Chapter 2: Chemistry and Measurements – Study Notes

Chapter 2: Chemistry and Measurements

Section 2.1: Units of Measurement

Understanding units of measurement is fundamental in chemistry, as it ensures accurate communication and calculation of scientific data. The metric and SI (International System of Units) systems are standard in scientific work.

• Metric Units: Commonly used for length (meter, m), mass (gram, g), volume (liter, L), temperature (degree Celsius, °C), and time (second, s).

• SI Units: The official system for scientific measurements, including meter (m), kilogram (kg), cubic meter (m3), kelvin (K), and second (s).

• Unit Conversions: Essential for translating between different measurement systems (e.g., 1 kg = 2.20 lb, 1 m = 100 cm, 2.54 cm = 1 in, 1 L = 1000 mL, 1 L = 1.06 qt).

• Application Example: The Air Canada Flight 143 incident highlights the importance of correct unit conversions in real-world scenarios.

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

Section 2.2: Measured Numbers and Significant Figures

Significant figures (sig figs) reflect the precision of a measured value. They are crucial for reporting scientific data accurately.

• Rules for Significant Figures:

  • All nonzero digits are significant (e.g., 45.6 g has 3 sig figs).

  • Zeros between nonzero digits are significant (e.g., 205 m has 3 sig figs).

  • Zeros at the end of a decimal number are significant (e.g., 50.0 L has 3 sig figs).

  • Zeros at the beginning of a decimal number are not significant (e.g., 0.0004 s has 1 sig fig).

  • Zeros used as placeholders in large numbers without a decimal point are not significant (e.g., 850,000 m has 2 sig figs).

  • In scientific notation, only the digits in the coefficient are significant (e.g., 4.8 × 105 m has 2 sig figs).

• Exact Numbers: Numbers obtained by counting or defined relationships (e.g., 1 kg = 1000 g) have infinite significant figures and do not limit the precision of calculations.

Rule	Measured Number	Number of Significant Figures
Not a zero	45 g	2
Zero between nonzero digits	205 m	3
Zero at the end of a decimal	50.0 L	3
Zero at the beginning of a decimal	0.0004 s	1
Placeholder zero in large number	850,000 m	2

Section 2.3: Significant Figures in Calculations

When performing calculations, the number of significant figures in the result is determined by the least precise measurement.

• Multiplication and Division: The answer should have the same number of significant figures as the measurement with the fewest significant figures.

• Addition and 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.

Number to Round Off	Three Significant Figures	Two Significant Figures
8.4234	8.42	8.4
14.780	14.8	15
3256	3260	3300

Example (Multiplication):

$24.66\ \text{cm} \times 0.35\ \text{cm} = 8.631 \rightarrow 8.6\ \text{cm}^2$ (2 sig figs)

Example (Addition):

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

Section 2.4: Prefixes

Prefixes are used in the metric system to indicate multiples or fractions of units, allowing for concise expression of very large or small quantities.

Prefix	Symbol	Numerical Value	Scientific Notation	Equality
kilo	k	1,000	103	1 km = 1 × 103 m
mega	M	1,000,000	106	1 Mg = 1 × 106 g
centi	c	0.01	10-2	1 cm = 1 × 10-2 m
milli	m	0.001	10-3	1 mg = 1 × 10-3 g
micro	μ	0.000001	10-6	1 μg = 1 × 10-6 g
nano	n	0.000000001	10-9	1 nm = 1 × 10-9 m

Example: 2 mg of fentanyl is a lethal dose; the prefix 'milli-' is critical for safety.

The Cubic Centimeter

The cubic centimeter (cm3 or cc) is the volume of a cube with sides of 1 cm. It is equivalent to 1 milliliter (mL), and these units are used interchangeably in chemistry and medicine.

Equality: 1 cm3 = 1 cc = 1 mL

Section 2.5: Writing Conversion Factors

Conversion factors are ratios derived from equalities that allow conversion between units. They are essential for solving problems involving different measurement systems.

• Equalities: Express the same quantity in different units (e.g., 1 m = 100 cm, 1 lb = 16 oz, 1 kg = 2.20 lb).

• Conversion Factor Example: $\frac{1\ \text{kg}}{2.20\ \text{lb}}$ or $\frac{2.20\ \text{lb}}{1\ \text{kg}}$

• Significant Figures in Conversion Factors: Numbers in definitions (e.g., 1 kg = 1000 g) are exact and do not affect significant figures in calculations. Numbers from measurements (e.g., 1 kg = 2.20 lb) are not exact and do affect significant figures.

Quantity	Metric (SI)	U.S.	Metric-U.S.
Length	1 m = 1000 mm	1 ft = 12 in.	2.54 cm = 1 in. (exact)
Volume	1 L = 1000 mL	1 qt = 4 cups	946 mL = 1 qt
Mass	1 kg = 1000 g	1 lb = 16 oz	1 kg = 2.20 lb
Time	1 min = 60 s	1 min = 60 s	1 min = 60 s

Section 2.6: Problem Solving Using Unit Conversion Factors

Unit conversion is a systematic process for solving problems involving different units. The process involves three main steps:

1. State the given and needed quantities.

2. Find the equalities and write conversion factors.

3. Set up the problem to cancel units and calculate the answer.

Example: Convert 25 ms to s:

$25\ \text{ms} \times \frac{1\ \text{s}}{1000\ \text{ms}} = 0.025\ \text{s}$

Example: If a person weighs 164 lb, what is their body mass in kilograms?

Given: 164 lb Needed: kg Conversion: $1\ \text{kg} = 2.20\ \text{lb}$

Set up: $164\ \text{lb} \times \frac{1\ \text{kg}}{2.20\ \text{lb}} = 74.5\ \text{kg}$

Unit Conversions Involving Powers

When converting units raised to a power (e.g., cm2 to m2), the conversion factor must also be raised to that power.

Example: $2659\ \text{cm}^2 \times \left(\frac{1\ \text{m}}{100\ \text{cm}}\right)^2 = 0.2659\ \text{m}^2$

Equalities and Conversion Factors Within a Problem

Sometimes, equalities are specific to a problem (e.g., 1 tablet contains 500 mg of vitamin C). These can be used as conversion factors for calculations within that context.

Conversion Factors: Percentage

A percentage can be used as a conversion factor by expressing the relationship as parts per hundred.

Example: 18% body fat means 18 kg body fat per 100 kg body mass.

Section 2.7: Density

Density is a physical property that compares the mass of a substance to its volume. It is commonly used to identify substances and solve problems involving mass and volume.

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

• Units: For solids and liquids: $\frac{g}{cm^3}$ or $\frac{g}{mL}$; for gases: $\frac{g}{L}$

• Equality: 1 mL = 1 cm3

Example: An unknown liquid has a density of 1.32 g/mL. What is the volume of a 14.7 g sample?

$\text{Volume} = \frac{14.7\ \text{g}}{1.32\ \text{g/mL}} = 11.1\ \text{mL}$

Practice: John took 2.0 tsp of cough syrup. If the syrup had a density of 1.20 g/mL and there is 5.0 mL in 1 tsp, what was the mass in grams?

Mass = 2.0 tsp × 5.0 mL/tsp × 1.20 g/mL = 12 g

Additional info: These notes are structured to provide a comprehensive overview of measurement concepts, significant figures, unit conversions, and density, as covered in a typical GOB Chemistry curriculum.