Quantitative Chemical Analysis: Principles, Calculations, and Experimental Procedures for Titrations

Fundamentals of Analytical Chemistry

• Analytical chemistry provides a toolbox of methods used to investigate the composition of matter.
• The primary aims of chemical analysis are:
  • Quantitative analysis: Determining the quantity of a substance.
  • Qualitative analysis: Determining the identity of a substance.
• Sample: The material being investigated during a chemical analysis.
• Analyte: The specific substance in the sample for which the identity or amount needs to be determined.
• Wet Chemical Analysis (Classical Analysis): The oldest classification of analysis techniques.
  • These methods involve chemical reactions and stoichiometry.
  • No electronic instrumentation is used, with the exception of a balance.
  • Common school-level examples include volumetric analysis, gravimetric analysis, and tests for anions.
• Instrumental Analysis: Involves modern, sophisticated electronic instrumentation and computer software.
  • Analytical instruments measure physical quantities that can be linked to the identity or quantity of chemical substances.
  • Examples of measured quantities: Absorption of electromagnetic radiation, potential difference, current, resistance, and thermal conductivity.

Volumetric Analysis and Titrations

• A titration is a specific type of quantitative classical analysis classified as volumetric analysis.
• During a titration, a solution containing the analyte (of unknown mass and concentration) is placed in a conical flask.
• A suitable reagent is chosen that will react completely with the analyte.
• A standard solution of this suitable reagent is added from a burette into the conical flask.
• The objective is to determine the exact volume of the reagent required to react completely with all of the analyte.
• Indicator: A colouring agent (dye) added to the conical flask. It changes colour at the point where the reaction is complete, signaling the end of the titration.
• Using stoichiometric calculations, the unknown concentration of the analyte in the solution can be calculated.

Molar Concentration and Solution Preparation

• When a solid dissolves in a liquid, molecules or ions are spread homogeneously throughout the liquid.
• Molar Concentration (Molarity): Defined as the number of moles of dissolved substance present per cubic decimetre ($dm^3$) or litre ($L$) of solution.
• Concentration of substance $A$ is denoted as $[A]$ or $c_A$.
• Units for concentration: $mol \cdot dm^{-3}$, $mol \cdot L^{-1}$, and $M$ (molar) are all equivalent.
• Standard Relationship Equation: The following equation relates mass, concentration, volume, and molar mass:
  • $m = c \times V \times M$
  • Where $m$ is mass, $c$ is concentration, $V$ is volume, and $M$ is molar mass.
• Volume Unit Conversions:
  • $1\,dm^3 = 1\,L = 1000\,cm^3 = 1000\,ml$

Practical Skills for Preparing a Standard Solution

• To prepare a solution of known concentration, follow these steps:
  1. Place the weighed mass of the substance (e.g., $0.584\,g$ of $NaCl$) into a volumetric flask.
  2. Add some distilled water and swirl the flask to dissolve the substance. Do not fill the flask completely at this stage.
  3. Once dissolved, add more distilled water to bring the volume almost to the mark.
  4. Use a dropper (propette) to add the final drops of distilled water to avoid overfilling and ensure the bottom of the meniscus is on the mark.
• Volumetric flasks are available in various capacities, including $10\,mL$, $25\,mL$, $50\,mL$, $100\,mL$, $250\,mL$, $500\,mL$, $1000\,mL$, $2000\,mL$, and $5000\,mL$.

Determination of Analyte Concentration using Stoichiometry

• For a general reaction: $n_A A + n_B B \rightarrow n_C C + n_D D$
• A shortcut equation relating concentration, volume, and stoichiometric coefficients ($n_A$ and $n_B$) is:
  • $\frac{c_A \times V_A}{n_A} = \frac{c_B \times V_B}{n_B}$
• Example Calculation: Determination of $NaOH$ concentration with standard oxalic acid ($H_2C_2O_4$):
  • Reaction: $2NaOH(aq) + H_2C_2O_4(aq) \rightarrow Na_2C_2O_4(aq) + 2H_2O(l)$
  • Given: $V_{NaOH} = 10.0\,cm^3$, $c_{oxalic\ acid} = 0.201\,mol \cdot dm^{-3}$, $V_{oxalic\ acid} = 28.15\,cm^3$.
  • Equation Setup: $\frac{c_{NaOH} \times 10}{2} = \frac{0.201 \times 28.15}{1}$
  • Resulting Concentration: $c_{NaOH} = 1.13\,M$.

Standardization of Reagents

• A standard solution has a precisely known concentration. Preparation methods include:
  • Using a Primary Standard: A substance whose exact concentration can be calculated directly from its mass and the volume of the solution. These substances are stable and of high purity.
  • Standardization against a Primary Standard: Many substances, like sodium hydroxide ($NaOH$), are not primary standards because they absorb water vapour and carbon dioxide from the atmosphere, which lowers their concentration over time:
  • $NaOH(aq) + CO_2(g) \rightarrow Na_2CO_3(aq)$.
• Standardization Definition: The process of determining the true concentration of a reagent that is not a primary standard.
• Example Comparison: If preparing a $0.100\,M\ NaOH$ solution by dissolving $0.400\,g$ in $100.0\,mL$, the actual concentration will often be between $0.099\,M$ and $0.110\,M$. To find the exact value, it must be titrated against a primary standard like oxalic acid dihydrate ($(COOH)_2 \cdot 2H_2O$).

Purities of Chemical Substances

• The price of a chemical depends on its preparation difficulty, import status, and degree of purity.
• Percent Purity Definition:
  • $\%\text{Purity} = \frac{\text{mass of pure substance}}{\text{mass of sample}} \times 100$
• The purest grade chemicals are the most expensive and are reserved for analytical work (quantitative and qualitative analysis).
• Chemicals of lower purity are often suitable for preparing other substances, as the purity of a prepared product is usually more dependent on the purification techniques used during its preparation than on the initial reagent purity.

Case Study: Quantitative Analysis of an Impure Oxalic Acid Sample

• Scenario: An impure sample of $H_2C_2O_4$ with a mass of $2.034\,g$ is dissolved in $100\,cm^3$ distilled water. $10.0\,cm^3$ samples are titrated with standardized $0.25\,mol \cdot dm^{-3}\ NaOH$. The average titration value is $16.50\,cm^3$.
• Step 1: Calculate moles of $NaOH$ used:
  • $n_{NaOH} = c \times V_{tit} = 0.25 \times \frac{16.50}{1000} = 4.125 \times 10^{-3}\,mol$
• Step 2: Relate to Oxalic Acid moles using stoichiometry:
  • Reaction: $H_2C_2O_4(aq) + 2NaOH(aq) \rightarrow Na_2C_2O_4(aq) + 2H_2O(l)$
  • $n_{oxalic\ acid} = \frac{1}{2} \times n_{NaOH} = 2.061 \times 10^{-3}\,mol$
• Step 3: Calculate mass of pure oxalic acid in the $10.0\,cm^3$ sample:
  • $m_{oxalic\ acid} = n \times M = (2.061 \times 10^{-3}\,mol) \times (90.035\,g \cdot mol^{-1}) = 0.186\,g$
• Step 4: Scale to the original volume ($100\,cm^3$):
  • Since $10/100 = 1/10$ of the sample was used, multiply the mass by 10.
  • $Total\ mass = 1.860\,g$
• Step 5: Calculate Percentage Purity:
  • $\%\text{Analyte} = \frac{1.860}{2.034} \times 100 = 91.4\%$

Experimental Procedures: Acetic Acid Concentration

• Apparatus: $50\,cm^3$ Burette, $10\,cm^3$ Pipette, Pipette pump, Propette.
• Chemicals: Acetic acid solutions, Phenolphthalein indicator, Sodium hydroxide ($\sim 0.035\,M$).
• Burette Preparation:
  • Use a funnel to add sodium hydroxide.
  • Ensure there are no air bubbles in the tip and tap sections. This is achieved by opening the tap wide or tapping the burette with a fingernail while the solution flows.
  • Fill to approximately the $0.00\,cm^3$ mark and remove the funnel before beginning.
• Titration Step-by-Step:
  1. Place $10.0\,cm^3$ of acetic acid into a conical flask using a pipette.
  2. Add $2-3$ drops of phenolphthalein and place on a white paper to clearly see colour changes.
  3. Rough Titration: Add $NaOH$ in $1\,cm^3$ increments until the pink end point is reached to estimate the volume ($V_B = V_2 - V_1$).
  4. Accurate Titration: Add $NaOH$ until the volume is $1.5\,cm^3$ less than the rough estimate, then add drop-by-drop while swirling.
  5. Stop when a single drop turns the indicator to a light, almost invisible shade of pink.
  6. Repeat until three titration values do not differ by more than $0.10\,cm^3$ from one another.
• Measurement Precision: Burette readings are noted to two decimals. For Class B pipettes, the second decimal is estimated as 0 or 5.

Determination of Benzoic Acid Purity

• Sample Preparation:
  • Weigh approximately $0.5\,g$ of benzoic acid (prepared in Experiment 2) to three decimal places.
  • Use a funnel to wash the benzoic acid into a $100.0\,cm^3$ volumetric flask with $50\,cm^3$ ethanol.
  • Shake to dissolve, then fill to the mark with distilled water using a propette for the last bit.
• Titration Procedure:
  • Perform a rough titration using a $10.0\,cm^3$ sample and $3$ drops of phenolphthalein.
  • Use standardized $0.035\,mol \cdot dm^{-3}\ NaOH$.
  • Perform accurate titrations to obtain three concordant values (within $0.10\,cm^3$ difference).
  • Calculate percentage purity using the average titration value.

Safety and Maintenance

• Corrosive Solutions: $NaOH$ solution is corrosive and can damage the skin. In case of accidental contact, wash the area thoroughly with large amounts of water.
• Waste Disposal: All chemical substances used or produced must be discarded into the specified waste containers.
• Lab Hygiene: Wash and pack away all apparatus. Ensure the workspace is clean and dry. Confirm all gas and water taps are fully closed before leaving the laboratory.