Measurements in Chemistry: SI Units, Temperature, Density, and Significant Figures

Measurements in Chemistry

International Standard (SI System)

The International System of Units (SI) is the globally accepted standard for scientific measurements. It provides a consistent framework for expressing physical quantities, ensuring clarity and uniformity in scientific communication.

• Origin: Established in France in 1790.

• Reference: Depends on a standard for reference (Earth).

• Decimal System: Units are based on 10 or multiples of 10.

• SI Revision: SI is a revised version of the metric system used in science.

• Global Use: Official measurement system of all but 3 countries (including the United States).

SI Base Units

SI base units are the fundamental units from which all other units are derived. Each physical quantity has a unique base unit.

Quantity	Unit Name	Symbol
Distance	meter	m
Time	second	s
Mass	kilogram	kg
Temperature	kelvin	K
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cd

SI Derived Units

Derived units are combinations of base units used to express other physical quantities.

Quantity	Unit Name	Symbol
Energy	joule	J
Force	newton	N
Pressure	pascal	Pa
Power	watt	W

Unit Prefixes

Prefixes are used to indicate multiples or fractions of units, making it easier to express very large or very small quantities.

Macro Prefixes

Factor	Prefix	Symbol
$10^1$	deca-	da-
$10^2$	hecto-	h-
$10^3$	kilo-	k-
$10^6$	mega-	M-
$10^9$	giga-	G-

Micro Prefixes

Factor	Prefix	Symbol
$10^{-1}$	deci-	d-
$10^{-2}$	centi-	c-
$10^{-3}$	milli-	m-
$10^{-6}$	micro-	μ-
$10^{-9}$	nano-	n-

Temperature Scales

Temperature is a fundamental physical property measured using different scales. The most common in chemistry are Celsius and Kelvin.

Celsius Scale

• Origin: Named after Swedish scientist Anders Celsius.

• Freezing Point of Water: 0 °C

• Boiling Point of Water: 100 °C

• Equal Intervals: The space between freezing and boiling points is divided into 100 equal parts.

Kelvin Scale (SI)

• Absolute Zero: Sometimes called the absolute zero scale; zero point is absolute zero.

• Origin: Named after Lord Kelvin.

• Freezing Point of Water: 273 K

• Boiling Point of Water: 373 K

• No Degree Symbol: Kelvin does not use the degree symbol.

• Conversion: $K = ^ ext{°C} + 273$ $^ ext{°C} = K - 273$

Temperature Conversion Examples

• Example 1: Convert 170 °C to K. $K = 170 + 273 = 443$ K

• Example 2: The boiling point of argon is 87 K. What is this in °C? $^ ext{°C} = 87 - 273 = -186$ °C

Units of Volume

Volume is the amount of space occupied by matter. It is commonly measured in cubic meters (m3) or liters (L).

• Calculation: Volume = length × width × height

• SI Unit: Cubic meter (m3)

• Liter: The volume of a cube 10 cm on each edge (1 L = 1000 cm3)

• Milliliter: 1 mL = 1 cm3

Measuring Density

Density is a physical property that relates the mass of an object to its volume. It is useful for identifying substances and predicting whether objects will float or sink.

• Definition: Density is the ratio of mass to volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: Commonly expressed as g/cm3 or g/mL.

Density Example Calculations

• Example 1: A metal with mass 614 g and volume 78 cm3: $\text{Density} = \frac{614}{78} = 7.87$ g/cm3

• Example 2: A plastic ball with mass 15.8 g and volume 19.7 cm3: $\text{Density} = \frac{15.8}{19.7} = 0.80$ g/cm3 (would float in gasoline, which has a density ~0.7 g/cm3)

• Example 3: Gold with density 19.3 g/cm3 and volume 0.93 cm3: $\text{Mass} = 19.3 \times 0.93 = 17.95$ g

• Example 4: Silicon with density 2.33 g/cm3 and mass 62.9 g: $\text{Volume} = \frac{62.9}{2.33} = 27.0$ cm3

• Example 5: Substance with density 3.26 g/cm3 and volume 0.350 cm3: $\text{Mass} = 3.26 \times 0.350 = 1.14$ g

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one estimated digit. They reflect the precision of a measurement.

• Reporting: Measurements are reported using significant figures.

• Accuracy: An answer cannot be more accurate than the least accurate measurement.

• Rounding: To round off, decide how many significant figures are needed and count from the left.

Rules for Significant Figures

• Non-zero digits: Always significant.

• Zeros between significant digits: Significant.

• Trailing zeros in decimal portion: Significant.

Significant Figures in Calculations

• Addition/Subtraction: The answer can have no more digits to the right of the decimal point than the measurement with the least number of digits to the right of the decimal point.

• Multiplication/Division: The answer must contain no more significant figures than the measurement with the least number of significant figures.

• Decimal Point: The position of the decimal point does not affect the number of significant figures.

Dimensional Analysis

Dimensional analysis is a method of problem solving that uses conversion factors to move from one unit to another. It is essential for converting unfamiliar or familiar units in chemistry.

• Method: Multiply by conversion factors to cancel units and obtain the desired unit.

• Example: $15 \text{ mg} \times \frac{1 \text{ g}}{1000 \text{ mg}} = 0.015 \text{ g}$

Scientific Notation

Scientific notation is a method for expressing very large or very small numbers in a compact form, making them easier to handle in calculations.

• Format: Exactly one non-zero digit is placed in front of the decimal point.

• Exponent: Indicates the number of times the decimal must be moved.

• Examples:

  • 5000 m = $5 \times 10^3$ m

  • 0.0006 g = $6 \times 10^{-4}$ g

  • 14 km = $1.4 \times 10^1$ km

  • 12 mg = $1.2 \times 10^1$ mg

Additional info: The notes cover foundational measurement concepts essential for General Chemistry, including SI units, conversions, density, significant figures, and scientific notation. These are critical for laboratory work and quantitative problem solving in chemistry.