Solution Concentration, Stoichiometry, and Reactions in Aqueous Solutions

Solution Concentration and Molarity

Calculating Solution Concentration

Solution concentration is commonly expressed as molarity (M), which is the number of moles of solute per liter of solution. Molarity is a key concept for preparing solutions and performing stoichiometric calculations in chemistry.

• Moles of solute (mol): The amount of substance dissolved.

• Volume of solution (L): The total volume of the solution.

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Example: If you dissolve 25.5 g KBr in enough water to make 1.75 L of solution, calculate the molarity of the solution.

Using Molarity in Calculations

Molarity allows chemists to relate the volume of a solution to the amount of solute present, which is essential for quantitative chemical analysis.

• To find moles: $\text{moles} = M \times \text{volume (L)}$

• To find volume: $\text{volume (L)} = \frac{\text{moles}}{M}$

Example: How many moles of LiCl are in 2.35 L of a 3.0 M solution?

Solution Dilution

Dilutions and Molarity

To prepare a less concentrated solution from a more concentrated one, use the dilution equation:

• $M_1V_1 = M_2V_2$

• Where $M_1$ and $V_1$ are the molarity and volume of the concentrated solution, and $M_2$ and $V_2$ are those of the diluted solution.

Example: What volume of 1.50 M NaOH is needed to make 0.200 L of 0.120 M NaOH?

Solution Stoichiometry

Stoichiometry with Solutions

Solution stoichiometry involves using molarity as a conversion factor to relate the volume of a solution to the amount of substance present, and then using balanced chemical equations to determine the relationships between reactants and products.

• Convert volume to moles using molarity.

• Use the coefficients in the balanced equation to relate moles of different substances.

• Convert moles back to volume if needed.

Example: How many mL of 0.162 M NaOH are needed to neutralize 35.0 mL of 0.125 M H2SO4?

Types of Aqueous Solutions and Solubility

Solubility Rules

Solubility rules help predict whether an ionic compound will dissolve in water. Compounds are classified as soluble or insoluble, with some exceptions.

Compounds Containing	Are Generally Soluble	Exceptions
Group 1A ions, NH4+, NO3-, C2H3O2-, ClO4-	Yes	None
Cl-, Br-, I-	Yes	Ag+, Pb2+, Hg22+
SO42-	Yes	Sr2+, Ba2+, Pb2+, Ag+, Ca2+
CO32-, PO43-	No	Group 1A, NH4+
OH-	No	Group 1A, Ca2+, Sr2+, Ba2+

Example: Predict whether AgNO3 is soluble in water and list the ions present in solution.

Precipitation Reactions

Formation of Precipitates

Precipitation reactions occur when two aqueous solutions combine to form an insoluble solid, called a precipitate. The reaction can be predicted using solubility rules.

• Write the balanced molecular equation.

• Identify the precipitate using solubility rules.

• Write the complete ionic and net ionic equations.

Example: $\text{Na}_2\text{SO}_4(aq) + \text{SrCl}_2(aq) \rightarrow \text{SrSO}_4(s) + 2\text{NaCl}(aq)$

Ionic and Net Ionic Equations

Writing Ionic Equations

Ionic equations show all of the ions present in a reaction. Net ionic equations show only the species that actually change during the reaction.

• Complete ionic equation: All strong electrolytes are written as ions.

• Net ionic equation: Only the ions and molecules directly involved in the reaction are shown.

Example: $\text{AgNO}_3(aq) + \text{NaCl}(aq) \rightarrow \text{AgCl}(s) + \text{NaNO}_3(aq)$ Net ionic: $\text{Ag}^+(aq) + \text{Cl}^-(aq) \rightarrow \text{AgCl}(s)$

Naming Acids

Oxyacids and Their Names

Oxyacids are acids that contain hydrogen, oxygen, and another element. Their names are based on the polyatomic ion they contain.

Oxyacid	Anion	Anion Name	Oxyacid Name
HClO	ClO-	hypochlorite	hypochlorous acid
HClO2	ClO2-	chlorite	chlorous acid
HClO3	ClO3-	chlorate	chloric acid
HClO4	ClO4-	perchlorate	perchloric acid

• Nitric acid: HNO3

• Chloric acid: HClO3

• Carbonic acid: H2CO3

• Sulfuric acid: H2SO4

• Phosphoric acid: H3PO4

Acid-Base Reactions

Writing Equations for Acid-Base Reactions

Acid-base reactions involve the transfer of protons (H+) from acids to bases. These reactions can be written as molecular, complete ionic, and net ionic equations.

• Strong acid + strong base: $\text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l)$

• Weak acid + strong base: $\text{HC}_2\text{H}_3\text{O}_2(aq) + \text{NaOH}(aq) \rightarrow \text{NaC}_2\text{H}_3\text{O}_2(aq) + \text{H}_2\text{O}(l)$

Acid-Base Titration

Titration is a technique used to determine the concentration of an unknown acid or base by reacting it with a solution of known concentration.

• At the equivalence point, moles of acid = moles of base (according to the balanced equation).

• Use the titration equation: $M_1V_1 = M_2V_2$ (for monoprotic acids and bases).

Gas Evolution Reactions

Types and Guidelines

Gas evolution reactions produce a gas as a product. Common types include:

• Sulfides produce H2S gas.

• Carbonates and bicarbonates produce CO2 gas.

• Sulfites and bisulfites produce SO2 gas.

• Ammonium compounds produce NH3 gas.

Reactant Type	Reacts with	Gas Formed	Example
M2S	acid	H2S	K2S(aq) + 2HCl(aq) → 2KCl(aq) + H2S(g)
MCO3	acid	CO2	Na2CO3(aq) + 2HCl(aq) → 2NaCl(aq) + H2O(l) + CO2(g)
NH4X	base	NH3	NH4Cl(aq) + NaOH(aq) → NaCl(aq) + H2O(l) + NH3(g)

Oxidation and Reduction (Redox)

Oxidation Numbers: Rules

Oxidation numbers are used to keep track of electron transfer in redox reactions. The rules for assigning oxidation numbers are:

1. The oxidation number of an atom in a free, uncombined element is zero.

2. The sum of the oxidation numbers in a compound is zero.

3. The sum of the oxidation numbers in a polyatomic ion equals the ion's charge.

4. Fluorine is always -1 in its compounds.

5. Other halogens are usually -1, except when combined with oxygen or other halogens.

Example: Assign the oxidation number to each atom in H2SO4 and KMnO4.

Identifying Redox Reactions

Redox reactions involve the transfer of electrons between species. Oxidation is the loss of electrons, and reduction is the gain of electrons.

• Oxidizing agent: The species that is reduced (gains electrons).

• Reducing agent: The species that is oxidized (loses electrons).

Example: $4\text{Li}(s) + \text{O}_2(g) \rightarrow 2\text{Li}_2\text{O}(s)$

Cumulative Problems

Integrated Application

Cumulative problems require the integration of multiple concepts, such as solution stoichiometry, limiting reactants, theoretical yield, and percent yield.

• Identify the limiting reactant by comparing the mole ratios of reactants.

• Calculate the theoretical yield based on the limiting reactant.

• Percent yield is calculated as: $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Example: If you collect 1.01 g of PbSO4 from a reaction, determine the limiting reactant, theoretical yield, and percent yield.