CHEm 211

Background on Analytical Concepts

• Concentration Calculation: A student adds 0.01009 g of PbCl₂ to 40 mL of deionized water.

  • Initial concentration of dissolved lead salt can be calculated using the formula:

    [PbCl₂] = (mass of PbCl₂) / (molar mass of PbCl₂ * volume of solution)

• Signal(s): Measured quantities that correlate to the amount of analyte present in a sample.

  • Noise: Random fluctuations in the measured signal.

  • Signal-to-Noise Ratio (S/N): Magnitude of analyte signal compared to background noise.

Analytical Terminology

• Limit of Detection (LOD): The smallest quantity of analyte that can be detected but not quantitated.

  • Conceptually defined as:LOD = Smb + z * (𝍳 mb)

    • Where z = 3 for LOD.

• Limit of Quantitation (LOQ): The smallest concentration of analyte that can be quantitatively measured with acceptable precision and accuracy.

  • Defined as:LOQ = Smb + z * (𝍳 mb)

    • Where z = 10 for LOQ.

Signal Averaging in Analysis

1. Calculate LOD and LOQ from raw data.

2. Interconvert between signal LOD or LOQ and concentration LOD or LOQ.

3. Articulate the meanings for signal and concentration being:

   • Below LOD

   • Between LOD and LOQ

   • Above LOQ

Controls in Analytical Methodology

• Positive Control: A standard sample known to contain the analyte, ensuring the method functions correctly.

• Negative Control: A standard sample without analyte to identify false positives.

Figures of Merit

• Used to characterize and validate analytical methods includes:

  1. Accuracy: Closeness of measured value to the true value.

  2. Precision: Agreement amongst repeated measurements.

  3. Sensitivity: The ability to measure small changes in analyte concentration.

  4. Selectivity: Ability to measure the analyte without interference from other species.

  5. Dynamic Range: Range of analyte concentration over which the method provides a valid response.

  6. Robustness: Method's resilience to small changes in experimental conditions.

Uncertainty

• Random Uncertainty: Variation in measurements due to unpredictable factors (e.g., environmental conditions).

• Systematic Uncertainty: Consistent deviations from the true value, often due to flaws in the measurement system.

Types of Errors in Measurements

1. Instrument Errors: Calibration drift, voltage fluctuations, etc.

2. Method Errors: Issues such as incomplete reactions or interferences.

3. Personal Errors: Mistakes made by the experimenter (e.g., recording errors).

Propagation of Uncertainty

• Propagation in mathematical operations needs to consider:

  • Total uncertainty when adding or subtracting as:(a ± σ_a) + (b ± σ_b) = (a + b) ± √(σ_a² + σ_b²)

  • For multiplying or dividing:resulting RSD = √(RSD_a² + RSD_b²)

Statistical Testing

• Tests are used to determine if differences between values are significant. Commonly discussed tests:

  1. t-test: Compares the means between two populations.

  2. F-test: Compares variances between two populations.

Equilibrium Constant

• The equilibrium constant ( K = [products]^{coefficients} / [reactants]^{coefficients}

• Pure solids and liquids excluded from equilibrium expressions as their activities equal 1.

Strong and Weak Acids/Bases

• Strong acids/bases ionize completely in solution, while weak acids/bases do not; they have equilibrium constants (Ka for acids and Kb for bases).

Polyprotic Acids

• Acids that can donate more than one proton (e.g., phosphoric acid), showing sequential ionization with distinct equilibrium constants (Ka).

Amphiprotic Substances

• Substances that can act as either an acid or a base (e.g., bicarbonate) and can participate in multiple equilibria.