Measurement and Data Processing (IB)

Qualitative Analysis

Analysis based on measurements and associated uncertainties.

Quantitative Analysis

Comes from measurements and is always associated with uncertainties determined by either the apparatus or human limitations such as reaction times and sight.

Precision

Closeness of agreement between test results.

Accuracy

Closeness of agreement between a measurement result and the true value.

Scientific Notation

A way to express extremely large/small numbers in a compact form as a coefficient multiplied to a power of 10 (a x 10^n).

Significant Figures

Digits reflecting the precision of a measurement.

Experimental Error

Uncertainty associated with a measurement due to systematic or random errors.

Systematic Error

A flaw in experimental design or methodology. This affects the accuracy of the results.

Random Error

Occurs because of uncontrolled variables. Cannot be eliminated. This affects the precision of the results.

Absolute Uncertainty

Margin of uncertainty associated with a measurement result.

Relative Uncertainty

Ratio comparing the size of absolute uncertainty to the measurement.

Graphical Techniques

Methods to show the relationship between variables in graphs.

Sketched Graph

Graphs with labeled but unscaled axes, used to show qualitative trends such as proportional or inversely proportional relationships. Units are not required.

Drawn Graph

Graphs with labeled and scaled axes, based on quantitative measurements. They always display appropriate units for variables.

Dependence

Any statistical relationship between two sets of data or random variables.

Independent Variable

The variable that represents the cause, plotted on the x-axis in a graph of Y versus X.

Dependent Variable

The variable that represents the effect, plotted on the y-axis in a graph of Y versus X.

Correlation

Statistical measure indicating the relationship between variables.

Positive Correlation

A relationship where two variables increase or decrease in parallel.

Negative Correlation

A relationship where one variable increases while the other decreases, or vice versa.

Correlation Coefficient ( r )

A measure of the strength of the relationship between two variables, represented by the symbol r.

Scatter Plot

A graph that shows the scatter of various points, representing the relationship between two variables.

Degree of Unsaturation

Index used to determine the number of rings or double bonds in a compound.

Electromagnetic Spectrum

Range of electromagnetic radiation used in spectroscopy techniques.

r = +1

Indicates a perfect positive linear relationship where all points lie on a straight line.

r=0

Indicates no linear relationship; the points are completely scattered.

r=−1

Indicates a perfect negative linear relationship where all points lie on a straight line.

Slope (m)

The tangent of the angle (θ) that the line makes with the positive direction of the x-axis.

Intercept (c)

The point where the line cuts the y-axis at x=0.

Extrapolation

The process of estimating values beyond the given data range based on the trend of the data.

Equation of a Line

Represented as y=mx+b, where m is the slope and b is the y-intercept.

Best Fit Line

A straight line that minimizes the distance between itself and the data points in a scatter plot.

Degree of Unsaturation (IHD)

A measure used to determine the number of rings or double bonds in a molecular formula.

Double Bond

Contributes 1 IHD.

Triple Bond

Contributes 2 IHD.

Ring

Contributes 1 IHD.

Aromatic Compound

Contributes 4 IHD (3 double bonds + 1 ring).

IHD Formula

For CcHhNnOoXx: IHD=0.5(2c+2−h−x+n).

Electromagnetic Spectrum (EMS)

The range of all types of electromagnetic radiation. Different regions of the spectrum form the basis for various types of spectroscopy.

Planck's Equation

Relates the energy of radiation (E) to its frequency (v): E=hv, where h=6.63×10−34 J⋅s.

X-ray Spectroscopy

Uses high-energy X-rays to remove electrons from inner atomic energy levels, providing structural information such as bond distances and angles (basis of X-ray crystallography).

UV-Vis Spectroscopy

Based on visible and UV light causing electronic transitions, providing information about the electronic energy levels in atoms or molecules.

Infrared (IR) Spectroscopy

Uses IR radiation to cause molecular vibrations (stretching, bending, twisting) that provide information about functional groups.

Microwave Spectroscopy

Causes molecular rotations and provides information about bond lengths.

NMR Spectroscopy

Uses radiowaves in a strong magnetic field to induce nuclear spin transitions, giving information about the chemical environments and connectivity of atoms in a molecule.

Infrared Spectroscopy (Spring Model)

Covalent bonds are modeled as springs that stretch, bend, or twist, causing molecular vibrations. This model forms the basis for IR spectroscopy.

Hooke's Law

Describes the force required to cause vibration in the spring model of IR spectroscopy.

Vibration Frequency

Lighter atoms vibrate at higher frequencies; heavier atoms vibrate at lower frequencies.

Multiple Bonds

Multiple bonds (e.g., double and triple bonds) follow the same trend as lighter atoms, vibrating at higher frequencies.

Bond Enthalpy and Absorption

Different molecules absorb at different frequencies due to variations in bond enthalpy.

Wavenumber

IR absorptions are typically reported as wavenumber (1/λ), measured in cm−1.

Proton NMR Spectroscopy (¹H NMR)

Provides information about the different chemical environments of hydrogen atoms in a molecule.

Spin States of Hydrogen Nuclei

Based on the principle that hydrogen nuclei have two possible spin states and act like tiny magnets.

Chemical Shift

The position of the spin relative to the standard spin (tetramethylsilane, TMS).

Hydrogen Ratio

Provides the relative number of hydrogens in each environment, presented as a ratio.

Area Under the Curve

The area under the curve in an NMR spectrum corresponds to the number of hydrogens in that environment.

Mass Spectroscopy

Provides additional information about functional groups in a molecule.

Molecular Ion (M⁺)

Formed when a gaseous molecule is ionized; represents the intact molecule's ion.

Fragmentation Pattern

The pattern in a mass spectrum showing the masses of fragments after functional groups are removed.

Molecular Ion Peak

The peak in a mass spectrum corresponding to the molecular mass of the compound.