Chap 1.2 Measurements, SI Units, and Significant Figures in Chemistry

Measurements in Chemistry

Types and Importance of Measurements

In chemistry, accurate measurements are essential for describing physical quantities and conducting experiments. Every measurement must include both a number and a unit to be meaningful. Using standardized units prevents costly errors and ensures clear communication among scientists.

• Number: Indicates the magnitude of the measurement.

• Unit: Specifies the scale or standard of the measurement (e.g., liters, grams).

• Example: The average adult has about 5.5 liters of blood.

SI Units and Metric System

Standard Units in Chemistry

The International System of Units (SI) is the standard system used in science. It is based on the metric system and includes specific base units for different physical quantities.

Quantity	SI Unit (Symbol)	Metric Unit (Symbol)	Equivalent
Mass	Kilogram (kg)	Gram (g)	1 kg = 1000 g
Length	Meter (m)	Meter (m)	1 m = 100 cm
Volume	Cubic meter (m3)	Liter (L)	1 m3 = 1000 L
Temperature	Kelvin (K)	Celsius degree (°C)	See conversion formulas below
Time	Second (s)	Second (s)	—

Additional info: Students should memorize the Quantity, SI Unit, and Metric Unit columns for common laboratory measurements.

Prefixes for Multiples of Units

Prefixes are used to express very large or very small quantities more conveniently. Each prefix represents a specific power of ten.

Prefix	Symbol	Base Unit Multiplied By	Example
mega	M	1,000,000 = 10^6	1 megameter (Mm) = 1,000,000 m
kilo	k	1,000 = 10^3	1 kilogram (kg) = 1,000 g
centi	c	0.01 = 10^-2	1 centimeter (cm) = 0.01 m
milli	m	0.001 = 10^-3	1 milligram (mg) = 0.001 g
micro	μ	0.000001 = 10^-6	1 micrometer (μm) = 0.000001 m
nano	n	0.000000001 = 10^-9	1 nanogram (ng) = 0.000000001 g
pico	p	0.000000000001 = 10^-12	1 picogram (pg) = 0.000000000001 g

• Example: The radius of a lithium atom is 0.000000000152 m, which is more conveniently written as 152 picometers (pm).

Significant Figures

Definition and Importance

Significant figures are the digits in a measurement that are known with certainty plus one estimated digit. They reflect the precision of a measurement and are crucial for reporting scientific data accurately.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros (at the beginning) are not significant.

• Trailing zeros to the right of the decimal point are significant.

• Exact numbers (e.g., counted items) have an infinite number of significant figures.

• Example: 0.0032 has two significant figures; 4.20 × 103 has three significant figures.

Measuring with Significant Figures

When reading a measurement from a device (e.g., a graduated cylinder), always record all certain digits plus one estimated digit. The last digit is uncertain by ±1.

• Example: A graduated cylinder reading between 17 and 18 mL may be recorded as 17.5 mL or 17.6 mL, depending on estimation.

Rules for Calculations with Significant Figures

• Multiplication/Division: The result should have no more significant figures than the measurement with the fewest significant figures.

• Addition/Subtraction: The result should have no more decimal places than the measurement with the fewest decimal places.

• Rounding:

  • If the first digit to be dropped is less than 5, drop it and all following digits.

  • If the first digit to be dropped is 5 or greater, increase the last retained digit by 1.

• Example: 2.4271 rounded to two significant figures is 2.4; 4.5832 rounded to two significant figures is 4.6.

Scientific Notation

Purpose and Format

Scientific notation is used to express very large or very small numbers in a compact form. Numbers are written as a product of a number between 1 and 10 and a power of ten.

• Format: $a \times 10^n$ where 1 ≤ a < 10 and n is an integer.

• Example: 215,000 = $2.15 \times 10^5$; 0.000215 = $2.15 \times 10^{-4}$

• Scientific notation clarifies the number of significant figures (e.g., $1.500 \times 10^8$ has four significant figures).

Mathematical Operations and Rounding

Rules for Calculations

• For multiplication or division, the answer cannot have more significant figures than the least precise measurement.

• For addition or subtraction, the answer cannot have more decimal places than the least precise measurement.

• Round only at the end of multi-step calculations.

Factor-Label Method (Dimensional Analysis)

Unit Conversions

The factor-label method (also called dimensional analysis) is a systematic way to convert one unit to another using conversion factors.

• General form: (Starting quantity) × (Conversion factor) = Equivalent quantity

• Conversion factors are ratios equal to 1, such as $1 \text{ km} = 0.6214 \text{ mi}$, so $\frac{1 \text{ km}}{0.6214 \text{ mi}}$ or $\frac{0.6214 \text{ mi}}{1 \text{ km}}$.

• Arrange conversion factors so that unwanted units cancel, leaving only the desired units.

• Example: Convert 0.22 mi to km: $0.22 \text{ mi} \times \frac{1 \text{ km}}{0.6214 \text{ mi}} = 0.354 \text{ km}$

1. Identify the information given.

2. Identify what is needed.

3. Find relationships and plan conversion steps.

4. Solve and check for reasonable units and values.

Common Laboratory Measurements

Mass, Length, Volume, and Temperature

• Mass: Amount of matter in an object (measured in grams or kilograms).

• Length: Distance between two points (measured in meters, centimeters, etc.).

• Volume: Space occupied by an object (measured in liters, milliliters, or cubic centimeters).

• Temperature: Measure of how hot or cold an object is (measured in degrees Celsius, Kelvin, or Fahrenheit).

Note: Mass does not depend on location, but weight (the force of gravity on an object) does.

Volume Units and Conversions

Unit	Equivalent
1 cubic meter (m3)	1000 liters (L)
1 liter (L)	1000 milliliters (mL) = 1000 cubic centimeters (cm3)
1 milliliter (mL)	0.001 liter (L) = 1 cubic centimeter (cm3)
1 quart (qt)	0.9464 liters (L)
1 fluid ounce (fl oz)	29.57 milliliters (mL)

Temperature Scales and Conversions

• Celsius (°C): Water freezes at 0°C and boils at 100°C.

• Kelvin (K): Absolute temperature scale; 0 K is absolute zero.

• Fahrenheit (°F): Water freezes at 32°F and boils at 212°F.

• To convert Celsius to Kelvin: $T(K) = T(°C) + 273.15$

• To convert Kelvin to Celsius: $T(°C) = T(K) - 273.15$

• To convert Celsius to Fahrenheit: $T(°F) = (1.8 \times T(°C)) + 32$

• To convert Fahrenheit to Celsius: $T(°C) = \frac{T(°F) - 32}{1.8}$

Energy and Heat

Definitions and Units

• Energy: The capacity to do work or supply heat.

• Kinetic energy: Energy of motion.

• Potential energy: Stored energy, often due to position.

• SI unit: Joule (J)

• Calorie (cal): Amount of heat needed to raise 1 g of water by 1°C.

• 1 kilocalorie (kcal): 1000 cal; 1 Calorie (used in nutrition) = 1 kcal.

• Conversion: $1 \text{ cal} = 4.184 \text{ J}$

Density and Related Concepts

Density

Density is the mass of an object divided by its volume. It is a physical property used to identify substances and compare materials.

• Formula: $\text{Density} = \frac{\text{Mass (g)}}{\text{Volume (mL or cm}^3)}$

• Common units: g/cm3 for solids, g/mL for liquids.

• Example: If two objects have the same mass, the one with higher density will have a smaller volume.

Specific Heat and Specific Gravity

• Specific heat: Amount of heat needed to raise the temperature of 1 g of a substance by 1°C. For water, specific heat = 1.00 cal/g°C.

• Specific gravity: Ratio of the density of a substance to the density of water at the same temperature. Measured with a hydrometer.

Additional info: Students should practice making measurements of mass, volume, temperature, and density in the laboratory to reinforce these concepts.