Units of Measurement and Scientific Calculations in GOB Chemistry

Chapter 2: Units of Measurement

Measurement Systems

In chemistry, measurements are fundamental for quantifying substances and their properties. The Metric system and the International System of Units (SI) are standard systems used globally.

• Metric System: Uses base units such as meter (length), liter (volume), and gram (mass).

• SI Units: Internationally agreed units for scientific measurements.

Common Units and Their Applications

• Volume: The space occupied by a substance. Common units: Liter (L), milliliter (mL), centimeter cube (cm3).

• Length: Measured in meter (m). Subunits include centimeter (cm) and millimeter (mm).

• Mass: Measured in gram (g). Subunits include kilogram (kg), milligram (mg).

• Temperature: Measured in Celsius (°C), Kelvin (K), Fahrenheit (°F).

• Time: Measured in seconds (s), minutes, hours, days, weeks, months.

Examples of Unit Applications

• Indicate whether the unit describes length, mass, or volume:

  1. A person is 1.7 meter tall: Length

  2. A medication contains 500 mg of aspirin: Mass

  3. A bottle contains 1.5 liters of water: Volume

Measured and Exact Numbers

Measured Numbers

Measured numbers are obtained from measuring tools and are subject to uncertainty. Examples include height, weight, and temperature.

Exact Numbers

Exact numbers are counted or defined values and do not affect significant figures in calculations. Examples:

• 8 cookies

• 1 ft = 12 in

• 1 kg = 1000 g

Significant Figures (Sig Figs)

Definition and Identification

Significant figures are all the digits in a measured number, including the estimated digit. Rules for identifying sig figs:

• All non-zero numbers are significant.

• Zeros between non-zero numbers are significant.

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

• Leading zeros are not significant.

Examples of Significant Figures

Number	Sig Figs
4.5	2
2.65	3
2500	2
5.00 x 103	3
0.00045	2
85000 (no decimal)	2
1250000 (no decimal)	3

Calculations with Significant Figures

• Multiplication and Division: The answer should have the same number of sig figs as the measured number with the least sig figs.

• Addition and Subtraction: The answer should have the same number of decimal places as the measured number with the least decimal places.

Examples

• Multiplication: $1.34 \times 5.7 = 7.6$

• Addition: $23.445 + 7.83 = 31.28$

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, round up the last retained digit.

Prefixes and Equalities

Metric Prefixes

Prefixes are used to indicate multiples or fractions of units by powers of ten.

• Kilo-: $1 \text{ kilometer} = 1000 \text{ meters}$

• Milli-: $1 \text{ milligram} = 0.001 \text{ gram}$

Equalities

Equalities use two different units to describe the same quantity. They are used for conversions between metric and US systems, or within metric units.

• $1 \text{ in} = 2.54 \text{ cm}$

• $1 \text{ gal} = 3.78 \text{ L}$

Conversion Factors

Steps for Unit Conversion

Unit conversions are essential for translating measurements between different systems.

1. State the given and desired unit.

2. Write the equality and conversion factor.

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

Example: To convert gallons to liters, use the conversion factor $1 \text{ gal} = 3.78 \text{ L}$.

Temperature Conversion

Temperature Scales

Temperature can be measured in Kelvin, Celsius, or Fahrenheit. Each scale has its own conversion formula.

• Kelvin (K)

• Celsius (°C)

• Fahrenheit (°F)

Conversion formula:

• $T_{\text{Kelvin}} = T_{\text{Celsius}} + 273$

Density

Definition and Units

Density is a physical property defined as mass per unit volume. It is used to characterize substances.

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

• Units: g/mL or g/cm3

Additional info: These notes cover foundational measurement concepts essential for GOB Chemistry, including unit conversions, significant figures, and density calculations.