CHEM 1412 Concept Review: Solutions & Colligative Properties

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Solution:  a homogenous mixture of 2 or more substances

Solvent:  the dissolving medium of a solution (usually this is the largest component of the solution)

Solute:  the substance that is dissolved by the solvent (usually this is the smaller component of the solution)

Aqueous solution:  a solution where water is the solvent

Solubility:  the MAXIMUM amount of a given solute that is capable of being dissolved in a specified amount of solvent or solution at a certain temperature. (Units can be “M”, “g solute/ L soln”, “g/100 mL solvent”, etc.)

Entropy:  a measure of the energy randomization or energy dispersal in a system.  This quantity is sometimes simply described as “the disorder of a system”.

2^nd Law of Thermodynamics:  For any spontaneous process, the entropy of the universe is increased.  (This law is the driving force behind the formation of solutions.)

 

 

Energetics of Solution Formation

Solute-Solute interactions: the interactions (attractions) between solute particles (This is based on the molecular structure of the solute and the intermolecular forces that result from that structure.)

Solvent-Solvent interactions: the interactions (attractions) between solvent particles (This is based on the molecular structure of the solvent and the intermolecular forces that result from that structure.)

Solute-Solvent interactions: the interactions (attractions) between solute particles and solvent particles (This is based on the molecular structure of the solute and solvent and their respective intermolecular forces.)

The formation of a solution can be thought of as being broken down into the above 3 steps, which are represented in the equation below. ∆H₁ is also called ∆H_solvent and ∆H₂ is also called ∆H_solute.  These 2 quantities are always endothermic, whereas ∆H₃ (also called ∆H_mix) is always exothermic.

$\Delta H_{solute}+\Delta H_{solvent}+\Delta H_{mix}=\Delta H_{solution}$

ΔH_solute is the energy required to separate solute particles, ΔH_solvent where is the energy required to separate solvent particles, and ΔH_mix is the energy released when the separated particles mix, and ΔH_solution is the change in energy of the whole solution process.

Furthermore, ∆H_solute is equal to the -∆H_lattice for ionic solutes.  ($\Delta H_{solute}=-\Delta H_{lattice}$)

 

∆H_solvent and ∆H_mix are sometimes combined into a single quantity called the heat of hydration or ∆H_hydration.  This quantity is always very exothermic for ionic compounds.

$\Delta H_{hydration}=\Delta H_{solvent}+\Delta H_{mix}$

 

 

Solution Key Terms

Dynamic Equilibrium: An equilibrium achieved when the forward and reverse rates of a process become equal.  For saturated solutions, the undissolved solid is in dynamic equilibrium with the dissolved solute.  In other words, the solute is recrystallizing back into a solid as fast as it is being dissolved.

Saturated solution:  a solution in which the maximum equilibrium amount of solute is dissolved.

Unsaturated solution:  a solution that contains less than the maximum equilibrium amount of solute.  (more can dissolve)

Supersaturated solution:  an unstable solution that can form under certain conditions which contains more than the maximum equilibrium amount of solute.

Recrystallization:  A purification technique involving the creation of a saturated solution at higher temperatures and then cooling that solution to lower temperatures where the solubility of the solute is lower, causing the solute to crystallize out of solution.  In recrystallization, impurities in the original crystal structure are removed.

 

 

 

Effects of Temperature and Pressure on Solubility

For Solid Solutes:

• Trend for Temperature:  Solubility of solids generally increases with increased temperature.
• Why?:  At higher temperatures, molecules have more energy, making it easier for them to separate from one another and collide into other molecules.  This action aids in the efficiency of the solvation process of solids.
  
• Trend for Pressure:  Neither increased nor decreased pressures have a discernable effect.
• Why?:  Neither increased nor decreased pressure will affect the energy or frequency of collisions for solid solutes. 

 

 

For Gaseous Solutes:

• Trend for Temperature:  Solubility of gases generally decreases with increased temperature.
• Why?:  Gas particles are high energy to begin with, so the faster they move, the harder it is for the solvent to “capture” them.  At higher temperatures, gas molecules are moving more quickly and can escape the solution.
  
  
• Trend for Pressure:  Solubility of gases generally increases with increased pressure.
• Why?:  Greater pressure of a gas above a solution increases the number of collisions the gas particles have with the solvent molecules which increases the frequency of the gas molecules being “captured” and absorbed into the solution.

 

 

This latter trend gives rise to Henry’s Law, which states that the solubility of a gas is directly proportional to the pressure of that gas above a given solvent.  The equation for this law is as follows:

$S_{gas}=k_H\cdot P_{gas}$

Where S_gas is the solubility of the gas, k_H is the Henry’s law constant, and P_gas is the pressure of the gas over the solvent.  The Henry’s law constant is specific to a particular solvent and gas combination.  These values can be looked up.

 

 

Calculating Concentrations of Solutions

Concentration:  Some measure of how much solute is dissolved in a given amount of solution or solvent.  There are numerous different measures of concentration in chemistry.  The table of some of these is below:

Different Measures of Concentration and Their Corresponding Equations

Molarity (M) $M=\frac{moles\:of\:solute}{L\:of\:solution}$ To use as a conversion factor,  $1.25\:M\longrightarrow\left(\frac{1.25\:mol}{1\:L\:soln}\right)$	Molality (m)  $m=\frac{moles\:of\:solute}{kg\:of\:solvent}$    To use as a conversion factor,  $1.25\:m\longrightarrow\left(\frac{1.25\:mol}{1\:kg\:solvent}\right)$	Mole Fraction (X) $X_A=\frac{moles\:of\:A}{total\:moles}$    (For mole fraction, “A” can be either a solute or the solvent)
Mass Percent (% m/m)  $\%\left(m/m\right)=\frac{mass\:of\:solute}{mass\:of\:solution}\times100\%$  $\left(solution=solute+solvent\right)$ To use as a conversion factor, $15\%\left(m/m\right)\longrightarrow\left(\frac{15\:g\:solute}{100\:g\:solution}\right)$	Parts per Million (ppm)  $ppm=\frac{mass\:of\:solute}{mass\:of\:solution}\times10^6$    *This equation can alternatively be used with volumes of solute and solvent.	Parts per Billion (ppb)  $ppb=\frac{mass\:of\:solute}{mass\:of\:solution}\times10^9$    *This equation can alternatively be used with volumes of solute and solvent.
Mole Percent (mol %)  $mol\:\%=\frac{moles\:of\:solute}{total\:moles}\times100\%$ $\left(solution=solute+solvent\right)$ To use as a conversion factor, $15\%\:\left(mol\:\%\right)\longrightarrow\left(\frac{15\:mol\:solute}{100\:mol\:solution}\right)$	Mass/Volume Percent (% m/v) $\%\left(m/v\right)=\frac{mass\:of\:solute\:\left(g\right)}{volume\:of\:solution\:\left(mL\right)}\times100\%$   To use as a conversion factor, $15\%\:\left(m/v\right)\longrightarrow\left(\frac{15\:g\:solute}{100\:mL\:solution}\right)$	Volume Percent (% v/v)  $\%\left(v/v\right)=\frac{volume\:of\:solute}{volume\:of\:solution}\times100\%$   To use as a conversion factor, $15\%\:\left(v/v\right)\longrightarrow\left(\frac{15\:mL\:solute}{100\:mL\:solution}\right)$

 

 

Colligative Properties:  Definitions, Formulas, and Explanations

Colligative Properties:  Properties that are dependent only on the number of particles dissolved in solution and the identity and properties of the solvent, but NOT on the identity and properties of the solute particles.

Vapor Pressure:  a colligative property referring to the partial pressure of the gaseous vapor of solvent that exists above a solution containing nonvolatile solutes. 

Trend:  In general, the greater the number of dissolved particles, the smaller the vapor pressure will be. 

Reason:  When more particles are dissolved in solution, there is a lower the proportion of solvent to solute particles in the solution.  This causes there to be fewer solvent particles exposed on the surface of the solution which are capable of escaping the solution and turning into gaseous vapor, resulting in a lower vapor pressure. This relationship is represented mathematically in Raoult’s Law, which is shown below:

$P_{solution}=X_{solution}\cdot P^{\circ}_{solvent}$           (Raoult's Law)

Where P_solution is the vapor pressure of the solution, X_solvent is the mole fraction of the solvent, and P^o_solvent is the vapor pressure of the pure solvent.

 

When the solution contains one or more volatile solutes, the total vapor pressure of the solution is the sum of the vapor pressures of each volatile component and can be calculated as follows:

$P_{solution}=\left(X_{solvent}\cdot P^{\circ}_{solvent}\right)+\left(X_A\cdot P_A^{\circ}\right)+\left(X_B\cdot P^{\circ}_B\right)+...$

 

 

Freezing Point Depression:  A colligative property of solutions affecting their freezing point.

Trend:  In general, the more dissolved particles are present in solution, the lower the freezing point will be.

Reason:  When more particles are present in solution, those solute particles prevent solvent particles from being able to align into a stable crystal structure which makes it harder for the solvent particles to freeze into a solid.  As a result, more energy must be removed from the solvent particles (lower temperature) to get them to align into a solid state crystal structure. 

$\Delta T_{\:f}=-K_{\:f}m$          (Freezing Point Depression Equation)           

Where ∆T_f is the change in freezing point temperature, K_f is the freezing point depression constant which is specific to the solvent of the solution, and m is the molality of particles in the solution.  ($\Delta T_{\:f}=T_{f\:of\:solution}-T_{f\:of\:solvent}$)

 

 

Boiling Point Elevation:  A colligative property of solutions affecting their boiling point.

Trend:  In general, the more dissolved particles are present in solution, the higher the boiling point will be.

Reason:  When more particles are dissolved in solution, there is a lower the proportion of solvent to solute particles in the solution.  This causes there to be fewer solvent particles exposed on the surface of the solution which are capable of escaping the solution and turning into gaseous vapor.  In addition, the solute particles often have greater forces of attraction to the solvent particles than the solvent particles have to one another.  For both of these reasons, it requires more energy (higher temperature) for the molecules to effectively transition to the gaseous state by boiling.

$\Delta T_b=K_b\cdot m$         (Boiling Point Elevation Equation)

Where ∆T_b is the change in boiling point temperature, K_b is the boiling point elevation constant which is specific to a given solvent, and m is the molality of particles in the solution.  ($\Delta T_b=T_{b\:of\:solution}-T_{b\:of\:solvent}$)

 

 

Osmotic Pressure:  A colligative property that refers to the pressure that drives a solvent to pass through a semi-permeable membrane (osmosis) in order to restore equilibrium between the solutions on both sides of the membrane.  Osmotic pressure can also be defined as the pressure required to stop osmotic flow.

Trend:  In general, the more dissolved particles are present in solution, the greater its osmotic pressure will be.

Reason:  When a solution has a greater number of dissolved particles, the concentration gradient between the two sides of the membrane is greater.  This pushes the system farther away from equilibrium, and the farther away a system is from equilibrium, the greater will be the driving force to restore equilibrium, resulting in a greater osmotic pressure. 

$\Pi=MRT$            (Osmotic Pressure Equation)

Where Π is osmotic pressure, M is molarity of particles, R is the ideal gas law constant, and T is the temperature in Kelvins.

 

 

 

Concentration of Particles

For all molecular compounds, the concentration of particles in solution is the same as the concentration of the compound.  For weak electrolytes, such a small amount of the compound separates that we usually do not have to take it into account.  However, for strong electrolytes, we measure the degree of separation of particles using the van’t Hoff factor (i)

 

The van’t Hoff factor (i):  The ratio of the moles of particles in a solution to the moles of formula units dissolved.  The equation below expresses this relationship:

$i=\frac{moles\:of\:particles\:in\:solution}{moles\:of\:formula\:units}$

 

Molarity of Particles		Molality of Particles
$M_{particles}=i\cdot M_{compound}$		$m_{particles}=i\cdot m_{compound}$