Chemistry and Measurements: Structured Study Notes for GOB Chemistry

Chemistry and Measurements

Units of Measurement

The metric system and the International System of Units (SI) are the standard systems used by scientists worldwide for measuring length, volume, mass, temperature, and time. Understanding these units is fundamental for accurate scientific communication and calculations.

• Length: Measured in meters (m) and centimeters (cm). 1 m = 100 cm; 1 m = 39.4 in; 2.54 cm = 1 in.

• Volume: Measured in liters (L) and milliliters (mL). 1 L = 1000 mL; 1 L = 1.06 qt; 946 mL = 1 qt.

• Mass: Measured in grams (g) and kilograms (kg). 1 kg = 1000 g; 1 kg = 2.20 lb; 454 g = 1 lb.

• Temperature: Measured in degrees Celsius (°C) and Kelvin (K). Water freezes at 0°C and boils at 100°C; Kelvin scale starts at 0 K.

• Time: Measured in seconds (s), minutes (min), hours (h), days, and years (yr). SI unit is the second (s).

Measured Numbers and Significant Figures

Measured numbers are obtained by measuring physical quantities. The precision of these measurements is indicated by significant figures (SFs), which include all certain digits plus one estimated digit.

• Significant Figures: All nonzero digits, zeros between digits, and zeros at the end of a decimal number are significant. Zeros before the first nonzero digit are not significant.

• Scientific Notation: Used to clarify which zeros are significant in large numbers.

• Exact Numbers: Obtained by counting or definitions; they have unlimited significant figures and do not affect SF calculations.

Rules for Rounding Off

• 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.

Operations with Significant Figures

When performing calculations, the number of significant figures in the result depends on the operation:

• Multiplication/Division: The result has the same number of SFs as the measurement with the fewest SFs.

• Addition/Subtraction: The result has the same number of decimal places as the measurement with the fewest decimal places.

Metric System Prefixes

Prefixes are used to indicate multiples or fractions of units in the metric system. They help express measurements in convenient sizes.

• Common Prefixes: kilo (1000), centi (0.01), milli (0.001), micro (0.000001).

• In medicine, 'mc' is used for micro to avoid confusion.

Metric Prefixes Table

Prefix	Symbol	Value
kilo	k	1000
centi	c	0.01
milli	m	0.001
micro	mc	0.000001
nano	n	0.000000001

Equalities and Conversion Factors

Equalities express relationships between units and are used to create conversion factors for unit conversions.

• Example: 1 L = 1000 mL can be written as $\frac{1000\ mL}{1\ L}$ or $\frac{1\ L}{1000\ mL}$.

• Conversion factors are used in calculations to change units.

• Exact numbers in equalities do not affect significant figures; measured numbers do.

Problem Solving Using Unit Conversion

Unit conversion is a systematic process involving the identification of given and needed units, selection of appropriate conversion factors, and calculation.

1. State the given and needed quantities.

2. Write a plan to convert the units.

3. State the equalities and conversion factors.

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

Example Calculation

• Convert 164 lb to kg: $\frac{1\ kg}{2.20\ lb}$; $164\ lb \times \frac{1\ kg}{2.20\ lb} = 74.5\ kg$

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

Density and Specific Gravity

Density is a physical property that compares the mass of an object to its volume. Specific gravity is the ratio of the density of a substance to the density of water.

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

• Units: g/mL or g/cm3 for solids and liquids; g/L for gases.

• Specific Gravity: $\text{Specific Gravity} = \frac{\text{Density of sample}}{\text{Density of water}}$ (unitless)

Example Density Calculation

• Mass = 48.0 g; Volume displacement = 33.0 mL - 25.0 mL = 8.0 mL

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

Applications in Health and Toxicology

Measurements and conversions are essential in health sciences for calculating dosages, evaluating toxicity, and expressing nutrient requirements.

• Toxicology: Dosage is measured in mg/kg or mcg/kg. LD50 is the lethal dose for 50% of test animals.

• Nutrition: Daily values are expressed using metric prefixes.

Concept Map: Chemistry and Measurements

Measurements in chemistry involve metric units, significant figures, prefixes, equalities, conversion factors, density, and specific gravity. These concepts are interconnected and essential for accurate scientific calculations.

Summary Table: Common Equalities and Conversion Factors

Equality	Conversion Factor 1	Conversion Factor 2
1 L = 1000 mL	$\frac{1000\ mL}{1\ L}$	$\frac{1\ L}{1000\ mL}$
1 kg = 2.20 lb	$\frac{2.20\ lb}{1\ kg}$	$\frac{1\ kg}{2.20\ lb}$
1 m = 100 cm	$\frac{100\ cm}{1\ m}$	$\frac{1\ m}{100\ cm}$
1 day = 24 h	$\frac{24\ h}{1\ day}$	$\frac{1\ day}{24\ h}$
1 h = 60 min	$\frac{60\ min}{1\ h}$	$\frac{1\ h}{60\ min}$

Example: Multi-Step Conversion

• How many minutes are in 1.4 days?

• Step 1: $1.4\ days \times \frac{24\ h}{1\ day} \times \frac{60\ min}{1\ h} = 2.0 \times 10^3\ min$

Example: Dosage Calculation

• Prescribed: 0.150 mg Synthroid; Tablet contains 75 mcg Synthroid.

• Step 1: $0.150\ mg \times \frac{1000\ mcg}{1\ mg} \times \frac{1\ tablet}{75\ mcg} = 2\ tablets$

Example: Density Problem

• John took 2.0 tsp of cough syrup (density = 1.20 g/mL; 1 tsp = 5.0 mL).

• Step 1: $2.0\ tsp \times \frac{5.0\ mL}{1\ tsp} \times \frac{1.20\ g}{1\ mL} = 12\ g$

Example: Volume from Density

• Sample mass = 14.7 g; density = 1.32 g/mL.

• Step 1: $14.7\ g \times \frac{1\ mL}{1.32\ g} = 11.1\ mL$

Summary

Mastery of units, significant figures, conversion factors, and density calculations is essential for success in GOB Chemistry. These skills are foundational for laboratory work, health sciences, and everyday applications.