry to account for the effect of solute particles in a solution on its properties. It allows us to estimate the nature and magnitude of colligative properties like boiling point elevation, freezing point depression, and osmotic pressure.
02

Calculation

In theory, the van鈥檛 Hoff factor equals the number of particles (ions or molecules) a substance can produce in solution. For example, for non-electrolytes like sucrose that do not dissociate in solution, 'i' equals 1. For electrolytes that do dissociate in solution, like NaCl, 'i' is typically greater than 1. However, in practice, 'i' can be less than the theoretical value due to interactions between solute particles in highly concentrated solutions that briefly bring them together as though they are a single particle.
03

Information 'i' provides

The van't Hoff factor is crucial in predicting the extent of a solute's effect on the colligative property of a solution, helping scientists and chemists understand the solution's behavior. Through 'i', you can estimate whether a substance will dissociate in solution and the extent of its dissociation - whether it's a non-electrolyte, weak electrolyte, or strong electrolyte. Moreover, knowing 'i' can aid in calculating the colligative properties of more complex solutions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Colligative Properties
Colligative properties are unique characteristics of solutions that depend on the number of solute particles rather than the type of solute itself. This makes them extremely useful in chemistry because they allow us to predict how a solution will behave under various conditions.
Here are the primary colligative properties:
  • Boiling Point Elevation: When solute is added to a solvent, the boiling point increases. This is because the solute particles disrupt the formation of vapor, requiring more heat to reach the boiling point.
  • Freezing Point Depression: Conversely, the freezing point of a solution is lower than that of the pure solvent. Solute particles interfere with the orderly arrangement necessary for the solvent to solidify.
  • Osmotic Pressure: This is the pressure required to stop the flow of solvent through a semipermeable membrane. It increases when more solute particles are present.
These phenomena are directly influenced by the van 't Hoff factor, 'i', which gives insight into how many effective particles are in a solution.
Electrolytes
Electrolytes are substances that dissolve in a solvent to produce a solution capable of conducting electricity. They do this by dissociating into ions, which are charged particles.
Let's categorize electrolytes:
  • Strong Electrolytes: These dissociate completely in solution, releasing more ions. Examples include salts like NaCl and strong acids like HCl.
  • Weak Electrolytes: These only partially dissociate, producing fewer ions. Acetic acid (CH鈧僀OOH) is a classic example.
The presence of electrolytes significantly affects the colligative properties of a solution. Since they generate multiple ions, their van 't Hoff factor, 'i', is usually greater than 1, indicating a larger number of particles affecting the solution's properties.
Solute Dissociation
Solute dissociation refers to the process by which solute particles break apart into smaller constituents, such as ions, when dissolved in a solvent. This process is essential for understanding the behavior of solutions in chemistry.
Key points about solute dissociation include:
  • Complete Dissociation: Observed in strong electrolytes, where the solute fully separates into ions. This complete separation leads to a maximum change in colligative properties.
  • Partial Dissociation: Seen in weak electrolytes, where dissociation is not exhaustive, resulting in fewer ions in the solution.
The degree of dissociation for a solute directly impacts its van 't Hoff factor 'i'. For instance, a solute that fully dissociates into two ions would ideally have an 'i' of 2, but real-world interactions may slightly alter this value. Understanding solute dissociation helps in making precise predictions about a solution's behavior and its colligative effects.

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Most popular questions from this chapter

Calculate the molarity and the molality of an \(\mathrm{NH}_{3}\) solution made up of \(30.0 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) in \(70.0 \mathrm{~g}\) of water. The density of the solution is \(0.982 \mathrm{~g} / \mathrm{mL}\).

The density of an aqueous solution containing \(10 . \overline{0}\) percent of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) by mass is \(0.984 \mathrm{~g} / \mathrm{mL} .\) (a) Calculate the molality of this solution. (b) Calculate its molarity. (c) What volume of the solution would contain 0.125 mole of ethanol?

What is solvation? What factors influence the extent to which solvation occurs? Give two examples of solvation; include one that involves ion-dipole interaction and one in which dispersion forces come into play.

Describe how you would use freezing-point depression and osmotic pressure measurements to determine the molar mass of a compound. Why are boiling-point elevation and vapor-pressure lowering normally not used for this purpose?

A nonvolatile organic compound \(Z\) was used to make up two solutions. Solution A contains \(5.00 \mathrm{~g}\) of \(Z\) dissolved in \(100 \mathrm{~g}\) of water, and solution \(\mathrm{B}\) contains \(2.31 \mathrm{~g}\) of \(\mathrm{Z}\) dissolved in \(100 \mathrm{~g}\) of benzene. Solution A has a vapor pressure of \(754.5 \mathrm{mmHg}\) at the normal boiling point of water, and solution \(\mathrm{B}\) has the same vapor pressure at the normal boiling point of benzene. Calculate the molar mass of \(Z\) in solutions \(\mathrm{A}\) and \(\mathrm{B}\) and account for the difference.
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