Chapter 11: Solutions- Properties and Behavior

Tf = T°f - ∆Tf Tf = freezing point of the solution T°f = freezing point of pure solvent ∆Tf = change in freezing point of solvent

Equation for the freezing point of a solution

∆Tb= I x Kb x m ∆Tf= I x Kf x m

Equations for ∆Tb and ∆Tf including the van't Hoff factor

colligative property

Properties of solutions that depend only on the concentration of particles and not on their identities

colligative properties

Properties of solutions that depend only on the concentration of solute particles but not on the identity of the solute

ionic charge increases and as ionic size decreases

The attractive force between two ions increases as

lattice energy (U)

The change in energy when free ions in the gas phase combine to form 1 mole of a solid ionic compound

The concentration of solutes or own cells is just 1/3 the concentration of solutes in seawater. When cells are exposed to seawater, this substantial difference in solute concentration is the driving force for osmosis, with the cell membrane acting as the semipermeable membrane. Because the solute concentration is higher outside the cell, water from inside the cell crosses the membrane and enters the seawater, moving from the low-solute concentration side of the membrane to the high-solute concentration side. As water leaves the cell, the cell shrivels and ultimately ceases to function.

Why can't we drink seawater?

Because of the intermolecular forces between solvent and solute particles

Why do solutions and pure liquids behave differently?

reverse osmosis

a process in which solvent is forced through semipermeable membranes, leaving a more concentrated solution behind

π = iMRT i = van't Hoff factor M= molarity of the solute R= .08206 Latm/molK T= absolute temperature

Equation for osmotic pressure

Solvent flows across a semipermeable membrane from a more dilute solution side to the more concentrated solution side to balance the concentration of solutes on both sides of the membrane.

A dilute solution is separated from a more concentrated solution by a semipermeable membrane. In which direction does the solvent flow across the membrane, and why?

Born-Haber cycle

A series of steps with corresponding enthalpy changes that describes the formation of an ionic solid from its constituent elements

fractional distillation

A type of distillation used to separate the volatile components of a mixture; Based on the observation that the boiling point of a mixture changes as the liquid is distilled.

the sum of the vapor pressures of each component multiplied by the mole fraction of that component in the solution

According to Raoult's law, the total vapor pressure of a solution equals

semipermeable membrane

Allows particles of solvent to pass it but not particles of solute

The mass of the solution does not change. though the volume, and thus the molarity of the solution does. At 90°C, the molarity has decreased its value at 5°C.

As a solution of NaCl is heated from 5°C to 90°C, does the difference between its molarity and its molality increase or decrease?

molality (m)

Concentration expressed as the number of moles of solute per kilogram of solvent; n (solute)/ kg (solvent)

E is proportional to (Q1Q2)/d

Coulombic interaction

enthalpy of solution (ΔHsoln)

Defines the overall change in enthalpy when an ionic solute is dissolved in a polar solute

When a solute dissolves in a solvent, first... 1. Ions must be separated from each other, a process that requires energy to break the ion-ion interactions that hold the particles in the crystal lattice. ΔHion-ion 2. The solvent molecules must also be separated from one another so they can bind to the ions. This requires energy to break the dipole-dipole interactions between solvent molecules. ΔHdipole-dipole 3. Last, energy is released when the solvent molecules associate with the solute ions via ion-dipole interactions and form hydrated ion. Δion-dipole

Describe the steps involved in the overall enthalpy change when an ionic solute is dissolved in a polar solvent.

solute-solute interactions are much stronger than solvent-solvent inmteractions

Deviations ideal behavior in solutions typically occur when

the ionic radii

Distance between ions is the sum of

product of their charges

Dominant factor in determining ion-ion strength

∆Tb = Kb x m ∆Tb = the increase in temperature above the boiling point of the pure solvent Kb = boiling point elevation constant of the solvent m= molality

Equation for boiling point elevation

Tb = T°b + ∆Tb Tb = boiling point of solution T°b = boiling point of pure solvent ∆Tb = boiling point elevation

Equation for boiling point of solution

∆π = (iMx - iMy)RT ∆π = πx - πy

Equation for difference between osmotic pressures

ΔHhydration= ΔHdipole-dipole + ΔHion-dipole

Equation for enthalpy of hydration ΔHhydration

ΔHsoln = ΔHion-ion + ΔHdipole-dipole + ΔHion-dipole ΔHsoln = ΔHion-ion + ΔHhydration -U= ΔHion-ion ΔHsoln= -U + ΔHhydration

Equation for enthalpy of solution

∆Tf = Kfm ∆Tf = the change in the freezing temperature of the solvent Kf = freezing point depression of the solvent m= molarity of the solution

Equation for freezing point depression

Solutions usually have greater densities than the solvent alone, and an aqueous solution containing a nonvolatile solute has a higher boiling point and a lower freezing point than pure water. (boiling point elevation, freezing point depression, osmotic pressure)

Examples of colligative properties

Reverse osmosis transfers solvent across a semipermeable membrane from a region of higher solute concentration to a region of lower solute concentration. Because reverse osmosis goes against the natural flow of solvent across the membrane, the key component that is needed is a pump to apply pressure to the more concentrated side of the membrane. Other components needed include a containment system, piping to introduce and remove the solutions, and a tough semipermeable membrane that can withstand the high pressures needed.

Explain reverse osmosis.

A nonvolatile solute is a compound that dissolves into a solvent and does not enter appreciably into the gas phase, under conditions that maintain the solution.

Explain the term, nonvolatile solute.

In a solution, the ionic compounds dissociate to form ions. Each separate ion affects the observed colligative property. The amount of dissociated ions in a solution is represented by the van't Hoff factor, which is an experimentally determined value and cannot be used to determine molality (and thus the formula mass) for an ionic solute.

Explain why freezing point depression, boiling point elevation, and the osmotic pressure of ionic solutes cannot be used to measure their formula masses.

U= k(Q1Q2)/d k is used for all compounds that have the same or nearly the same arrangement of ions

Formula for lattice energy

Energy is negative for any salt because the dominant interaction is between cations and anions (+Q,-Q). Oppositely charged ions attract each other to form an arrangement characterized by a lower potential energy than the potential energy of the separated ions. When the ions are far apart, the d term is large and the E is a small negative number. When the ions are close together in a salt, d is small and E is a large negative number which corresponds to a lower energy.

How does Coulombic interaction define ion-ion interactions?

As a mixture of volatile liquids is heated, the vapor that rises and fills the space above the liquid has a different composition has a different composition from the composition of the mixture. The concentration of the component with the lowest boiling point is higher in the vapor than in the liquid. If this enriched vapor is collected, condensed and redistilled, the vapor this time is even richer in the component with the lowest boiling point. In a fractional distillation apparatus, repeated distillation steps allow components with only slightly different boiling points to be separated from one another.

How does fractional distillation work?

i= the number of ions in one formula unit

If a solute is a strong electrolyte, what does i equal?

i=1 because each mole of solute produces 1 mole of dissolved particles

If a solute is molecular and therefore a nonelectrolyte, what does i equal?

When we talk about colligative properties, we frequently deal with the properties of systems as a function of temperature. Because volume changes with temperature, molarity changes with temperature. Because solvent mass does not change with temperature, a concentration expressed in molality does not change with temperature.

If we want to quantify colligative properties, why don't we use molarity?

greater

In all aqueous solutions, molality is ------- than molarity

C5H12, because it is more volatile

In an equimolar mixture of C5H12 and C7H16, which compound is present in higher concentration in the vapor pressure above the solution?

Psolution = Xsolvent x Psolvent

Raoult's law equation

ideal solutions

Solutions that obey Raoult's law; The solute and solvent experience similar intermolecular forces

lattice energies and electron affinities

The Born-Haber cycle can be used to calculate

volatile

The higher the vapor pressure at a given temp, the more -------- the substance

condensation

The lower the vapor pressure, the higher the rate of

identity

The lower vapor pressure of a solution in relation to the vapor pressure of pure solvent depends only on the concentration of particles and not on their ------

osmosis

The movement of a solute through semi-permeable membrane from a region of lower solute concentration to a region of higher solute concentration

solute concentration and with solution temperature

The osmotic pressure of a solution increases with

Osmotic pressure (π)

The pressure required to halt the flow of solvent from a solution through a semipermeable membrane into pure solvent. Exactly balances the pressure driving solvent through the membrane so that no net flow of solvent takes place

ionic compounds are most likely to be solid and room temp

The strengths of ion-ion interactions means that

When 1 mole of a strong electrolyte such as solid sodium chloride dissolves, it produces 2 moles of particles. Thus we should expect that the freezing point depression (or boiling point elevation) that results from the dissolution of a given number of moles of NaCl should be twice as great as that produced when the same number of moles of a nonelectrolyte dissolves.

The van't Hoff factor "I" is based on the definition of colligative properties: changes due to the total concentration of dissolved particles in solution. Explain.

False, the molarity of NaCl would be greater (1.5 times) the molarity of CaCl2.

True or false. For solutions of the same reverse osmotic pressure at the same temperature, the molarity of a solution of NaCl will always be less than the molarity of a solution of CaCl2.

°C/m

Units for boiling-point-elevation constant of the solvent

This means that the formation of ion-dipole interactions must release more energy than is needed to disrupt the dipole-dipole interactions in the solvent.

What does it mean if ΔHhydration is negative?

(a) increases (b) decreases (c) increases

What effect does dissolving a solute have on the following properties of a solvent? (a) osmotic pressure (b) its freezing point (c) its boiling point

Molarity is the number of moles of solute per liter of solution. Molality is the number of moles of solute per kilogram of solvent.

What is the difference between molarity and molality?

molality

What unit do we use to quantify colligative properties?

multiple temperatures

When a pure liquid is being distilled, the phase change occurs at a constant temp. When a mixture is being distilled phase change occurs at --------.

Solutions obey Raoult's law when the strengths of the solvent-solvent, solute-solute, and solute-solvent interactions are similar. If the solute-solvent interactions are stronger than the solvent-solvent or solute-solute interactions, the solute inhibits the solvent from vaporizing and the solvent inhibits the solute from vaporizing. This situation produces negative deviations from the vapor pressures predicted by Raoult's law. In such a solution, the rate of vaporization is slower because the vapor pressure of the mixture is lower than predicted. Because solute and solvent molecules are held at the surface by solute-solvent interactions, more energy is required to separate them from the surface, and fewer vaporize at a given temperature. If solute-solvent interactions are much weaker than solvent-solvent interactions, less energy is required to separate the solute molecules from the surface, and more solute molecules vaporize. In this case, the vapor pressure is greater than the value predicted by Raoult's law.

When does a solution behave ideally? And when does it not?

NaCl is more soluble in water. The lower solubility of CaSO4 correlates with greater ion-ion interactions between its ions, which result from greater charges on these ions (2+,2-) than on NaCl (1+,1-)

Why does CaSO4 precipitate out of evaporating sea water before NaCl even though the concentration of Ca2+ and SO42- are much lower than Na+ and Cl-?

Melting an ionic structure in which ions are held together tightly should require more thermal energy than melting a structure where the ions are held together less tightly

Why does lattice energy of an ionic solid affect its melting point as well as its solubility?

When the average kinetic energy of the liquid molecules increases, more of the molecules can escape the liquid phase and enter the gas phase. An increase in the number of molecules in the gas phase causes an increase in the vapor pressure.

Why does the vapor pressure of a liquid increase with increasing temperature?

The ion-ion bond in CaSO4 is stronger than in NaCl because of the higher charges on the cation and anion. For CaSO4, this is greater than the ion-dipole interactions that would occur when Ca2+ and SO42- dissolve, so CaSO4 is not very soluble in water. NaCl has a lower ion-ion bond strength and its ion-dipole interactions with water are strong, so it dissolves in water.

Why is CaSO4 less soluble in water than NaCl?

Ionic solvents are strong electrolytes that completely dissociate in solvent. This dissociation yields two or more particles in solution from one dissolved solute particle. This results in greater changes in the melting and boiling points compared to those of a solute that does not dissociate. Since molecules compounds cannot dissociate in water, whereas ionic compounds do, we must know what type of compound we have if we are to properly predict its effects, including the van't Hoff factor.

Why is it important to know if a substance is a molecular compound or an ionic compound before predicting its effect on the boiling and freezing points of a solvent?

The reason is that the cations and anions produced when strong electrolytes dissolve may not be totally independent of one another. As concentration increases, cations and anions may form clusters. Thus, the overall concentration of particles is reduced when these clusters form (making the i factor smaller). The larger the concentration, the smaller the i factor because particles are associating in solution (behaving nonideally).

Why is it that experimentally measured freezing point depressions and boiling point elevations are smaller than the theoretical values obtained using the van't Hoff factor?

U is defined as the enthalpy change when gas-phase ions combine to form an ionic solid. In this equation we are calculating the enthalpy change associated with separating the ions in an ionic compound

Why is lattice energy (U) negative in the equation for enthalpy of solution?

Ideal behavior refers to solutions in which the solvent-solvent, solute-solute, and solvent-solute interactions are all similar in strength. In this structure, cyclohexane is the solute, and benzene is the solvent. Both components of the solution are similar size, and both are nonpolar. It is reasonable that the magnitude of the intermolecular forces would be similar and the solution would behave ideally.

Would you expect a solution of cyclohexane, C6H12, in benzene, C6H6, to behave ideally?

ion pair

a cluster formed when a cation and an anion associate with each other in solution

Raoult's law

the principle that the vapor pressure of the solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution

van't Hoff factor

the ratio of the experimentally measured value of a colligative property to the theoretical value expected for that property if the solute were a nonelectrolyte