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 allows for accurate communication and calculation of physical quantities. The International System of Units (SI) is the standard system used in science.

• SI Units: Standardized units for length, mass, volume, temperature, and time.

• Common Units:

  • Length: meter (m)

  • Mass: gram (g), kilogram (kg)

  • Volume: liter (L), cubic meter (m3)

  • Temperature: degree Celsius (°C), kelvin (K)

  • Time: second (s)

• Conversion Examples:

  • 1 kg = 1000 g

  • 1 kg = 2.20 lb

  • 1 m = 100 cm

  • 2.54 cm = 1 in

  • 1 L = 1000 mL

  • 1 L = 1.06 qt

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) indicate the precision of a measured value. The rules for determining significant figures are essential for reporting and calculating scientific data.

• Significant Figure Rules:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Zeros at the end of a decimal number are significant.

  • Zeros at the beginning of a decimal number are not significant (placeholders).

  • Zeros at the end of large numbers without a decimal point are not significant.

  • Numbers in scientific notation: only the digits in the coefficient are significant.

• Exact Numbers:

  • Obtained by counting, not measured.

  • Have unlimited significant figures.

  • Used in definitions and unit relationships (e.g., 1 kg = 1000 g).

Rule	Measured Number	Number of Significant Figures
Not a zero	4.5 g	2
Zero between nonzero digits	205 m	3
Zero at end of decimal number	50.0 L	3
Zero at beginning of decimal number	0.00045 s	2
Zero at end of large number without decimal	850000 m	2

Example: 0.0050830 has 5 significant figures (leading zeros are not significant; all other digits are).

Section 2.3: Significant Figures in Calculations

When performing calculations, the number of significant figures in the result depends on the precision of the input values.

• 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.

• 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.

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): $24.66\ \text{cm} \times 0.35\ \text{cm} = 8.631$ (calculator display) Final answer: $8.6\ \text{cm}^2$ (two significant figures)

Example (Addition): $2.012 + 61.09 + 3.0 = 66.102$ (calculator display) Final answer: $66.1$ (rounded to tenths place)

Section 2.4: Prefixes

Metric and SI prefixes are used to express quantities that are much larger or smaller than the base unit. Understanding prefixes is crucial for interpreting scientific measurements.

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

Example: 2 mg of fentanyl is a very small but potent amount; the prefix 'milli' indicates 1/1000 of a gram.

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 often 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).

• Conversion Factor: A ratio used to convert from one unit to another (e.g., $\frac{1\ \text{m}}{100\ \text{cm}}$ or $\frac{100\ \text{cm}}{1\ \text{m}}$).

• Exact Numbers: Numbers in definitions (e.g., 1 kg = 1000 g) are exact and do not affect significant figures.

• Measured Numbers: Numbers obtained by measurement affect significant figures in calculations.

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 gal = 4 qt	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

Section 2.6: Problem Solving Using Unit Conversion Factors

Unit conversion is a systematic process used to change one unit to another using conversion factors. 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 mass in kg? $164\ \text{lb} \times \frac{1\ \text{kg}}{2.20\ \text{lb}} = 74.5\ \text{kg}$

Unit Conversions Involving Powers

When converting units involving powers (e.g., area or volume), the conversion factor must be raised to the appropriate power.

Example: Convert 2659 cm2 to m2: $2659\ \text{cm}^2 \times \left(\frac{1\ \text{m}}{100\ \text{cm}}\right)^2 = 0.2659\ \text{m}^2$

Equalities and Conversion Factors Within a Problem

Sometimes, equalities are specific to a problem, such as dosage in medicine or speed in physics.

• Example: One tablet contains 500 mg of vitamin C.

• Example: The car was traveling at a speed of 85 km/h.

Conversion Factors: Percentage

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

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

Equality	Conversion Factor	Significant Figures or Exact
18 kg body fat / 100 kg body mass	$\frac{18\ \text{kg body fat}}{100\ \text{kg body mass}}$	18 kg is measured; 100 kg is exact

Section 2.7: Density

Density is a physical property that compares the mass of an object to its volume. It is commonly used to identify substances and solve problems in chemistry.

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

• Units: g/mL for liquids, g/cm3 for solids, g/L for gases

• Example: An unknown liquid has a density of 1.32 g/mL. What is the volume of a 214.7 g sample? $\text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{214.7\ \text{g}}{1.32\ \text{g/mL}} = 162.7\ \text{mL}$

Practice: John took 2.0 teaspoons (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? $2.0\ \text{tsp} \times 5.0\ \text{mL/tsp} \times 1.20\ \text{g/mL} = 12\ \text{g}$

Additional info: These notes expand on the original slides by providing definitions, formulas, and examples for each concept, ensuring a self-contained study guide for GOB Chemistry students.