Problem 126 - Chemistry The Molecular Science

Question

Criticize these statements. (a) A saturated solution is always a concentrated one. (b) A \(0.10-\mathrm{mol} / \mathrm{kg}\) sucrose solution and a \(0.10-\mathrm{mol} / \mathrm{kg} \mathrm{KCl}\) solution have the same osmotic pressure.

Step-by-Step Solution

Answer

(a) False, saturated solutions can be dilute. (b) False, due to different ionization.

Step 1: Understanding Statement (a)

The first step is to clarify the definitions involved. A saturated solution contains the maximum possible amount of solute that can dissolve at a given temperature. Concentration, however, refers to the amount of solute present in a given volume of solution. A saturated solution can have varying concentrations depending on the nature of the solute, solvent and temperature, so being saturated does not necessarily equate to being concentrated.

Step 2: Critiquing Statement (a)

Based on the understanding from Step 1, Statement (a) is not always true. A saturated solution can be dilute if the solute has low solubility. Saturation simply indicates that no additional solute can dissolve in the solvent beyond a certain concentration, regardless of how high or low that concentration may be.

Step 3: Understanding Statement (b)

Now examine the critical factors influencing osmotic pressure. Osmotic pressure depends on the molarity of solute particles in solution. While both solutions have equal molalities, the dissociation of solutes into particles is crucial. Sucrose does not ionize in solution, so it contributes only one type of particle. In contrast, KCl dissociates into two ions: K⁺ and Cl⁻.

Step 4: Calculating Osmotic Pressure in Statement (b)

The osmotic pressure (π) is given by the formula: \[ π = iMRT \]where \(i\) is the van 't Hoff factor, \(M\) is the molarity, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. For sucrose, \(i = 1\), whereas for KCl, \(i = 2\), since it dissociates into two ions.

Step 5: Critiquing Statement (b)

For the same molality and temperature, the osmotic pressure of the KCl solution will be roughly twice that of the sucrose solution because it produces more particles (molecules or ions). Therefore, the assertion that both solutions have the same osmotic pressure is incorrect.

Key Concepts

Saturated Solution

A saturated solution is a chemical solution that holds the maximum concentration of a solute dissolved in a solvent at a given temperature. What does this mean? Imagine a cup of tea; if you keep adding sugar to it, there comes a point where no more sugar will dissolve because the solution has become saturated.

It's important to note that being saturated is not synonymous with being highly concentrated. A saturated solution can be dilute if the solute has a very low solubility. For example, if you have a solute that hardly dissolves in a solvent, even when you reach saturation, the concentration can still be low. Thus, saturation merely indicates a balance point where the solution holds just as much solute as it possibly can under the conditions, not necessarily that it is full of solute.

Concentration

Concentration refers to the amount of a substance, the solute, in a given volume or mass of solution or solvent. It is usually expressed in units such as molarity (moles per liter) or molality (moles per kilogram of solvent).

Concentration is a measure that can vary widely, and it doesn't necessarily indicate how 'full' a solution is—instead, it tells you how much of the solute is present compared to the solvent. A high concentration means more solute is present in a given volume, while a low concentration means there is less.

• The concentration can change with the addition of more solvent or solute.
• It doesn't always correspond with saturation; a concentrated solution isn't always saturated, and a saturated solution isn't always concentrated.

Understanding concentration is key to evaluating other properties of a solution, like its reactivity, boiling or freezing points, and osmotic pressure.

Van't Hoff Factor

The Van't Hoff factor, denoted as "i", indicates the number of particles a compound dissociates into when dissolved in a solution. This factor plays a crucial role in calculating properties that depend on the number of solute particles, such as osmotic pressure, boiling point elevation, and freezing point depression.

For non-electrolytes, like sucrose, the Van’t Hoff factor is typically 1 because they do not dissociate into smaller particles in solution. Electrolytes, on the other hand, such as potassium chloride (KCl), dissociate into separate ions, so KCl has a Van’t Hoff factor of 2 (one for each ion: K⁺ and Cl⁻).

• The factor affects how we calculate colligative properties of solutions.
• In the context of osmotic pressure, it is critical because osmotic pressure is directly related to the number of solute particles present.

This distinction helps in understanding why two solutions with identical molalities may not have the same osmotic pressure.

Solubility

Solubility is a property that describes the ability of a solute to dissolve in a solvent at a certain temperature and pressure. It's essentially the maximum concentration of the solute that can dissolve.

The solubility of a substance depends on various factors such as the nature of the solute and solvent, temperature, and pressure. For instance:

• A substance with high solubility will dissolve more easily and in greater amounts.
• Temperature often affects solubility; many solids become more soluble with an increase in temperature.

Solubility is a significant factor in determining if a solution is saturated. If a solute has low solubility, a solution may become saturated at a low concentration. Understanding solubility helps us predict how solutions behave in different conditions, which is essential in fields like chemistry and environmental science.