Chemistry 102: Study Guide for SI Units, Measurements, and Density (Ch. 1–2)

SI and Metric Units

Standard Units in Chemistry

The International System of Units (SI) is the standard for scientific measurements. Understanding these units is essential for accurate communication and calculation in chemistry.

• SI Unit for Length: The meter (m) is the base unit for measuring length.

• Other Common SI Units: kilogram (kg) for mass, second (s) for time, kelvin (K) for temperature, mole (mol) for amount of substance.

Unit Conversions

Converting Between Units

Unit conversions are performed using conversion factors, which are ratios that express how many of one unit are equal to another unit.

• Example: Convert 3.0 lb to kg. Use the conversion factor 1 lb = 0.4536 kg.

  • Calculation: $3.0 \text{ lb} \times \frac{0.4536 \text{ kg}}{1 \text{ lb}} = 1.36 \text{ kg}$ (rounded to 1.4 kg)

Scientific Notation

Expressing and Converting Numbers

Scientific notation is used to express very large or very small numbers in a compact form.

• Example: 248,000 in scientific notation is $2.48 \times 10^5$.

• Example: $3.4 \times 10^{-4}$ in decimal form is 0.00034.

Metric Prefixes

Prefixes, Abbreviations, and Proportions

Metric prefixes indicate multiples or fractions of base units.

• Kilo- (k): $10^3$ (1,000 times the base unit)

• Milli- (m): $10^{-3}$ (1/1,000 of the base unit)

• Micro- (μ): $10^{-6}$ (1/1,000,000 of the base unit)

• Nano- (n): $10^{-9}$ (1/1,000,000,000 of the base unit)

• Example: There are 1,000,000 micrograms (μg) in a gram (g).

Using Conversion Factors

Applying Ratios to Change Units

Conversion factors are used to switch between units by multiplying by appropriate ratios.

• Example: Convert 50 inches to centimeters. Use 1 inch = 2.54 cm.

  • Calculation: $50 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 127 \text{ cm}$ (rounded to 100 cm in the example)

Significant Figures

Rules and Applications

Significant figures (sig figs) reflect the precision of a measured or calculated quantity.

• Counting Sig Figs: All nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros in a decimal number are significant.

• Example: 3210 has 3 significant figures.

• Multiplication/Division: The result should have as many sig figs as the value with the fewest sig figs.

  • Example: $2.45 \times 3.0 = 7.4$ (2 sig figs)

• Addition/Subtraction: The result should have as many decimal places as the value with the fewest decimal places.

  • Example: $5.45 + 3.02 = 8.47$ (rounded to 8.5)

Density and Its Applications

Calculating and Using Density

Density is the mass of a substance per unit volume. It is a useful property for identifying substances and converting between mass and volume.

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

• Example: What is the volume of 800.0 g of gasoline with a density of 0.740 g/mL?

  • Calculation: $\text{Volume} = \frac{800.0 \text{ g}}{0.740 \text{ g/mL}} = 1081 \text{ mL}$ (rounded to 1080 mL)

• Example: A lead weight raises water in a cylinder from 35 mL to 67 mL (volume change = 32 mL). Density of lead = 11.34 g/mL.

  • Calculation: $\text{Mass} = 32 \text{ mL} \times 11.34 \text{ g/mL} = 362.88 \text{ g}$ (rounded to 360 g)

Specific Gravity

Definition and Applications

Specific gravity is the ratio of the density of a substance to the density of water (at 4°C, 1.00 g/mL). It is a unitless quantity.

• Formula: $\text{Specific Gravity} = \frac{\text{Density of Substance}}{\text{Density of Water}}$

• Example: Cement with a density of 1.44 g/mL has a specific gravity of 1.44.

• Application: An object with a specific gravity less than 1 will float in water because its density is less than that of water.