Module 2 day 1

Module 2: Measurements

Lecture Schedule

• Today’s Topics:

  • Introduction to Measurements

  • International System of Units

  • Temperature Conversions

  • Derived Quantities

  • Significant Figures

  • Accuracy and Precision

• Upcoming Topics:

  • Day 2 (February 3rd): Significant Figures in Calculations, Dimensional Analysis: Single-Step Conversions

  • Day 3 (February 5th): Dimensional Analysis: Multistep Conversions, Dimensional Analysis: Derived Units

Scientific Measurement

• Definition: Quantities that can be measured such as length, mass, volume, temperature, etc.

• Requires both a number and a unit to describe a physical quantity.

• Measurement includes indication of uncertainty.

• Example: 61.2 kilograms.

• Without units, a number can be meaningless or confusing.

• In chemistry, we use the International System of Units (SI), an updated version of the metric system established in 1964.

Base Quantities and Units of the SI System

• Base Quantities:

  • Time: Symbol: t, Unit: second (s)

  • Mass: Symbol: m, Unit: kilogram (kg)

  • Amount of Substance: Symbol: n, Unit: mole (mol)

  • Luminous Intensity: Symbol: lv, Unit: candela (cd)

  • Temperature: Symbol: T, Unit: kelvin (K)

  • Electric Current: Symbol: I, Unit: ampere (A)

  • Length: Symbol: l, Unit: meter (m)

Temperature and Heat

• Temperature: Measure of the "hotness" or "coldness" of an object.

  • Units: Celsius, Fahrenheit, Kelvin.

• Heat: Form of energy (thermal energy) transferred between objects.

  • Unit: Joules (J).

• Key Difference: Temperature measures thermal state; heat denotes energy transfer.

Boiling Point and Freezing Point of Water

• Fahrenheit Values:

  • Boiling Point: 212 °F

  • Freezing Point: 32 °F

• Celsius Values:

  • Boiling Point: 100 °C

  • Freezing Point: 0 °C

• Kelvin Values:

  • Boiling Point: 373.15 K

  • Freezing Point: 273.15 K

Temperature Conversion Formulae

• Celsius to Fahrenheit:

  • T°F = 2 × T°C + 32

• Celsius to Kelvin:

  • T(Kelvin) = T°C + 273.15

  • Example: Conversion of 27.60 °C to Kelvin:

    • T(Kelvin) = 27.60 + 273.15 = 300.75 K

Common Unit Prefixes

• Micro (µ):

  • Prefix: µ, Factor: 10^{-6}, Example: 1 × 10^{-6} = 0.000001 m

• Milli (m):

  • Prefix: m, Factor: 10^{-3}, Example: 1 × 10^{-3} = 0.001 m

• Centi (c):

  • Prefix: c, Factor: 10^{-2}, Example: 1 × 10^{-2} = 0.01 m

• Deci (d):

  • Prefix: d, Factor: 10^{-1}, Example: 1 × 10^{-1} = 0.1 m

• Kilo (k):

  • Prefix: k, Factor: 10^{3}, Example: 1 × 10^{3} = 1000 m

Dimensional Analysis

• Example of converting micrometers to meters: How many meters are in 3.781 micrometers?

  • Calculation: 3.781 × 10^{-6} m

SI Derived Units

• Derived from base units.

  • Volume: SI unit is cubic meter (m³).

  • Commonly used units: Liter (L, equivalent to dm³) and milliliter (mL, equivalent to cm³).

  • Density: Mass per unit volume

  • SI unit for density: kg/m³; Commonly used units: g/cm³ for solids and liquids, g/L for gases.

Significant Figures in Measurements

• Significant Figures are Always Significant:

  • Nonzero digits, captive zeros (between nonzero digits), trailing zeros to the right of the decimal point or in scientific notation.

• Never Significant:

  • Leading zeros, trailing zeros before the decimal point.

Examples of Significant Figures

• Example: 0.00004010 kg

  • Leading zeros: not significant

  • Captive zero: significant

  • Trailing zero (right of decimal): significant

• Total Significant Figures: 4

Rounding Rules

• If the first digit removed is < 5, leave the preceding number unchanged:

  • 0.056432 -> 0.0564

• If the first digit removed is > 5, increase the preceding number by 1:

  • 0.69174 -> 0.692

• If the first digit removed is exactly 5, round to the closest even number:

  • 4.7350 -> 4.74; 4.745 -> 4.74

Accuracy vs. Precision

• Accuracy: Closeness of measurement to the true value.

  • Influenced by equipment construction/calibration & user technique.

  • Use average of multiple trials for better accuracy.

• Precision: Closeness of a series of replicate measurements to one another.

  • Determined using statistical methods, reflected by significant figures.

  • Example: 25.0°C vs. 25.000°C - the latter is more precise.

Visual Representation of Precision

• Precision in measurement:

  • Example: 22.8 (least precise), 22.73, 22.725 (most precise)

• Visualize data distribution through significant figures.