Module 6.3: Solubility

6.3.1 Introduction

I Solubility depends on the relative strength of the interactions between the solvent and the solute

1. if solvent-solute interactions are comparable (equal or stronger) than between each type of molecule separately, the solute dissolves in the solvent

   1. like-dissolves-like: solvents that can mimic the cohesive forces of the solute- solute interactions are good for dissolving the solute

2. if solvent-solute interactions are not comparable (weaker) than between each type of molecule separately, the solute does not dissolve in the solvent

3. agitation such as shaking and stirring increases the rate of process, but does not increase the amount of solute dissolved

   1. new solvent molecules are continuously introduced with agitation, and therefore allows for new interactions much faster

4. saturated: when the solvent has dissolved all the solute it possibly can

   1. when a solution is saturated, the rate of the forward and reverse process is equal

   2. molar solubility (s): molar concentration of a saturated solution

II Henry's Law: the solubility of a gas is directly proportional to its partial pressure

1. $\textrm{k}_{H}$ is henry's constant and is dependent on the gas, the solvent, and temperature

2. as pressure increases, the rate at which the gas molecules strike the surface of the liquid increases

   $\textrm{s} = \textrm{k}_{H} \textrm{P}$ (Eq. 103)

III If the temperature increases, all solutes dissolve faster in a solvent

1. however, this does not mean that solubility is increased with temperature

   1. most gases become more insoluble with increasing temperature as their kinetic energy increases and can escape much more easily

   2. extensively hydrated solids such as lithium carbonate (small size and high polarizing power) decrease solubility with increasing temperature

6.3.2 Thermodynamics of Stability

IV enthalpy of solution ($\Delta \textrm{H}_{sol}$): the change in molar enthalpy when a substance dissolve

1. limiting enthalpy of solution: $\Delta \textrm{H}_{sol}$ in dilute solutions where solute-solute interactions are negligible

   1. this function is used more frequently when measuring $\Delta \textrm{H}$ calorimetrically to isolate solute-solvent interactions

2. $\Delta \textrm{H}_{sol}$ can be calculated with two hypothetical steps:

   1. the lattice enthalpy ($\Delta \textrm{H}_{L}$): the change in enthalpy resulting from the separation of the ionic solid into gaseous ions

   2. the enthalpy of hydration ($\Delta \textrm{H}_{hyd}$): the change in enthalpy resulting from the hydration gaseous ions

3. the addition of these two hypothetical steps result in the value of $\Delta \textrm{H}_{sol}$.

V prediction solubility is difficult because there are many factors that determine it

1. most substances with a negative $\Delta \textrm{H}_{sol}$ tend to be soluble, as long as $\Delta \textrm{G}_{sol} \lt 0$

2. although the entropy of the system typically increases as a solute is dissolved, there are some clear exceptions:

   1. when the solute is a gas, the entropy will most likely decrease.

   2. solvents with cage-like structures that capture the solute molecules such as EDTA, cryptands, and crown ethers also decrease entropy.

3. both enthalpy of hydration and lattice enthalpy share common factors

6.3.3 Colloids

VI colloids: the dispersion of small particles in a solvent, a heterogenous mixture

1. the solute particles are too small to be observed directly, but too big for light to pass through

   1. Tyndall effect: the dispersion of light in colloids

   2. milk is opaque due to the Tyndall effect and the fact that it is a colloid

2. there are many types of colloids, depending on the dispersed phase and medium

3. many precipitates (insoluble ionic compounds that come out of solution) form initially as colloidal suspensions

   1. Brownian motion: the random motion of particles due to constant collision with the fluid

   2. Brownian motion causes the precipitates from settling out of the solution

6.3.4 Concentration

VII Three measures of concentration are useful for the study of solutions (J is an example solution):

1. molar concentration (molarity), denoted as $\textrm{c}_{J}$ or [J]

   1. defined as mole of solute over volume of solution
   2. affected by temperature

2. mole fraction, denoted as $\textrm{x}_{J}$

3. molality, denoted as $\textrm{b}_{J}$

   1. defined as mole of solute over kilograms of solvent
   2. independent of temperature

VIII There are some useful conversions you should practice using (and learn how to derive them):

6.3.5 Colligative Properties

IX colligative properties: properties that only depend on the relative amounts of solute and solvent

1. independent of the solute and solvent’s chemical properties;

2. there are three colligative properties that will be covered in this section:

   1. boiling-point elevation
   2. freezing-point depression
   3. osmosis

X boiling-point elevation: the raising of boiling point due to presence of solute

1. the vapor pressure of the solvent is lowered by the presence of solute;

   1. requires a higher temperature for the solution to match the external pressure

2. comparing the molar Gibbs free energies of the liquid and vapor phases,

   1. With the assumption that $\textrm{G}_{m} \approx \textrm{H}_{m}$ at low temperatures, $\textrm{G}_{m} (\textrm{vapor}) \gt \textrm{G}_{m} (\textrm{liquid})$.

   2. As $\textrm{S}_{m} (\textrm{vapor}) \gt \textrm{S}_{m} (\textrm{liquid} )$, the slope is steeper for the vapor.

   3. As the entropy increases with presence of solute in a solvent, $\textrm {G}_{m} (\textrm{solvent}) \gt \textrm{G}_{m} (\textrm{solution})$

3. there must be a large amount of solute to make a noticeable difference

XI freezing-point depression: the lowering of the freezing point due to presence of solute

$\Delta \textrm{T}_{f} = \textrm{i} \textrm{k}_{j} \textrm{b}$ (Eq. 104)

1. a larger depression occurs for a certain molality compared to boiling-point elevation

   1. This is because the difference in entropy between the solid phase and liquid phase is not substantial as the gas phase

2. i is known as the van't Hoff factor and is the number of particles released from one solute molecule

   1. for soluble ionic compounds such as $\textrm{BaCl}_{2}$, i = 3.

   2. for insoluble or covalent compounds that don't dissociate in solvent, i = 1.

   3. for weak acids or slightly soluble ionic compounds, i is slightly less than what is predicted in the case of i.

   4. an accurate value of i must be determined experimentally.

3. Cryoscopy can be used to determine the molar mass of a solute by measuring the depression of $\textrm{T}_{f}$.

XII osmosis: the tendency of solvent to flow through a membrane into a more concentrated solution

1. a semipermeable membrane is used to only permit certain molecules (such as solvent) to pass through

2. addition of a solute to solvent lowers $\textrm{G}_{m}$; the pure solvent with a higher molar $\textrm{G}_{m}$ tends to flow into the solution

3. osmotic pressure ($\Pi$): the pressure needed to stop the flow of solvent into the more concentrated solution

   1. if both sides exert the same osmotic pressure, the system is in equilibrium $\Pi = \textrm{i} \textrm{R} \textrm{T} \textrm{c}$ (Eq. 105)

   2. reverse osmosis: solvent flows away from concentrated solution; occurs when the pressure exerted on the solution is greater than $\Pi$.