Chapter 11: Measurement and Data Processing

Qualitative data: non-numerical observations made during experiment - Eg. Precipitate forming, effervescence, colour change Quantitative data: numerical data - Eg. Mass, volume, time

Random uncertainties: uncertainties caused by limitations in the measuring apparatus or uncontrollable variables (wind/air pressure) that are inevitable in all experiments - Effect can be reduced by: taking repeated measurements (obtain a more reliable mean value that will more closely represent the true mean) - Will cause non-directional fluctuations (measurements will be distributed on both sides of the mean) • Represented by quoting an uncertainty (± ___) along with a value • Analogue instruments: uncertainty is half its smallest division • Digital instruments: uncertainty is its smallest division

Human limitations: random errors associated with the person conducting the experiment • Eg. Recording time to 3 d.p when human reaction time is 0.3s-0.5s (unrealistic data)

Precision: reproducibility of the results (how close the repeated values are to each other and the mean) - Affected by random uncertainties: the smaller the random uncertainty, the smaller the spread, and the higher the precision) Accuracy: how close the measured values are to the actual value - Affected by systematic error: low accuracy indicates systematic error

Systematic errors: errors introduced into an experiment by the experimental apparatus or procedure - Always causes directional fluctuations - Effect cannot be reduced by taking repeated measurements, and can only be reduced by modifying the experimental procedure • Represented by calculating percentage error and comparing it with the percentage uncertainty % error = Lit. value - Expt. value / Lit. value x 100% • If % error > %Δ, experiment has systematic error • If % error < %Δ, experiment worked well (random error > systematic error)

• Values should be quoted to the same number of decimal places as the uncertainty Eg. 157.47±0.1 –> 157.5±0.1 (1 d.p) 157.5±8 –> 158±8 (accurate to the ones place) 158±20 –> 160±20 (accurate to tens place) 160±100 –> 200±100 (accurate to the hundreds place)

Decimal places: number of digits after decimal point Significant figures: number of digits in a measurement, excluding leading zeroes and including/excluding lagging zeroes - Ambiguity of lagging zeroes can be avoided by expressing numbers in scientific notation

If calculation only involves addition and subtraction: - Final answer: same no. of d.p as piece of original data with the fewest d.p If calculation only involves multiplication and division: - Final answer: same no. of s.f as piece of original data with the fewest s.f

Percentage uncertainties (%Δ) = Absolute uncertainty/Value x 100% = Δa/a x 100% Absolute uncertainty (Δ) = Percentage uncertainty/100 x Value = %Δ/100 x a

Quantities added/subtracted: - Absolute uncertainties (Δ) are added together and rounded UP to the appropriate number of d.p Quantities multiplied/divided: - Percentage uncertainties (%Δ) are found and added up - Total %Δ is converted back to Δ

• Double bond/ring: IHD=1 • Triple bond: IHD=2 • Oxygen atom: does not affect IHD • Halogen atom: counted as H atom • Nitrogen atom: subtract 1 H atom for every N atom present • Benzene: IHD=4 (1 ring, 3 double bonds) C꜀HₕNₙOₒxₓ: IHD = 1/2 x [2c+2-h-x+n]

INFRARED SPECTROSCOPY: electromagnetic radiation passed through the sample, frequencies absorbed (peaks) correspond to bonds present - Below 1500 cm⁻¹: ‘fingerprint region’ - Above 1500 cm⁻¹: can identify bonds corresponding to functional groups based on % transmittance and intensity of peak (may not be able to distinguish between functional groups)

MASS SPECTROMETRY: sample bombarded with high-energy electrons to produce positive ions - Highest m/z value: molecular ion (M+: when just 1 electron is removed –> relative mR) - Fragmentation pattern: when molecule breaks apart into smaller fragments - (M+1)⁺ peak: presence of isotopes

NMR SPECTROSCOPY: energy from the radio frequency range of the electromagnetic spectrum - Provides information about the number of proton environments in a molecule and the ratio of the number of H atoms in each environment