3.13 Notes on Beer-Lambert Law and Spectroscopy

  • Introduction to Beer-Lambert Law

    • The topic focuses on the Beer-Lambert Law within the context of spectroscopy.
    • Spectroscopy involves exposing a sample to electromagnetic radiation and obtaining data to understand its properties.

  • Devices Used

    • Spectrophotometer or colorimeter is used to analyze the concentration of solutions.
    • A cuvette, a small plastic container, is filled with the solution for analysis.

  • Operation of Colorimeter

    • A beam of light with a specific wavelength is directed through the cuvette.
    • A detector measures the light transmitted through the sample, indicating its concentration.

  • Example of Absorbance

    • Concentrated solutions (e.g., cherry Kool Aid) absorb more light, resulting in lower transmitted light (high absorbance).
    • More dilute solutions allow more light to pass through, indicating lower absorbance.

  • Beer-Lambert Law Equation

    • The relationship between absorbance (A), molar absorptivity (a), path length (b), and concentration (c) is expressed as:
      A=a×b×cA = a \times b \times c
    • Where:
    • A = Absorbance (dimensionless)
    • a = Molar absorptivity (L/(mol·cm))
    • b = Path length in cm
    • c = Concentration in moles per liter (M)

  • Graphical Analysis

    • The greater the concentration, the greater the absorbance.
    • A higher concentration results in less transmitted light detected.

  • Sample Problem

    • A 3.89 g sample of ore dissolved in nitric acid and diluted to 25 mL was analyzed.
    • Given the absorbance of 0.45, the estimated molar concentration from a graph is 0.080 M.
    • To find the number of moles:
    • Convert 25 mL to liters: 25 mL=0.025 L25 \text{ mL} = 0.025 \text{ L}
    • Use the molarity formula:
      Moles=Molarity×Volume in Liters=0.080 M×0.025 L=0.002 moles\text{Moles} = \text{Molarity} \times \text{Volume in Liters} = 0.080 \text{ M} \times 0.025 \text{ L} = 0.002 \, \text{moles}
    • Calculate the mass percent of cobalt in the or sample to find that it is approximately 30.3%.

  • Common Experiment Errors

    • If absorbance is lower than expected (dot below the line), it suggests dilution may have occurred due to contamination (e.g., water droplets in cuvette).
    • If absorbance is higher than expected, it may be due to fingerprints on the cuvette blocking light, thus incorrectly showing higher absorbance.

  • Creating Standard Solutions

    • Dilution equation for creating a desired concentration of solutions:
      M<em>1V</em>1=M<em>2V</em>2M<em>1V</em>1 = M<em>2V</em>2
    • Example: Creating a 0.02 M solution from a 0.1 M solution.
    • Required final volume: 10 mL.
    • Calculation:
      • M<em>1=0.1 M,M</em>2=0.02 M,V2=10 mLM<em>1 = 0.1 \text{ M}, M</em>2 = 0.02 \text{ M}, V_2 = 10 \text{ mL}
      • Rearranging gives:
        V<em>1=M</em>2V<em>2M</em>1=0.02×100.1=2 mLV<em>1 = \frac{M</em>2V<em>2}{M</em>1} = \frac{0.02 \times 10}{0.1} = 2 \text{ mL}
      • Add 8 mL of water to 2 mL of the concentrated solution to achieve the desired concentration.

  • Conclusion

    • Understanding the Beer-Lambert Law is essential for accurately analyzing solutions using spectroscopy.
    • This unit has provided comprehensive knowledge to prepare for future applications of spectrophotometric analysis.