Solutions and Concentration Calculations

Molarity and Solution Preparation

Understanding how to calculate the concentration of solutions is fundamental in general chemistry. Molarity (M) is defined as the number of moles of solute per liter of solution.

• Definition: Molarity (M) = moles of solute / liters of solution

• Formula: , where n is moles of solute and V is volume in liters.

• Example: To find the molarity of a solution formed by dissolving 468 mg of MgI2 in enough water to yield 50.0 mL of solution:

  • Convert mass to moles:

  • Convert volume to liters:

  • Calculate molarity using the formula above.

Dilution of Solutions

Dilution involves adding solvent to a solution to decrease its concentration. The relationship between the concentrations and volumes before and after dilution is given by:

• Formula:

• Where: and are the initial molarity and volume, and are the final molarity and volume.

• Example: To find the concentration after diluting 25.0 mL of 0.188 M Ca(NO3)2 to 1500 mL:

  • Use to solve for .

Calculating Number of Molecules

To determine the number of molecules in a given volume and concentration of solution:

• Calculate moles: (with V in liters)

• Convert moles to molecules: , where (Avogadro's number)

• Example: Find the number of molecules in 14.3 mL of 0.140 M sucrose solution.

Precipitation Reactions and Solubility

Precipitate Formation

When two aqueous solutions are mixed, a precipitate may form if an insoluble compound is produced. Solubility rules help predict whether a precipitate will form.

• Definition: A precipitate is an insoluble solid formed from a reaction in solution.

• Example: Mixing solutions of BaCl2 and Na2SO4 forms a precipitate of BaSO4 because barium sulfate is insoluble in water.

• Common Solubility Rules:

  • Most nitrate (NO3-) salts are soluble.

  • Most salts of Na+, K+, and NH4+ are soluble.

  • Most chloride, bromide, and iodide salts are soluble, except those of Ag+, Pb2+, and Hg22+.

  • Most sulfate salts are soluble, except BaSO4, PbSO4, and CaSO4.

Spectator Ions

In precipitation reactions, spectator ions are ions that do not participate in the formation of the precipitate and remain unchanged in solution.

• Example: In the reaction between BaCl2 and Na2SO4:

  • Ba2+ + 2Cl- + 2Na+ + SO42- → BaSO4(s) + 2Na+ + 2Cl-

  • Na+ and Cl- are spectator ions.

Electrolytes and Acid-Base Strength

Strong and Weak Electrolytes

Electrolytes are substances that conduct electricity when dissolved in water. They are classified as strong or weak based on their degree of ionization.

• Strong Electrolytes: Completely dissociate into ions in solution (e.g., NaCl, HNO3).

• Weak Electrolytes: Partially dissociate in solution (e.g., HF, NH3).

• Nonelectrolytes: Do not produce ions in solution (e.g., sugar, ethanol).

• Example: HF and NH3 are weak electrolytes; HNO3 is a strong electrolyte.

Acids and Bases: Strength and Classification

Acids and bases are classified as strong or weak based on their ability to dissociate in water.

• Strong Acids: Completely ionize in water (e.g., HCl, HNO3, H2SO4).

• Weak Acids: Partially ionize (e.g., HF, HNO2).

• Strong Bases: Completely dissociate (e.g., NaOH, Ba(OH)2).

• Weak Bases: Partially dissociate (e.g., NH3).

• Example Table:

Stoichiometry and Chemical Equations

Balancing Chemical Equations

Balancing chemical equations ensures the law of conservation of mass is obeyed. The number of atoms of each element must be the same on both sides of the equation.

• Example: For the combustion of acetic acid:

  • Equation:

  • Balance the equation by adjusting coefficients so that the number of each type of atom is equal on both sides.

Summary Table: Key Concepts