Chapter 2: Chemistry and Measurements – Structured Study Notes

Chapter 2: Chemistry and Measurements

2.1 Units of Measurement

Understanding units of measurement is fundamental in chemistry, as it allows for the quantitative description of matter and its properties. The metric system and the International System of Units (SI) are the standard systems used globally.

• Metric System: A decimal-based system of measurement based on powers of ten.

• SI Units: The official system of measurement for scientific work, including units for volume, length, mass, temperature, and time.

Measurement	Metric	SI
Volume	liter (L)	cubic meter (m3)
Length	meter (m)	meter (m)
Mass	gram (g)	kilogram (kg)
Temperature	degree Celsius (°C)	kelvin (K)
Time	second (s)	second (s)

• Volume: The space occupied by a substance. 1 L = 1000 mL; 1 L ≈ 1.06 qt; 946 mL = 1 qt.

• Length: Based on the meter (m). 1 m = 100 cm; 1 m = 39.4 in.; 2.54 cm = 1 in.

• Mass: The quantity of material an object contains. 1 kg = 1000 g; 1 kg ≈ 2.20 lb; 454 g = 1 lb.

• Temperature: Measured in Celsius (°C) or Kelvin (K). Water freezes at 0°C (273.15 K) and boils at 100°C (373.15 K).

• Time: Measured in seconds (s), minutes (min), hours (h), days, and years (yr).

2.2 Measured Numbers and Significant Figures

Measured numbers are obtained when you measure a quantity, such as length, mass, or temperature. The accuracy of these measurements is communicated through significant figures (SFs).

• Measured Numbers: Determined by reading the value from a measuring instrument and estimating the last digit.

• Significant Figures: All the digits in a measured number, including the estimated digit, that represent the precision of the measurement.

Rule	Measured Number	Number of Significant Figures
Not a zero	4.5 g	2
Zero between nonzero digits	205 degrees Celsius	3
Zero at the end of a decimal number	50.0 L	3
Zero at the beginning of a decimal number	0.0004 s	1
Zero used as a placeholder in a large number without a decimal point	850 000 m	2

• Scientific Notation: Used to clearly indicate significant zeros. For example, 500 (3 SFs) vs. 3.0 x 102 (2 SFs).

2.3 Significant Figures in Calculations

When performing calculations, the number of significant figures in the result must reflect the precision of the measurements used.

• Multiplication/Division: The answer should have the same number of SFs as the measurement with the fewest SFs.

• Addition/Subtraction: The answer should have the same number of decimal places as the measurement with the fewest decimal places.

• Rounding Rules:

  • If the first digit to be dropped is 4 or less, 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 (Multiplication):

• 24.66 cm × 0.35 cm = 8.631 (calculator) → 8.6 cm2 (2 SFs)

Example (Addition):

• 2.012 + 61.09 + 3.0 = 66.102 (calculator) → 66.1 (rounded to tenths place)

2.4 Prefixes and Equalities

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

• Common Prefixes:

  • kilo- (k): 103

  • centi- (c): 10-2

  • milli- (m): 10-3

  • micro- (μ): 10-6

• Equality Example: 1 km = 1000 m; 1 mg = 0.001 g

Prefix	Symbol	Value	Scientific Notation
kilo	k	1,000	103
centi	c	0.01	10-2
milli	m	0.001	10-3
micro	μ	0.000001	10-6

2.5 Writing Conversion Factors

Conversion factors are ratios derived from equalities that allow conversion from one unit to another.

• Example: 1 m = 100 cm can be written as two conversion factors: $\frac{100\ \text{cm}}{1\ \text{m}}$ or $\frac{1\ \text{m}}{100\ \text{cm}}$

• Exact Numbers: Equalities between metric units or US units are exact and do not affect significant figures.

• Measured Numbers: Equalities between metric and US units (except 1 in. = 2.54 cm) are measured and affect significant figures.

2.6 Problem Solving Using Unit Conversion

Unit conversion is a key skill in chemistry, requiring the use of conversion factors to change from one unit to another.

• Steps:

  1. Identify the given and needed units.

  2. Determine the appropriate conversion factor(s).

  3. Set up the calculation so that units cancel appropriately.

• Example: Convert 2.44 m to cm: $2.44\ \text{m} \times \frac{100\ \text{cm}}{1\ \text{m}} = 244\ \text{cm}$

2.7 Density

Density is a physical property that relates the mass of a substance to its volume. It is useful for identifying substances and converting between mass and volume.

• Formula: $\text{Density} = \frac{\text{mass}}{\text{volume}}$

• Units: Commonly expressed as g/cm3 for solids and liquids, and g/L for gases.

• Application: Used to determine if an object will float or sink in a fluid, and to convert between mass and volume.

Example: If a metal sample has a mass of 48.0 g and displaces water from 25.0 mL to 33.0 mL, its density is:

• Volume displaced = 33.0 mL - 25.0 mL = 8.0 mL

• Density = $\frac{48.0\ \text{g}}{8.0\ \text{mL}} = 6.0\ \text{g/mL}$

Additional info:

• Tables and examples are included to reinforce concepts and provide practical applications relevant to health sciences and laboratory work.