MCAT General Chemistry - Solutions

521

Solutions

homogeneous mixtures of two or more substances that combine to form a single phase, usually the liquid phase

ex. salt water, soda, cocktails, alloys

homogeneous

the same throughout

mixtures

combinations of distinct compounds

gas molecules do not interact all that much chemically, thus are not exactly solutions

solute

the substance being dissolved; move about freely in the solvent and interact with it by way of intermolecular forces; also relatively free to interact with other dissolved molecules of different chemical identities

solvent

component of the solution that remains in the same phase or is present in greater quantity or is more commonly used to dissolve things after mixing

Solvation / dissolution

electrostatic interaction between solute and solvent molecules; maximises new intermolecular interactions

hydration

solvation in water

exothermic solvation

new interactions in solution are stronger than the original ones; favored at low temperatures

ex. gases into liquids

endothermic solvation

new interactions in solution are weaker than the original ones; favored at high temperatures

ex. sugar into water

ideal solution

overall strength of the new interactions in solution is equal to the overall strength of the original interactions; overall enthalpy change for the dissolution is close to / equals zero

entropy of dissolution

At constant temperature and pressure, entropy always increases upon dissolution

spontaneity of dissolution

depends on the change in Gibbs free energy

Solvation of NaCl Ions in Aqueous Solutions

component ions dissociate from each other and become surrounded by water molecules → endothermic

+3.87 kJ/mol

solubility

maximum amount of that substance that can be dissolved in a particular solvent at a given temperature

at 25°C, a maximum of 90.9 g glucose will dissolve in 100 mL H2O = 909 g/L

saturated

dissolved solute is in equilibrium with its undissolved state; at maximum equilibrium concentration; calculated IP is equal to the known Ksp

precipitating

solid form that removes itself from solution

dilute

solution in which the proportion of solute to solvent is small

concentrated

solution in which the proportion of solute to solvent is large

sparingly soluble salts

solutes that dissolve minimally in the solvent; molar solubility under 0.1 M

aqueous solution

solvent is water

hydronium ion (H₃O⁺)

protonated water; facilitated by the transfer of a hydrogen ion (H⁺) from a molecule in solution to a water molecule (H₂O)

solubility rules

1. ammonium (NH₄⁺) & alkali metal (Group 1) = water-soluble

2. nitrate (NO₃⁻) and acetate (CH₃COO⁻) = water-soluble

3. Halides (Cl−, Br−, I−), excluding fluorides = water-soluble, EXCEPT with Ag⁺, Pb²⁺, Hg₂²⁺

4. sulfate = water-soluble, EXCEPT Ca²⁺, Sr²⁺, Ba²⁺, Pb²⁺

5. metal oxides = insoluble, EXCEPT alkali metals, ammonium, CaO, SrO, and BaO

6. hydroxides = insoluble, EXCEPT alkali metals, ammonium, Ca²⁺, Sr²⁺, Ba²⁺

7. carbonates (CO₃^2-), phosphates (PO₄^3-), sulfides (S^2–), and sulfites (SO₃^2-) = insoluble, EXCEPT alkali metals and ammonium

complex ion / coordination compound

a molecule in which a cation is bonded to at least one ligand

ex. tetraaquadiox-ouranyl cation, haemoglobin

ligand

electron donor molecules attached to cations, can include water

coordinate covalent bonds

form very stable Lewis acid–base adducts

chelation

central cation bonded to the same ligand in multiple places; generally requires large organic ligands that can double back

ex. Iron with Two Molecules of Deferasirox

Concentration

the amount of solute dissolved in a solvent

volume percent

volume of solute divided by volume of solution times 100 percent

alcoholic proof

twice volume percent

degrees Brix (°Bx)

mass of glucose divided by mass of solution times 100 percent

percent composition by mass

m_solute/m_solution × 100%

used for: aqueous solutions, metal alloys, solid-in-solid solutions

mole fraction (X)

X_A = mol_A/mol_total

sum of all compounds = 1

used for: partial pressure, vapor pressure depression

molarity (M)

M = mol_solute/V_solution in mol/L or molar (M)

used for: rate laws, the law of mass action, osmotic pressure, pH and pOH, and the Nernst equation

molality (m)

M = mol_solute/m_solution in mol/kg

used for: boiling point elevation and freezing point depression

normality (N)

equal to the number of equivalents of interest per liter of solution

equivalent

measure of the reactive capacity of a molecule; equal to a mole of the species of interest (protons, hydroxide ions, electrons, or ions)

DIlution

when solvent is added to a solution of higher concentration to produce a solution of lower concentration

dilution equation

M_iV_i = M_fV_f

where M is molarity, V is volume, and the subscripts i and f refer to the initial and final values

saturation point

the solute concentration is at its maximum value for the given temperature and pressure

solubility product constant (Ksp)

equilibrium constant for its solubility in aqueous solution; temperature dependent.

K_sp = [Aⁿ⁺]^m[B^m–]ⁿ

where the concentrations of the ionic constituents are equilibrium (saturation) concentrations

ion product (IP)

analogous to the reaction quotient, Q, for other chemical reactions

IP = [Aⁿ⁺]^m[B^m–]ⁿ

concentrations used in the ion product equation are the concentrations of the ionic constituents at that given moment in time

unsaturated

salt’s IP is less than the salt’s Ksp

supersaturated

salt’s IP is greater than the salt’s Ksp

molar solubility

molarity of a solute in a saturated solution

formation or stability constant (K_f)

formation of the complex ion in solution to become more soluble in solution

common ion effect

solubility of a salt is considerably reduced when it is dissolved in a solution that already contains one of its constituent ions as compared to its solubility in a pure solvent; no effect on the value of the solubility product constant

colligative properties

physical properties of solutions that are dependent on the concentration of dissolved particles but not on the chemical identity of the dissolved particles

list of colligative properties

1. vapor pressure depression

2. boiling point elevation

3. freezing point depression

4. osmotic pressure

Raoult’s law

accounts for vapor pressure depression

P_A = X_AP_A°

where P_A is the vapor pressure of solvent A when solutes are present, X_A is the mole fraction of the solvent A in the solution, and P_A° is the vapor pressure of solvent A in its pure state.

vapor pressure depression

As solute is added to a solvent, the vapor pressure of the solvent decreases proportionately

Boiling Point Elevation

When a nonvolatile solute is dissolved into a solvent to create a solution, the boiling point of the solution will be greater than that of the pure solvent

ex. pasta water

boiling point

temperature at which the vapor pressure of the liquid equals the ambient (incident) pressure

boiling point elevation equation

ΔT_b = iK_bm

where ΔTb is the increase in boiling point, i is the van’t Hoff factor, Kb is a proportionality constant characteristic of a particular solvent and m is the molality of the solution

van’t Hoff factor

corresponds to the number of particles into which a compound dissociates in solution

Freezing Point Depression

The presence of solute particles in a solution interferes with the formation of the lattice arrangement of solvent molecules associated with the solid state

ex. road salt

Freezing Point Depression equation

ΔT_f = iK_fm

where ΔTf is the freezing point depression, i is the van’t Hoff factor, Kf is the proportionality constant characteristic of a particular solvent, and m is the molality of the solution

Osmotic pressure

“sucking” pressure generated by solutions in which water is drawn into a solution; formally, the amount of pressure that must be applied to counteract this attraction of water molecules for the solution

∏ = iMRT

where ∏ is the osmotic pressure, i is the van’t Hoff factor, M is the molarity of the solution, R is the ideal gas constant, and T is the temperature