4.5 | concentrations of solutions

Introduction to Concentrations of Solutions

• Dietary supplements have gained popularity, often containing trace elements essential in small quantities for health.

• Deficiencies and excesses of elements, such as iron, can lead to significant health issues.

  • Iron Levels: 2.3 g in adult women, 3.8 g in adult men.

  • Health Impacts:

    • Deficiency: Can cause anemia and fatigue.

    • Excess: Can lead to stomach pain and metabolic acidosis.

Need for Solution Chemistry

• Body chemistry fundamentally revolves around solutions, emphasizing the need to quantify the concentration of substances in solution.

• Understanding concentration allows for proper management of nutrient intake and health.

Definition of Concentration

• Concentration is defined as the amount of solute present in a specific quantity of solvent or solution.

• Greater solute amounts lead to higher concentrations.

Molarity

• Molarity (M) is a vital measurement in chemistry that expresses the concentration of a solution:

  • Formula:

    • [ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} ]

  • A 1.00 M solution contains 1 mole of solute per liter of solution.

  • Example Preparation: 0.25 L of 1.00 M CuSO4 solution.

    • Calculation: [ M = \frac{0.25 \text{ moles CuSO}_4}{0.25 ext{ L}} = 1.00 ext{ M} ]

Electrolyte Concentrations

• Total ion concentration in solutions is crucial in biological processes.

  • Example Ion Concentrations:

    • NaCl: 1.00 M Na+ and 1.00 M Cl- ions in solution.

    • Na2SO4: 2.00 M Na+ and 1.00 M SO4^(2-)

Sample Exercise: Calculating Molarity

• Given: 23.4 g of Na2SO4 in 125 mL of solution.

• Steps:

  • Convert grams to moles using molar mass (142.1 g/mol):

    • [ \text{Moles Na}_2\text{SO}_4 = \frac{23.4 \text{ g}}{142.1 \text{ g/mol}} = 0.165 \text{ moles} ]

  • Convert volume to liters:

    • [ 125 \text{ mL} = 0.125 \text{ L} ]

  • Calculate molarity:

    • [ M = \frac{0.165 \text{ moles}}{0.125 \text{ L}} = 1.32 M ]

Interconverting Molarity, Moles, and Volume

• Knowing any two quantities from the molarity definition allows calculation of the third.

• Example Calculation for HNO3:

  • Given: Molarity = 0.2 M, Volume = 2.0 L:

    • Moles HNO3 = 2.0 L x 0.2 moles/L = 0.4 moles HNO3.

• Example to find volume from moles:

  • Given: 2.0 moles of HNO3 using 0.3 M solution:

    • Volume = [ \frac{2.0 \text{ moles}}{0.3 \text{ moles/L}} = 6.67 \text{ L} ]

Calculating Molarity from Density and Mass

• Example: Finding ethanol concentration in beer (5% ethanol by volume):

  • 1.00 L of beer contains 0.05 L of ethanol.

  • Calculate moles of ethanol:

    • Molar mass of ethanol = 46 g/mol, Density = 0.789 g/mL.

    • Moles = [ \frac{0.05 \text{ L} \times 1000 \text{ mL/L} \times 0.789 \text{ g/mL}}{46 ext{ g/mol}} = 0.858 \text{ moles} ]

    • Ethanol concentration = 0.86 M.

Dilution of Solutions

• Stock solutions (concentrated) can be diluted for lower concentration.

• Example: Preparing 0.25 L of 0.1 M CuSO4 from stock:

  • Moles in dilute solution = [ 0.25 ext{ L} \times 0.1 ext{ M} = 0.025 ext{ moles} ]

  • Volume of stock solution needed:

    • [ V_{stock} = \frac{0.025 \text{ moles}}{1 M} = 0.025 ext{ L} ] or 25 mL.

• Important principle: Moles of solute conserved before and after dilution.

  • General formula: [ M_{conc} \times V_{conc} = M_{dil} \times V_{dil} ]