SI Units and Measurements

Numbers and Chemistry

• Numbers are foundational in chemistry
• Scientific phenomena are described using units that represent measurable quantities
• Concepts central to quantitative chemistry:
  • Units of measurement
  • Measured and calculated quantities
  • Uncertainty in measurement
  • Significant figures
  • Dimensional analysis

SI Base Units

• Système International d'Unités describes the International System of Units (SI).
• SI units serve as fundamental units from which all other units are derived
• Each measurable quantity has a unique base unit

Common SI Base Units

• Mass is measured in kilograms (kg)
• Length is measured in meters (m)
• Time is measured in seconds (s or sec)
• Temperature is measured in Kelvin (K)
• Amount of substance is measured in moles (mol)
• Electric current is measured in Amperes (A or amp)
• Luminous intensity is measured in Candelas (cd)

Metric System Prefixes

• Prefixes alter base units into more convenient measures
• Examples of prefixes and their corresponding powers of ten:
  • Peta (P): 10^15
  • Tera (T): 10^12
  • Giga (G): 10^9
  • Mega (M): 10^6
  • Kilo (k): 10^3
  • Deci (d): 10^-1
  • Centi (c): 10^-2
  • Milli (m): 10^-3
  • Micro (μ): 10^-6
  • Nano (n): 10^-9
  • Pico (p): 10^-12
  • Femto (f): 10^-15
  • Atto (a): 10^-18
  • Zepto (z): 10^-21

Non-SI Metric Units

• Length is measured in angstroms (Å); 1 Å = 10^-10 m
• Mass is measured in atomic mass units (u or amu); 1 u = 1.66054 x 10^-27 kg
• Mass is measured in metric tons (t); 1 t = 10^3 kg
• Time is measured in minutes (min); 1 min = 60 s
• Time is measured in hours (h); 1 h = 3600 s
• Temperature is measured in degrees Celsius (°C); TK = t°C + 273.15
• Volume is measured in liters (L); 1 L = 1000 cm³

Useful Conversions

• Length:
  • 1 inch (in) = 2.54 cm
  • 1 yard (yd) = 0.9144 m
  • 1 mile (mi) = 1.609 km
• Mass:
  • 1 pound (lb) = 453.6 g
  • 1 ounce (oz) = 28.35 g
• Volume:
  • 1 gallon (gal) = 3.785 L
  • 1 quart (qt) = 946.4 mL
  • 1 fluid ounce (oz) = 29.6 mL

Mass and Length

• Fundamental units in science are mass and length
• Kilogram is the SI unit for mass
• Gram is the base unit of mass in the metric system
• Meter is the base unit for length

Measuring Mass

• Mass reflects the amount of material in an object
• Kilogram is the SI unit for mass (kg)
• Grams are used in the laboratory more frequently than kilograms because they provide more reasonable units for calculation purposes in chemistry
• Mass is determined by balances, which compare the weight of a sample to standard masses

Laboratory Length Measurements

• Meter is the SI unit for length
• Centimeter (cm) is equal to 10^-2 meters
• Millimeter (mm) is equal to 10^-3 meters

Volume

• A measure of length in 3 dimensions; (length)³
• The SI unit for volume is m³
• The liter (L) is commonly used in chemistry
• 1 L = 1 dm³
• Most lab measurements use liters (L)
• Chemical glassware indicates volume in L or mL
• 1 L = 1,000 mL
• 1 mL is equivalent to 1 cm³

Convention

Relating units of length and volume:

• 10 mm = 1 cm
• 10 cm = 1 dm
• 10 dm = 1 m
• 1 cm3 = (1 x 10-2 m)3 = 1 x 10-6 m3
• 1 dm3 = (1 x 10-1 m)3 = 1 x 10-3 m3
• 1 mL = 1 cm3
• 1 L = 1000 mL = 1000 cm3 = 1 dm3

SI Units for Volume

• Volume is not a base unit in the SI system; it is derived as (m x m x m = m³)
• Liters (L) and milliliters (mL) are the most common metric units for volume
• Liter (L) is equivalent to a cube with 1 decimeter sides
• Milliliter (mL) is equivalent to a cube with 1 centimeter sides

Density

• Density is a physical property
• Defined as mass divided by volume
• Common units are g/mL or g/cm³

Kinds of Numbers

• Exact numbers are either counted or defined, like 12 eggs in a dozen
• Inexact (or measured) numbers rely on measurements, which have built-in limitations from instruments and observers

Uncertainty in Measurements

• Accuracy varies among measuring devices
• Measured numbers inherently possess some degree of inaccuracy

Expressing Measurement Uncertainty

• Absolute uncertainty describes instrument uncertainty and readability error
  • For analog instruments, this is half of the smallest increment
  • For digital instruments, it equals the smallest scale division
• A measurement result is expressed as (reading) ± (absolute uncertainty) unit

Concentrations

• Molarity (c) is the number of moles of a substance per liter of solution
  • c = (mol of substance) / (L of solution)
• Molality (m) is number of moles of a substance per kilogram of solvent
  • m = (mol of solute) / (kg of solvent)
  • Changes with temperature because volume (and thus density) of solution increases with heating

Percent Composition

• Weight percent (wt%) is the mass of solute divided by the mass of total solution or mixture, multiplied by 100
• • Example: 95wt% ethanol means 95g of ethanol per 100g of solution
• Volume percent (vol%) is the volume of solute divided by the volume of total solution or mixture, multiplied by 100
• Density (ρ) is the mass of solute per volume of total solution or mixture, with units of g/mL
• Specific gravity is the density of a substance divided by the density of water at 4°C, having no units itself

Minute Concentrations

• Parts per million (ppm) and parts per billion (ppb) express trace concentrations
  • ppm = (mass solute/mass sample) x 10^6
  • ppb = (mass solute/mass sample) x 10^9
• If pH2O = 1g/mL, 1ppm = 1µg/mL = 1mg/L & 1ppb = 1ng/mL = 1µg/L

Errors in Measurement

• Measurements rely on proven techniques
• Repeating a measurement reflects reproducibility (precision)
• Measuring the same quantity by different methods gives confidence about the reliability of said measurement (accuracy)
• Uncertainty in measurement is called experimental error

Systematic Errors

• Systematic (Determinate) errors are attributed to issues with the instrument, method, or analyst
  • Worn instruments, unlevelled balances, reagent storage and use
  • Error in instrument calibration
  • Technique with parallax
• Observers are less than perfect
• These errors are usually difficult to detect but can be eliminated
• These type of errors have definite size and sign and are traced to specific sources (bias)

Determining Systematic Errors

• Analyze samples of known compositions and standard reference materials
• Analyze blank samples with no analyte
• Use different analytical methods to measure the same quantity
• Conduct "round robin" experiments, where independent laboratories measure identical samples

Random Errors

• Random (Indeterminate) errors appear from physical measurement capability, resulting from minor uncertainties in repetitive measurements
• Random errors follow no pattern
• Causes: readability of instruments and external effects

Responding to Random Errors

• Use sensitive and precise instruments and the data generated from them
• Increase runs of experimental replicates
• Random errors averaged, and can be reduced
• A precise experiment has small random error

Accuracy vs. Precesion

• Accuracy is the measured data's proximity to the actual value
• Precision is the proximity of several measurements to each other, which indicates reproducibility

Rules for Significant Figures

• Non-zero numbers are always significant; e.g., 3.456 has 4 significant figures
• Zeros between non-zero numbers are significant; e.g., 20,089 has 5 significant figures
• Trailing zeros count if the number has a decimal point; e.g., 500. has 3 significant figures
• Final zeros are not significant if there's no decimal point; e.g., 104,956 has 6 significant figures
• Final zeros to the right of the decimal point are significant; e.g., 3.00 has 3 significant figures
• Leading zeros are never significant; e.g., 0.00012 has 2 significant figures

Scientific Notation and Significant Figures

• Scientific notation communicates the number of significant figures
  • Report the number between 1 and 10 with the correct power of 10
  • Examples of significant figures in numbers expressed as scientific notation
  • 1.03 × 10^4 g (three significant figures)
  • 1.030 × 10^4 g (four significant figures)
  • 1.0300 × 10^4 g (five significant figures)

Calculations and Significant Figures

• Round addition or substraction answers based on the least signficant decimal place
• The answer has same number of significant figures as the quantity with the least number of significant figures when multiplying or dividing

Logarithms and Antilogarithms

• For n = 10^a implies log n = a and n is the antilogarithm of a
• Antilog has characteristic which is an Integer, and mantissa which is decimal
• The No. of digits in mantissa of log x = the no. s.f. in x

Random Error

• Absolute Deviation/Uncertainty, expresses the margin of uncertainty associated with a measurement.
• Relative Deviation/Uncertainty, compares magnitude of an absolute uncertainty to its corresponding measurement and it is dimensionless.
  • R.U = absolute uncertainty / magnitude of measurement
  • %R.U = R.U x 100

Mean and Standard Deviation

• Mean - is the center of distribution. It is as the sum of the measured values divided by the number of measurements.
• Standard Deviation, is a measure of the width of the distribution and is more accurate.
  • S = √ 1/n-1 Σi=1(xi – x̄)2
• Average is the square deviations about the mean, called the Variance
  • σ2 = Σ ΐ=1(xi – x)2/ n-1

Bell-Shaped Curve

• Empirical rule for data (68-95-99), only applies to a set of data approximately bell-shaped:
  • ≈ 68% of all scores fall with 1 standard deviation of the mean
  • ≈ 95% of all scores fall with 2 standard deviation of the mean
  • ≈ 99.7% of all scores fall with 3 standard deviation of the mean

Test your knowledge of the International System of Units (SI). Questions cover prefixes, base units, mass vs. weight, and error analysis. Evaluate your understanding of metric system conversions.