Solutions and Colloids

Solution

a homogenous mixture composed of two or more substances in a single phase

Solute

The component of a solution present in a smaller amount relative to the solvent

Solvent

The component of a solution present in the largest amount, determining the phase of the solution

How to identify the better solvent?

To identify the better solvent, use “like dissolves like”: polar solutes dissolve best in polar solvents, and nonpolar solutes dissolve best in nonpolar solvents. For example, water is usually the better choice for ionic or polar substances, because polar solvents (like water) dissolve them better than nonpolar solvents.

Spontaneous process

A process that occurs under specified conditions without the requirement of energy from an external source

What is molarity?

Molarity is a measure of concentration in chemistry. It is defined as the number of moles of solute present in one liter of solution. The formula for calculating molarity is:

Molarity (M)=moles of solute/liters of solution

Unit	Symbol
Moles per liter	mol/L or M

Importance of Molarity

Molarity is crucial for various applications in chemistry, including:

• Chemical Reactions: It helps in determining the amount of reactants needed.

• Solution Preparation: It guides the preparation of solutions with specific concentrations.

• Dilution Calculations: Molarity is used to calculate how to dilute solutions to achieve desired concentrations.

What is molality?

Molality is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent. The formula for calculating molality is:

Molality(m)=moles of solute/kilograms of solvent

Key Characteristics

• Units: The unit of molality is moles per kilogram (mol/kg).

• Temperature Independence: Unlike molarity, which can change with temperature due to volume variations, molality remains constant because it is based on mass.

• Application: Molality is particularly useful in situations where temperature changes may affect the volume of the solution, such as in colligative properties.

Attribute	Molality (m)	Molarity (M)
Definition	Moles of solute per kg of solvent	Moles of solute per liter of solution
Dependence	Mass of solvent	Volume of solution
Temperature Effect	Independent	Dependent

How does the boiling point of a solution change with the amount of solute in solution?

As solute concentration increases, the boiling point increases.

• Boiling point elevation is represented mathematically by the equation ΔTb=mKb, where ΔTb is the increase in boiling point compared to pure solvent, m is the concentration of solute in units of molality, and Kb is the boiling point elevation constant of the solvent.

• As the amount of solute increases, the degree of boiling point elevation increases and the boiling point also increases.

The van't Hoff factor, i, is equal to _____.

• The van't Hoff factor is the ratio of the observed moles of particles dissolved in solution to the calculated moles of solute in solution.

• When an ionic solute is dissolved in solution, the compound dissociates into ions.

• Since there are individual ions instead of solute molecules, there are more particles dissolved in solution.

• The van't Hoff factor is the ratio of the observed moles of particles dissolved in solution to the calculated moles of solute in solution.

• For nonionic solutes, the van't Hoff factor is close to1.

• For ideal ionic solutes, the van't Hoff factor is equal to the number of ions that the solute dissociates into.

• However the higher the concentration of ionic solute, the more the solution deviates from ideal behavior and the van't Hoff factor gets closer to one.

Osmosis

Osmosis is a type of diffusion that occurs when two solutions of differing concentration are separated by a semipermeable membrane.

• Solvent molecules will spontaneously diffuse from the low concentration side to the side with high concentration until the concentration on both sides is equal.

Which equation correctly describes the relationship between the degree of freezing point depression and the concentration of the solution?

Freezing point depression is represented mathematically by the equation ΔTf=mKf:

• ΔT_f is the decrease in freezing point compared to pure solvent

• m is the concentration of solute in units of molality

• K_f is the freezing point depression constant of the solvent.

As the amount of solute increases, the degree of freezing point depression increases.

Electrolyte

A substance that produces ions when dissolved in water, yielding an electrically conductive solution

Nonelectrolyte

A substance that does not yield ions when dissolved in water, yielding a nonconductive solution

What is a strong electrolyte? What are some examples?

A compound that dissociates or ionizes completely when dissolved in water

Characteristics of Strong Electrolytes

• Complete Ionization

  • Strong electrolytes dissociate completely into ions when dissolved in water. This means that nearly all of the solute exists as ions, which are responsible for conducting electricity. For example, when hydrochloric acid (HCl) is dissolved in water, it ionizes completely into hydrogen ions (H⁺) and chloride ions (Cl⁻).

• Good Conductors of Electricity

  • Due to their complete ionization, strong electrolytes are excellent conductors of electric current. The presence of free-moving ions allows for efficient electrical conductivity in the solution.

Type	Examples
Strong Acids	Hydrochloric acid (HCl), Sulfuric acid (H₂SO₄)
Strong Bases	Sodium hydroxide (NaOH), Potassium hydroxide (KOH)
Salts	Sodium chloride (NaCl), Magnesium chloride (MgCl₂)

Characteristics of Weak Electrolytes

• Partial Ionization

  • Weak electrolytes only partially ionize in solution. This means that a significant portion of the solute remains in its molecular form rather than dissociating into ions.

• Poor Conductors of Electricity

  • Because weak electrolytes do not produce a large number of ions in solution, they are poor conductors of electricity. The limited presence of ions means that the solution cannot carry an electric current effectively.

What is a weak electrolyte? What are some examples?

A compound that ionizes only to a small extent when dissolved in water.

Characteristics of Weak Electrolytes

• Partial Ionization: Weak electrolytes do not completely break apart into ions in solution.

• Low Conductivity: Due to limited ionization, these solutions have lower electrical conductivity.

Type	Example
Weak Acid	Acetic acid (CH₃COOH)
Weak Base	Ammonium hydroxide (NH₄OH)
Weak Acid	Carbonic acid (H₂CO₃)

Solubility

The maximum concentration of a solute that can be dissolved in a given solvent at a specified temperature

Saturated solution

A solution containing a solute concentration equal to its solubility at a given temperature

Unsaturated solution

A solution containing a solute concentration less than its solubility at a given temperature

Supersaturated solution

A non-quilibrium state containing a solute concentration greater then its equilibrium solubility

A supersaturated solution is a type of solution that contains more dissolved solute than it can normally hold at a given temperature. This condition occurs when a solution is prepared at a higher temperature and then cooled, allowing it to hold more solute than it would at equilibrium.

Stability

• Unstable: Supersaturated solutions are often unstable and can easily revert to a saturated state.

• Metastable: They may remain in this state for a time but can crystallize if disturbed or if a seed crystal is introduced.

Behavior

• Crystallization: When a supersaturated solution crystallizes, the excess solute precipitates out, returning the solution to a saturated state.

• Temperature Dependence: The ability to create a supersaturated solution is highly dependent on temperature; higher temperatures generally allow for more solute to be dissolved.

Applications

• Crystal Growth: In laboratories and industries for producing crystals.

• Food Industry: In candy making, where sugar solutions are often supersaturated to create specific textures.

Henry’s Law Formula

C_g = kP_g

• C_g is gas solubility

• k is Henry’s law constant

• P_g is gas partial pressure

Miscible

Able to mix in all proportions to form a homogeneous solution

Immiscible

Two liquids that do not mix to an appreciable extent, forming separate layers

Colligative properties

Colligative properties are characteristics of solutions that depend solely on the ratio of solute particles to solvent particles. They do not depend on the identity of the solute. The main colligative properties include:

• Vapor Pressure Lowering

• Boiling Point Elevation

• Freezing Point Depression

• Osmotic Pressure

Dependence on Concentration

• Colligative properties are most accurately observed in dilute solutions.

• They are influenced by the number of solute particles relative to solvent particles, not the type of solute.

Historical Context

• The term "colligative" was introduced by Wilhelm Ostwald in 1891. He categorized solute properties into three types:

  • Colligative Properties: Depend only on concentration and temperature.

  • Additive Properties: Depend on the composition of the solute.

  • Constitutional Properties: Depend on the molecular structure of the solute.

Property	Description
Vapor Pressure Lowering	The addition of solute decreases the vapor pressure of the solvent.
Boiling Point Elevation	The boiling point of a solution is higher than that of the pure solvent.
Freezing Point Depression	The freezing point of a solution is lower than that of the pure solvent.
Osmotic Pressure	The pressure required to stop the flow of solvent into the solution through a semipermeable membrane

Raoult’s law formula

Raoult's law is a fundamental principle in physical chemistry that describes the behavior of vapor pressure in solutions. It states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent present.

Key Components

• Vapor Pressure: The pressure exerted by a vapor in equilibrium with its liquid or solid phase.

• Mole Fraction: The ratio of the number of moles of a component to the total number of moles in the solution.

Mathematical Expression

The law can be mathematically expressed as:

P_solution = P^o_solvent × χ_solvent​

Where:

• P_solution= vapor pressure of the solution

• P^o_solvent = vapor pressure of the pure solvent

• χ_solvent= mole fraction of the solvent in the solution

Raoult's law is applicable primarily to ideal solutions, which are characterized by:

• Similar intermolecular forces between different components.

• No heat change during mixing (enthalpy of mixing is zero).

Characteristics of Ideal Solutions

• Obey Raoult's law at all compositions.

• Exhibit similar molecular sizes and structures.

Limitations

Raoult's law does not hold for non-ideal solutions, where interactions between different molecules differ significantly from those between like molecules. In such cases, deviations from the predicted vapor pressures can occur.

Types of Deviations

• Positive Deviation: Observed vapor pressure is higher than predicted.

• Negative Deviation: Observed vapor pressure is lower than predicted.

Boiling point elevation formula

Boiling-point elevation refers to the phenomenon where the boiling point of a solvent increases when a non-volatile solute is added. This occurs because the solute lowers the vapor pressure of the solvent, requiring a higher temperature to reach the boiling point.

How It Works

• Vapor Pressure: The addition of a non-volatile solute decreases the vapor pressure of the solvent.

• Heat Requirement: More heat is needed to raise the vapor pressure to match the external pressure, thus elevating the boiling point.

Colligative Property

• Boiling-point elevation is classified as a colligative property, meaning it depends on the number of solute particles in a solution rather than their identity.

Practical Example

• When approximately 100 grams of sodium chloride (NaCl) is added to one liter of water, the boiling point increases by only a couple of degrees Celsius. This small increase illustrates that while boiling-point elevation is a real effect, the practical impact in cooking is limited.

Attribute	Description
Definition	Increase in boiling point due to solute addition
Cause	Lowered vapor pressure of the solvent
Type	Colligative property
Example	100 g NaCl in 1 L water raises boiling point slightly

Freezing point depression formula

Freezing point depression refers to the phenomenon where the freezing temperature of a solvent decreases when a non-volatile solute is added. This is a common occurrence in solutions, such as when salt is mixed with water.

• Definition: The freezing point of a solvent drops when a solute is added.

• Formula: The change in freezing point can be calculated using the formula:

  ΔT_f=K_f×m

  Where:

  • ΔT_fΔT_f​ = change in freezing point

  • K_f = freezing point depression constant (specific to the solvent)

  • m = molality of the solution (moles of solute per kilogram of solvent)

Factors Affecting Freezing Point Depression

Factor	Description
Concentration of Solute	Higher concentrations lead to greater depression.
Type of Solute	Different solutes have different KfKf​ values.
Nature of Solvent	Each solvent has its own freezing point and KfKf​.

Osmotic pressure formula

Osmotic pressure is the minimum pressure required to prevent solvent from passing through a semipermeable membrane into a more concentrated solution. This pressure is essential in various biological and industrial processes.

Π=MRT

Where:

• Π = osmotic pressure

• M = molar concentration of solutes

• R= ideal gas constant

• T = absolute temperature (in kelvins)

This equation shows that osmotic pressure is directly proportional to the concentration of solutes and temperature.

Biological Significance

• Cell Regulation: Osmotic pressure plays a crucial role in maintaining cell size and function. Cells regulate their internal osmotic pressure through mechanisms like osmoregulation.

• Plant Health: In plants, osmotic pressure contributes to turgor pressure, which helps maintain structural integrity and supports growth.

van ‘t Hoff factor (i)

The van 't Hoff factor (i) quantifies the effect of a solute on colligative properties, which include boiling point elevation, freezing point depression, and osmotic pressure. It is defined as the ratio of the actual number of particles in solution to the number of formula units of solute initially dissolved.

• Non-electrolytes: For substances that do not dissociate in solution, the van 't Hoff factor is always 1.

• Strong electrolytes: These completely dissociate into ions. The van 't Hoff factor equals the total number of ions produced per formula unit. For example:

  Compound	Dissociation	Van 't Hoff Factor (i)
  NaCl	Na⁺ + Cl⁻	2
  CaCl₂	Ca²⁺ + 2Cl⁻	3
  MgCl₂	Mg²⁺ + 2Cl⁻	3

• Weak electrolytes: These partially dissociate, resulting in a van 't Hoff factor between 1 and the maximum number of ions. For example, acetic acid (CH₃COOH) has a van 't Hoff factor less than 2 due to incomplete ionization.

Importance of the Van 't Hoff Factor

The van 't Hoff factor is crucial for calculating colligative properties, as it directly influences how solutes affect the physical properties of solvents.

• Boiling Point Elevation: The increase in boiling point when a solute is added.

• Freezing Point Depression: The decrease in freezing point due to solute presence.

• Osmotic Pressure: The pressure required to prevent the flow of solvent into a solution.

Hypertonic solution

A solution with a higher solute concentration relative to red blood cells, causing cells to shrink (crenation)

Hypotonic solution

A solution with a lower solute concentration relative to red blood cells, causing cells to swell and burst (hemolysis)

Colloid

A herterogeneous mixture in which solute-like particles remain suspended and do not settle out over time

Tyndall Effect

The Tyndall effect is the scattering of light by particles in a colloid, making the light beam visible, such as when light passes through fog or milk.

• This effect occurs because the particles are similar in size to the wavelength of light, causing shorter wavelengths like blue light to scatter more than longer wavelengths like red light.

Driving forces of solution formation

The formation of a solution is influenced primarily by two main factors: enthalpy changes and entropy increases. Understanding these concepts helps explain why certain substances dissolve in others.

Enthalpy Changes

• Breaking Intermolecular Interactions: When a solute dissolves, energy is required to break the intermolecular forces between solute particles. This step is typically endothermic, meaning it absorbs heat.

• Forming New Interactions: As the solute particles interact with solvent molecules, new intermolecular forces are established. This process can release energy, making it exothermic.

• Net Enthalpy Change: The overall enthalpy change for the solution formation is the sum of the energy changes from breaking and forming interactions. If the net change is negative, the process is exothermic; if positive, it is endothermic.

Entropy Increases

• Randomness of the System: The dissolution process generally leads to an increase in entropy, which is a measure of disorder or randomness. As solute particles disperse throughout the solvent, the system becomes more disordered.

• Spontaneous Mixing: The natural tendency for substances to mix and increase entropy often drives the solution formation process, even if it requires an input of energy.

Force Type	Description	Energy Change
Breaking Solute Interactions	Requires energy (endothermic)	Positive ΔH
Breaking Solvent Interactions	Requires energy (endothermic)	Positive ΔH
Forming Solute-Solvent Interactions	Releases energy (exothermic)	Negative ΔH
Overall Process	Depends on the balance of energy changes and entropy	Varies

Three energetic steps of solution formation

1) separating the solute particles from each other (endothermic)

2) separating the solvent particles from each other (endothermic)

3) combining the separated solute and solvent particles to form the solution (exothermic).

This process involves both energy absorption and release, determining whether the overall dissolution is endothermic or exothermic.

Step 1: Separating Solute Particles

• Description: The solute particles are separated from each other.

• Energy Change: This step is endothermic, meaning it requires energy input to overcome the intermolecular forces holding the solute particles together.

Step 2: Separating Solvent Particles

• Description: The solvent particles are also separated from each other.

• Energy Change: This step is similarly endothermic, as energy is needed to break the intermolecular forces between solvent molecules.

Step 3: Combining Solute and Solvent Particles

• Description: The separated solute and solvent particles combine to form a homogeneous solution.

• Energy Change: This step is exothermic, releasing energy as new interactions are formed between solute and solvent particles.

Overall Energetics

The overall enthalpy change (ΔHΔH) for the solution formation can be summarized as follows:

ΔHsolution=ΔH1+ΔH2+ΔH3ΔHsolution​=ΔH1​+ΔH2​+ΔH3​

• If the energy released in Step 3 is greater than the energy absorbed in Steps 1 and 2, the overall process is exothermic (ΔH<0ΔH<0).

• Conversely, if more energy is absorbed in Steps 1 and 2 than is released in Step 3, the process is endothermic (ΔH>0ΔH>0).

Ideal solution

A solution where solute-solvent intermolecular forces are equal in strength to solute-solute and solvent-solvent forces

Characteristics of Ideal Solutions

Property	Ideal Solution
Enthalpy of Mixing (ΔH mix)	0 (no heat change)
Volume of Mixing (ΔV mix)	0 (total volume equals the sum of components)
Raoult's Law Compliance	Yes (obeys across all concentrations)

Role of entropy in dissolving immiscible substances

Entropy and Dissolution

• Increase in Disorder: When substances dissolve, the overall entropy of the system tends to increase. This increase in disorder can drive the dissolution process.

• Dissolution of Immiscible Substances: Even substances that are typically immiscible can dissolve to some extent due to entropy. The tendency for systems to move towards higher entropy can lead to the mixing of certain components, despite their natural inclination to remain separate.

Factors Influencing Dissolution

1. Nature of the Substances: The molecular structure and interactions between the substances can affect how they behave when mixed.

2. Temperature: Higher temperatures generally increase kinetic energy, which can enhance the dissolution process and promote greater disorder.

3. Pressure: In some cases, changes in pressure can influence the solubility of gases in liquids, impacting the overall entropy of the system.

Conclusion

In summary, entropy significantly influences the dissolution of substances, including those that are immiscible. The drive towards increased disorder can lead to unexpected mixing behaviors, highlighting the complex interplay between thermodynamic principles and chemical interactions.

Like dissolves like principle

The "like dissolves like" principle states that substances with similar polarities tend to dissolve in each other; polar solvents dissolve polar solutes, while nonpolar solvents dissolve nonpolar solutes. This principle is crucial for predicting solubility in chemistry

Dissolution vs. crystalization in equilibrium

Definitions

• Dissolution: The process where a solute dissolves in a solvent, forming a solution.

• Crystallization: The process where solute particles come together to form solid crystals from the solution.

Dynamic Equilibrium

When dissolution and crystallization occur simultaneously in a saturated solution, the system reaches a state known as dynamic equilibrium. In this state:

• The rate of dissolution equals the rate of crystallization.

• The concentration of the solute remains constant over time, even though both processes are actively occurring.

Characteristics of Saturated Solutions

Property	Description
Saturated Solution	Contains the maximum amount of solute that can dissolve at a given temperature.
Unsaturated Solution	Contains less solute than the maximum, allowing more solute to dissolve.
Supersaturated Solution	Contains more solute than normally possible at a given temperature, often unstable.

Importance of Equilibrium

• Pharmaceuticals: Ensuring the correct concentration of active ingredients.

• Food Industry: Controlling the crystallization of ingredients for quality and texture.

• Chemical Manufacturing: Optimizing processes for yield and purity.

Effect of temperature on solid solubility

The solubility of solid solutes in liquids is primarily influenced by temperature. Here are the key points regarding this relationship:

Increase in Solubility with Temperature

• Endothermic Dissolution: For many solid solutes, the dissolution process is endothermic, meaning it absorbs heat. As temperature increases, the solubility of these solids typically increases.

• Examples: Common examples include sugar and salt, which dissolve more readily in hot water than in cold.

Exceptions to the Trend

• Decreased Solubility: Some solids may show decreased solubility as temperature rises. This is less common but can occur with specific compounds.

• Example: Cerium sulfate is one such solid that exhibits this behavior

Effect of temperature of gas solubility

The solubility of gases in liquids is inversely related to temperature. As the temperature increases, the solubility of gases typically decreases. This phenomenon can be attributed to the increased kinetic energy of gas molecules at higher temperatures.

Explanation of the Effect

• Kinetic Energy: Higher temperatures provide gas molecules with more kinetic energy. This increased energy makes it more difficult for gas molecules to be captured by solvent molecules.

• Molecular Behavior: As gas molecules gain energy, they tend to escape from the liquid phase back into the gas phase, reducing the amount of gas that can dissolve in the liquid.

Molecular mechanism of Henry’s Law

Henry's Law explains how gases dissolve in liquids, stating that the amount of gas dissolved is directly proportional to its partial pressure above the liquid.

Molecular Mechanism

• Gas Molecules: The behavior of gas molecules is influenced by their interactions with solvent molecules.

• Solvent Molecules: The nature of the solvent affects how gas molecules are absorbed.

• Pressure: Increasing the pressure of the gas above the liquid enhances the solubility of the gas in the liquid.

Interaction Dynamics

• At higher pressures, gas molecules are forced into closer contact with the solvent, leading to increased dissolution.

• The solubility of gases in liquids varies with temperature; generally, higher temperatures decrease gas solubility.

Applications of Henry's Law

Carbonated Beverages

• In sealed containers, carbon dioxide is under high pressure, resulting in a higher concentration of dissolved gas.

• Once opened, the pressure drops, and gas escapes, leading to fizzing.

Molecular cause of vapor pressure lowering

The addition of a non-volatile solute to a solvent is the primary molecular cause of vapor pressure lowering.

Mechanism of Vapor Pressure Lowering

• Solvent Molecule Escape: In a pure solvent, molecules can easily escape into the vapor phase, contributing to a higher vapor pressure.

• Space Occupation by Solute: When a non-volatile solute is added, it occupies space at the liquid's surface. This reduces the number of solvent molecules that can escape into the vapor phase.

• Reduced Vapor Pressure: As a result, the vapor pressure of the solution becomes lower than that of the pure solvent. This is because fewer solvent molecules are available to enter the vapor phase.

Concept	Description
Non-Volatile Solute	A solute that does not evaporate easily and has no vapor pressure of its own.
Vapor Pressure	The pressure exerted by vapor in equilibrium with its liquid at a given temperature.
Colligative Property	A property that depends on the number of solute particles in a solution, not their identity.

Molecular cause of boiling point elevation

Boiling point elevation occurs due to the addition of a non-volatile solute, which disrupts the intermolecular forces between solvent molecules, lowering the solvent's vapor pressure.

This results in a higher temperature being required for the vapor pressure to equal the external pressure, thus increasing the boiling point of the solution

Molecular cause of freezing point depression

Freezing point depression occurs when a solute is added to a solvent, which disrupts the formation of the solid structure of the solvent, thus lowering the temperature at which it freezes.

This phenomenon is commonly observed in solutions, such as salt in water, where the solute particles interfere with the solvent's ability to solidify.

Osmosis mechanism across a semipermeable membrane

Osmosis is the movement of solvent molecules, typically water, through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration.

• This process continues until the solute concentrations on both sides of the membrane are equalized, achieving equilibrium.

Osmotic pressure concept

Osmotic pressure is the force that must be applied to a solution to prevent the flow of solvent through a semipermeable membrane.

This flow occurs from a less concentrated solution to a more concentrated one, driven by differences in solute concentration and temperature.

Key Factors Influencing Osmotic Pressure

1. Solute Concentration

• Higher solute concentration increases osmotic pressure.

• The relationship is described by the formula:
  π=MRTπ=MRT
  where:

  • ππ = osmotic pressure

  • MM = molar concentration of solutes

  • RR = ideal gas constant

  • TT = temperature in kelvins

2. Temperature

• Increased temperature raises osmotic pressure due to higher kinetic energy of molecules.

Deviation of actual van ‘t Hoff factor (i) from ideal values

The van 't Hoff factor (i) is crucial in determining how solutes affect colligative properties, such as boiling point elevation and freezing point depression.

It represents the ratio of the actual number of particles in solution to the number of formula units initially dissolved.

Factor Type	Description
Ideal	Assumes complete dissociation of solutes into their constituent ions. For example, NaCl ideally dissociates into two ions (Na⁺ and Cl⁻), giving i = 2.
Actual	Reflects real behavior in solutions, often lower than the ideal due to incomplete dissociation and ion pairing.

Reasons for Deviation

1. Incomplete Dissociation: Ionic compounds may not fully dissociate in solution, especially at higher concentrations. This results in fewer particles than expected based on stoichiometry.

2. Ion Pairing: At elevated concentrations, ions can interact strongly, leading to temporary pair formations. This reduces the effective number of free ions in solution, causing the actual van 't Hoff factor to be lower than the ideal value.

3. Concentration Effects: In dilute solutions, ionic compounds typically dissociate almost completely, yielding a van 't Hoff factor close to the ideal. However, as concentration increases, the likelihood of ion pairing rises, further decreasing the effective particle count.

Molality (m) vs. molarity (M) for temperature stability

Molality (m) remains constant regardless of temperature changes because it is based on the mass of the solvent, while molarity (M) can change with temperature due to the expansion of the solution's volume