Chapter 11: Measurement and Data Processing

Question 1

Distinguish between qualitative and quantitative data

Answer 1

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

Quantitative data: numerical data
- Eg. Mass, volume, time

Question 2

What are random uncertainties in measurements?

Answer 2

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

Question 3

What are human limitations?

Answer 3

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)

Question 4

Distinguish between precision and accuracy

Answer 4

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

Question 5

What are systematic errors in experiments?

Answer 5

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)

Question 6

How are values with uncertainties quoted?

Answer 6

• 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)

Question 7

Distinguish between decimal places and significant figures

Answer 7

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

Question 8

How are results quoted to the appropriate number of d.p/s.f

Answer 8

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

Question 9

Calculate absolute and percentage uncertainties

Answer 9

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

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

Question 10

How are uncertainties combined?

Answer 10

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

Question 11

Calculate Index of Hydrogen Deficiency (IHD) based on molecular formula

Answer 11

• 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]

Question 12

Identify bonds present using infrared spectroscopy

Answer 12

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)

Question 13

Use mass spectrometry to gain information about the structure of an organic molecule

Answer 13

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

Question 14

Use nuclear magnetic resonance (NMR) spectroscopy to gain information about the structure of an organic molecule

Answer 14

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