Chem L7-8 Concentration & Titration

Concentration

• A solution consists of solvent and solute.
• Concentration = \frac{\text{Amount of solute}}{\text{Amount of solution}}
• Aqueous solution: Water is the solvent.
• Electrolyte: Compound that ionizes in solvent, e.g., NaCl (s) \rightarrow Na^+ (aq) + Cl^- (aq)
• Non-Electrolyte: Compound that doesn't ionize, e.g., C6H{12}O6 (s) \rightarrow C6H{12}O6 (aq)

Units of Concentration

1. Percent by mass: \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%, also written as %(m/m) or %(w/w)

   Example: 0.30 g NaCl in 0.50 g water gives a mass percent of \frac{0.30}{0.30 + 0.50} \times 100\% = 37.50\%.

2. Mass concentration: \frac{\text{mass of solute (g)}}{\text{volume of solution (L)}} (g/L)
   Example: 0.35 g NaCl in 1 L solution gives a mass concentration of 0.35 g/L.

3. Molality (m): \frac{\text{moles of solute (mol)}}{\text{mass of solvent (kg)}} (mol/kg)

   Example: 0.30 mol NaCl in 0.50 kg water gives a molality of \frac{0.30}{0.50} = 0.6 mol/kg.

4. Molarity (M): \frac{\text{moles of solute (mol)}}{\text{volume of solution (L)}} (mol/L), also written as [solute]

   Example: 0.30 mol NaCl in 0.60 L solution gives a molarity of \frac{0.30}{0.60} = 0.50 mol/L.

Preparation of Solutions

• Ordinary Glassware: Less precise volume calibrations
• Volumetric Glassware: Calibrated at specific temperatures to deliver or contain PRECISE amounts of liquid

Methods

1. Dissolution: Dissolving a solid solute in a solvent.

2. Dilution: Adding solvent to a stock solution to lower concentration.

   • M1V1 = M2V2 where:
     • M_1 = Molarity before dilution (stock solution)
     • V_1 = Volume before dilution (stock solution)
     • M_2 = Molarity after dilution
     • V_2 = Volume after dilution
   • Dilution factor = \frac{M1}{M2} = \frac{V2}{V1}

3. Serial Dilution: Stepwise dilution of a substance in solution.

   • Total dilution factor = Dilution factor 1 x Dilution factor 2

Practical Uses

• Prepare dilute solutions for titration
• Prepare calibration standards for advanced chemical analysis (e.g. HPLC)
• Estimate the number of microorganisms in a sample
• Determine the minimum inhibitory concentration (MIC) of drugs

pH

• pH = -log_{10}[H^+] or [H^+] = 10^{-pH}
• pOH = -log_{10}[OH^-]
• pH + pOH = 14
• Monoprotic acids: Donate one H+ ion per molecule (e.g., HCl, HNO_3).
• Diprotic acids: Donate two H+ ions per molecule (e.g., H2SO4, H2CO3).
• pH indicators change color depending on the pH of the solution allowing estimation of pH value.

Titration

• Titration: determining the concentration of an unknown sample (analyte) by controlled addition of a reagent (titrant).
• Acid-base Titration: determining the concentration of an acid or base by neutralizing it with a standard solution of a base or acid having known concentration.
• The molar ratio between HCl and NaOH is 1:1
• At neutralization: Moles of HCl = Moles of NaOH. So,
  Molarity{HCl} \times Volume{HCl} = Molarity{NaOH} \times Volume{NaOH}
• A suitable indicator for titration is a indicator which will change colour as close as possible to the equivalence points.