08/14 Solutions and Aqueous Reactions

A progressive guide to aqueous solutions, concentration, solubility, precipitation, acid–base reactions, titrations, and quantitative solution stoichiometry.

How aqueous solutions behave

A solution is a homogeneous mixture, so its composition is uniform throughout a thoroughly mixed sample. The substance present in the greater amount is the , and the dissolved substance is the . An uses water as its .

When an ionic compound dissolves, polar water molecules surround and separate its ions. For example:

\mathrm{NaCl(s) \rightarrow Na^+(aq) + Cl^-(aq)}

The label $\mathrm{(aq)}$ indicates that a species is dissolved in water. An produces ions and conducts electricity. Soluble ionic compounds and strong acids or bases are generally strong electrolytes, whereas molecular substances such as sucrose can dissolve as intact molecules and behave as nonelectrolytes.

Takeaway: Identify the , , and particles present in solution before analyzing a reaction.

and precipitation prediction

is the maximum concentration that can dissolve under specified conditions. A solution is unsaturated when it contains less dissolved than the limit, saturated when it contains the maximum amount at equilibrium, and supersaturated when it temporarily contains more than normally permitted.

If the concentration of a dissolved substance exceeds its , a solid may form. General guidelines help predict which ionic compounds are soluble:

Group 1 metal salts and ammonium salts are generally soluble.
Nitrates, acetates, bicarbonates, and chlorates are generally soluble.
Chlorides, bromides, and iodides are generally soluble, with common exceptions involving silver, mercury(I), and lead(II) salts.
Sulfates are generally soluble, but exceptions include salts of silver, barium, calcium, mercury(I), lead(II), and strontium.
Carbonates, phosphates, chromates, and sulfides are generally insoluble except with Group 1 cations and ammonium.
Hydroxides are generally insoluble except for Group 1 hydroxides and, to a lesser extent, barium hydroxide.

These guidelines are empirical rather than absolute. More rigorous equilibrium calculations use -product constants, $K_{sp}$ . Temperature often affects the of solids, while pressure strongly affects the of gases.

Takeaway: A precipitate is likely when an ion pair produces a compound whose limit is exceeded.

Measuring concentration

Concentration compares an amount of with a specified amount of solution or . uses the final volume of solution:

M=\\frac{n_{\\text{solute}}}{V_{\\text{solution}}}

The volume must be in liters. For example, a solution containing $0.125$ mol of $\mathrm{KNO_3}$ in $250.0$ mL has a volume of $0.2500$ L and a of:

M=\\frac{0.125\\ \mathrm{mol}}{0.2500\\ \mathrm{L}}=0.500\\ \mathrm{M}

Other concentration units use different reference quantities:

Mass percent is mass of divided by mass of solution, multiplied by $100\%$ .
Volume percent is volume of divided by volume of solution, multiplied by $100\%$ .
Mass/volume percent gives grams of per $100$ mL of solution.
Parts per million is approximately milligrams of per liter of dilute .
Molality is moles of per kilogram of : $m=\frac{n_{\text{solute}}}{\text{kg solvent}}$ .
Mole fraction is $X_i=\frac{n_i}{\sum n_j}$ .

Do not confuse solution volume with volume. is based on solution volume, while molality is based on mass and is useful when temperature-dependent volume changes matter.

Takeaway: Before calculating concentration, determine whether the denominator is solution volume, mass, or another specified quantity.

Preparing solutions and dilutions

A known-concentration solution can be prepared by dissolving a measured amount of and diluting to a calibrated final volume. In careful work, a volumetric flask is filled until the bottom of the meniscus reaches the calibration mark, then stoppered and inverted several times to mix the solution uniformly.

decreases concentration by adding while conserving the amount of . Because the amount of is related to concentration and volume by

n=MV

the initial and final solutions satisfy

M_1V_1=M_2V_2

or, more generally,

C_1V_1=C_2V_2

For example, the volume of $2.00\ \mathrm{M}$ stock solution needed to prepare $100.0$ mL of $0.250\ \mathrm{M}$ solution is:

V_1=\\frac{M_2V_2}{M_1}=\\frac{(0.250\\ \mathrm{M})(100.0\\ \mathrm{mL})}{2.00\\ \mathrm{M}}=12.5\\ \mathrm{mL}

Measure the stock volume, transfer it to an appropriate volumetric flask, and add water to the final volume. When handling concentrated acid, add acid to water rather than water to acid to reduce localized boiling and splattering.

Takeaway: A changes concentration through volume, not through loss or gain of .

Writing ionic equations

A occurs when dissolved ions form an insoluble solid. Consider mixing aqueous barium nitrate and sodium sulfate. The molecular equation is:

\\mathrm{Ba(NO_3)_2(aq) + Na_2SO_4(aq) \rightarrow BaSO_4(s) + 2NaNO_3(aq)}

The complete ionic equation is:

\\mathrm{Ba^{2+}(aq) + 2NO_3^-(aq) + 2Na^+(aq) + SO_4^{2-}(aq) \rightarrow BaSO_4(s) + 2Na^+(aq) + 2NO_3^-(aq)}

The sodium and nitrate ions are . After canceling them, the is:

\\mathrm{Ba^{2+}(aq) + SO_4^{2-}(aq) \rightarrow BaSO_4(s)}

Use this sequence to predict and represent a precipitate:

List the ions present after the solutions are mixed.
Pair each cation with each possible anion.
Apply guidelines.
Balance the molecular equation.
Dissociate strong aqueous electrolytes for the complete ionic equation.
Cancel and check atom and charge balance.

For a quantitative example, mixing $50.0$ mL of $0.100\ \mathrm{M}$ silver nitrate with $25.0$ mL of $0.150\ \mathrm{M}$ sodium chloride produces silver chloride:

\\mathrm{Ag^+(aq) + Cl^-(aq) \rightarrow AgCl(s)}

The available amounts are $0.00500$ mol of $\mathrm{Ag^+}$ and $0.00375$ mol of $\mathrm{Cl^-}$ . Because the ratio is one-to-one, chloride is the and $0.00375$ mol of $\mathrm{AgCl}$ forms. With a molar mass of $143.32\ \mathrm{g\ mol^{-1}}$ , the precipitate mass is:

m(\\mathrm{AgCl})=(0.00375\\ \mathrm{mol})(143.32\\ \mathrm{g\\ mol^{-1}})=0.537\\ \mathrm{g}

Takeaway: Net ionic equations isolate the particles responsible for the observed chemical change, while stoichiometry determines how much product forms.

Acid–base reactions and titrations

In the Brønsted–Lowry model, an acid donates a proton and a base accepts a proton. In water, the proton is associated with water molecules as hydronium. For example:

\\mathrm{HCl(aq) + H_2O(l) \rightarrow H_3O^+(aq) + Cl^-(aq)}

Neutralization is an acid–base reaction in which an acid reacts with a base. For a strong acid and strong base, the can be written as:

\\mathrm{H_3O^+(aq) + OH^-(aq) \rightarrow 2H_2O(l)}

It is also commonly represented as:

\\mathrm{H^+(aq) + OH^-(aq) \rightarrow H_2O(l)}

A determines an unknown concentration by reacting an analyte with a titrant of known concentration. At the , the reacting amounts follow the balanced-equation mole ratio. The endpoint is the observed experimental signal, often an indicator color change, used to estimate the .

For a one-to-one reaction between hydrochloric acid and sodium hydroxide, a $25.00$ -mL hydrochloric acid sample requiring $18.60$ mL of $0.1000\ \mathrm{M}$ sodium hydroxide contains:

n(\\mathrm{NaOH})=(0.01860\\ \mathrm{L})(0.1000\\ \mathrm{mol\\ L^{-1}})=0.001860\\ \mathrm{mol}

The same amount of hydrochloric acid reacts, so:

[\\mathrm{HCl}]=\\frac{0.001860\\ \mathrm{mol}}{0.02500\\ \mathrm{L}}=0.07440\\ \mathrm{M}

For reactions with coefficients other than one-to-one, use the balanced-equation ratio explicitly. Weak acids and bases react incompletely and establish equilibria, but the stoichiometric relationship at the still follows the balanced reaction.

Takeaway: Acid–base calculations require both the proton-transfer model and the mole ratio from the balanced equation.

A reliable problem-solving workflow

Most quantitative aqueous-reaction problems follow the same workflow:

Write and balance the chemical equation.
Identify the requested quantity and the relevant reactant or product.
Convert each solution amount to moles using $n=MV$ , with volume in liters.
Apply the mole ratio from the balanced equation.
Convert the resulting moles to the requested unit.
Check for a when more than one reactant amount is provided.
Evaluate units, significant figures, and the reasonableness of the magnitude.

For example, if a reaction requires $2$ mol of $\mathrm{A}$ for every $1$ mol of $\mathrm{B}$ , then:

n_{\\mathrm{B}}=n_{\\mathrm{A}}\\left(\\frac{1\\ \mathrm{mol\\ B}}{2\\ \mathrm{mol\\ A}}\\right)

A common error is to use solution volumes directly in a mole ratio. Volume must first be multiplied by concentration to obtain moles. When measurements are involved, read liquid volumes at eye level from the bottom of the meniscus, mix solutions completely before removing an aliquot, use clean labeled glassware, and record measurements with appropriate precision. The quality of a calculated concentration cannot exceed the quality of the measured masses, volumes, and standard solutions.

Wear splash goggles and appropriate gloves, and follow the laboratory's chemical-waste procedures.

Final takeaway: Convert measured solution data to moles, use the balanced reaction to connect substances, and then convert to the requested result while checking measurement quality.