AP Chemistry 3.7-3.8: Solutions and Their Representations

Solution

A solution is a homogeneous mixture of two or more substances. Its components are dispersed uniformly on the molecular scale and do not settle out over time.

Solvent versus solute

The solvent is the component present in the greatest relative amount and dissolves the other components. Solutes are the substances present in lesser relative amounts.

What does the designation $(aq)$ indicate in a chemical equation?

It indicates that a species is dissolved in water as an aqueous solute. The species may be an intact molecule or a solvated ion, depending on the substance.

What characteristics distinguish a solution from a heterogeneous mixture?

A solution has uniform composition throughout, contains solute particles dispersed at the molecular or ionic scale, and does not have components that visibly separate or settle under the stated conditions.

How does the physical state of a solution usually relate to the physical state of its solvent?

The solution generally has the same physical state as the solvent. For example, a gas dissolved in a liquid produces a liquid solution, while one metal dissolved in another can produce a solid solution.

Can the solute and solvent in a solution be gases, liquids, or solids?

Yes. Solutions can contain components in any combination of phases, such as air (gas in gas), alcohol in water (liquid in liquid), saltwater (solid-derived solute in liquid), or brass (solid in solid).

Why do dissolved sucrose molecules not settle to the bottom of an aqueous solution despite being heavier than water molecules?

Sucrose molecules are dispersed uniformly among water molecules on a molecular scale. Their thermal motion and interactions with the solvent prevent gravitational settling in a true solution.

Write the molecular equation for sucrose dissolving in water.

The process can be represented as $\mathrm{C_{12}H_{22}O_{11}(s) \rightarrow C_{12}H_{22}O_{11}(aq)}$. Sucrose remains as intact covalent molecules rather than dissociating into ions.

Write the dissolution equation for potassium dichromate in water.

$\mathrm{K_2Cr_2O_7(s) \rightarrow 2K^+(aq) + Cr_2O_7^{2-}(aq)}$. The ionic solid separates into solvated potassium and dichromate ions.

What limits the continuous variation of a solution's composition?

The composition can vary continuously only within limits set by the solubility of the components. Once the solubility limit is exceeded, additional solute may remain undissolved.

Spontaneous solution formation

Dissolution is spontaneous when it occurs under specified conditions without continuous energy supplied by an external source. Stirring can increase the rate of dissolution but is not required for a solution to form eventually.

Which two factors generally favor spontaneous formation of a solution?

A decrease in the system's internal energy, corresponding to an exothermic change, and an increase in the dispersal of matter, corresponding to increased entropy, both favor solution formation. Neither factor alone guarantees spontaneity.

Why does mixing two gases generally form a solution spontaneously?

Gas particles diffuse into the available volume, greatly increasing the dispersal of matter. Because ideal gases have negligible intermolecular attractions, mixing causes little or no enthalpy change.

Ideal solution

An ideal solution forms when solute-solute, solvent-solvent, and solute-solvent intermolecular attractions are approximately equal. Mixing then produces essentially no energy change, as in structurally similar liquids such as methanol and ethanol.

Which three types of intermolecular attractions must be considered when predicting dissolution?

The relevant interactions are solute-solute, solvent-solvent, and solute-solvent attractions. Dissolution requires separating the first two types and establishing the third.

Why are the first two conceptual steps of dissolution endothermic?

Separating solute particles from one another and solvent particles from one another requires energy to overcome attractive forces. These steps therefore absorb energy.

Solvation

Solvation is the formation of attractive interactions between solute particles and solvent particles. Establishing these interactions releases energy and is therefore exothermic; when water is the solvent, the process is called hydration.

How can the overall energy change of dissolution be predicted from its component steps?

The energy absorbed to separate solute and solvent particles is compared with the energy released during solvation. If solute-solvent attractions are stronger overall, dissolution tends to be exothermic; if separation requires more energy than solvation releases, it tends to be endothermic.

Why might calcium carbonate have very low solubility in water?

The strong electrostatic attractions in the ionic lattice may require more energy to overcome than is released when water solvates the ions. Consequently, dissolution is not appreciable under ordinary conditions.

Why is sodium hydroxide highly soluble in water according to the dissolution-energy model?

The ion-dipole attractions between water and the ions are sufficiently strong to compensate for, or exceed, the energy required to separate the ionic solid. Its dissolution is substantially exothermic and highly favorable.

Why can an endothermic dissolution still occur spontaneously?

Dissolution increases the dispersal of matter and therefore increases entropy. This entropy increase can favor spontaneity even when the process absorbs heat, as in ammonium nitrate dissolving in an instant cold pack.

Why does an ammonium nitrate instant cold pack become cold when activated?

Ammonium nitrate dissolves endothermically, so the dissolving process absorbs thermal energy from the surrounding water and injured area. The surroundings therefore decrease in temperature.

Electrolyte

An electrolyte is a substance that produces mobile ions when dissolved in water, allowing the solution to conduct electricity. Ionic compounds and acids or bases that ionize in water can be electrolytes.

Nonelectrolyte

A nonelectrolyte dissolves without producing appreciable mobile ions, so its aqueous solution conducts little or no electricity. Molecular substances such as ethanol and sucrose are examples.

Strong electrolyte versus weak electrolyte

A strong electrolyte produces ions essentially completely when dissolved, whereas a weak electrolyte produces ions from only a fraction of the dissolved substance. Strong electrolytes generally give higher ion concentrations and conduct more strongly at comparable conditions.

How can electrical conductivity be used to classify a dissolved substance?

A solution conducts electricity when it contains freely mobile charged particles. High conductivity indicates a relatively large concentration of mobile ions, weak conductivity indicates fewer ions, and negligible conductivity indicates a nonelectrolyte, assuming comparable concentrations and conditions.

Why do ionic compounds usually behave as strong electrolytes when they dissolve?

Water molecules surround and stabilize the separated ions, reducing the electrostatic attractions holding the ionic solid together. The portion that dissolves therefore dissociates nearly completely, even if the compound itself is only sparingly soluble.

Ion-dipole attraction

An ion-dipole attraction is the electrostatic attraction between an ion and the oppositely charged end of a polar molecule. These interactions help water dissolve ionic compounds.

Hydration of an ion in water

Hydration occurs when water molecules orient around and solvate an ion. The oxygen end of water points toward cations, while the hydrogen end points toward anions.

Dissociation

Dissociation is the physical separation of ions that were already present in an ionic solid as it dissolves. For example, $\mathrm{KCl(s) \rightarrow K^+(aq) + Cl^-(aq)}$.

Why does water conduct electricity poorly even though it can contain ions?

Pure water undergoes only slight self-ionization: $\mathrm{2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)}$. At $25\ ^\circ\mathrm{C}$, only about two water molecules per billion are ionized, so the ion concentration is very small.

How does a covalent substance such as HCl become an electrolyte in water?

HCl molecules react chemically with water, transferring a proton to form hydronium and chloride ions: $\mathrm{HCl + H_2O \rightarrow H_3O^+ + Cl^-}$. Because this reaction is essentially complete, aqueous HCl is a strong electrolyte.

How do dissolution processes differ for ionic and covalent electrolytes?

An ionic electrolyte generally undergoes dissociation, a physical separation of preexisting ions. A covalent electrolyte produces ions through a chemical reaction or ionization with the solvent.

Why are weak acids and weak bases classified as weak electrolytes?

They react with water only partially, establishing an equilibrium that produces relatively low concentrations of ions. Their solutions therefore conduct electricity less effectively than solutions of strong acids or bases at comparable concentrations.

A solution of a sparingly soluble ionic compound contains a small amount of dissolved material. Is it necessarily a weak electrolyte?

No. Solubility and electrolyte strength are different properties. The small amount that dissolves from a sparingly soluble ionic compound generally dissociates essentially completely, so the compound is still a strong electrolyte.

How can bubbles affect the classification of a liquid mixture as a solution?

Visible bubbles indicate a separate gas phase, making the mixture heterogeneous rather than a single homogeneous solution at that moment. A solution must have uniform composition throughout.

Molarity

Molarity is the amount of solute, in moles, divided by the total volume of solution in liters: $M = \frac{n_{\text{solute}}}{V_{\text{solution}}}$. Its units are $\mathrm{mol\,L^{-1}}$, or M.

How is the molarity of a solution calculated from solute mass?

Convert the solute mass to moles using its molar mass, measure the total solution volume in liters, and calculate $M = \frac{n_{\text{solute}}}{V_{\text{solution}}}$.

What is the difference between molarity and molality?

Molarity is moles of solute per liter of solution, $M = \frac{n_{\text{solute}}}{V_{\text{solution}}}$. Molality is moles of solute per kilogram of solvent, $m = \frac{n_{\text{solute}}}{m_{\text{solvent}}}$.

Molality

Molality is the amount of solute, in moles, divided by the mass of solvent in kilograms: $m = \frac{n_{\text{solute}}}{m_{\text{solvent}}}$. Its units are $\mathrm{mol\,kg^{-1}}$, or m.

Why does molality use the mass of solvent rather than the volume of solution?

Mass is essentially unaffected by temperature, whereas solution volume can change with temperature. Molality therefore remains constant when temperature changes, provided the composition does not change.

How should a particulate diagram represent an aqueous solution of a soluble ionic compound?

It should show separated cations and anions dispersed throughout the water, with water molecules oriented so their oxygen ends face cations and their hydrogen ends face anions. The ions should be present in the stoichiometric ratio required by the compound.

How should a particulate diagram represent an aqueous solution of a molecular nonelectrolyte?

It should show intact, neutral solute molecules distributed among water molecules. The solute should not be depicted as separated ions.

How can particulate representations distinguish strong and weak electrolytes?

A strong electrolyte is represented primarily or entirely as separated ions, while a weak electrolyte is represented as a mixture of mostly intact neutral molecules and a smaller number of ions. The relative numbers of particles indicate the degree of ionization.

What does a more concentrated particulate representation of a solution show?

It shows a greater number of solute particles in a given volume of solution, or a smaller amount of solvent per solute particle. Concentration depends on the ratio of solute amount to solution volume, not simply on the total number of particles drawn.

How can dilution be represented at the particulate level?

Dilution increases the amount of solvent while leaving the number of solute particles unchanged. The same solute particles are therefore spread through a larger volume, producing a lower concentration.