Unit Conversion and Fundamental Quantities in Chemistry

Matter and Measurements

Unit Conversions in Chemistry

Understanding and converting between different units is essential in chemistry for accurate measurement and calculation. The following are the key units and conversion factors commonly used in non-majors chemistry courses.

• Length:

  • 1 kilometer (km) = 1000 meters (m)

  • 1 meter (m) = 100 centimeters (cm) = 1000 millimeters (mm)

• Mass:

  • 1 kilogram (kg) = 1000 grams (g)

  • 1 gram (g) = 1000 milligrams (mg) = 1,000,000 micrograms (mcg or µg)

• Volume:

  • 1 Liter (L) = 1000 milliliters (mL)

  • 1 milliliter (mL) = 1 cubic centimeter (cm3 or cc)

• Density:

  • Density (d) is defined as mass per unit volume.

  • Formula: $d = \frac{\text{mass}~(m)}{\text{volume}~(v)}$ Common units: $\frac{g}{cm^3}$ or $\frac{g}{mL}$

• Energy:

  • 1 kilocalorie (kcal) = 1,000 calories (cal) = 1 food Calorie (Cal)

  • 1 calorie (cal) = 4.184 Joules (J)

• Moles:

  • 1 mole (mol) = $6.02 \times 10^{23}$ items (atoms, molecules, particles, etc.)

  • 1 mole of gas at STP (Standard Temperature and Pressure) = 22.4 L

• Pressure:

  • 1 atmosphere (atm) = 760 mm Hg = 760 torr

Examples of Unit Conversions

• Length Example: To convert 5 kilometers to meters: $5~\text{km} \times \frac{1000~\text{m}}{1~\text{km}} = 5000~\text{m}$

• Mass Example: To convert 2 grams to milligrams: $2~\text{g} \times \frac{1000~\text{mg}}{1~\text{g}} = 2000~\text{mg}$

• Volume Example: 250 mL is equal to 250 cm3 since 1 mL = 1 cm3

• Energy Example: 3 kcal = $3 \times 1000 = 3000$ cal

• Mole Example: 1 mole of water contains $6.02 \times 10^{23}$ molecules of H2O

• Pressure Example: 2 atm = $2 \times 760 = 1520$ mm Hg

Summary Table of Key Unit Conversions

Quantity	Unit Conversion
Length	1 km = 1000 m; 1 m = 100 cm = 1000 mm
Mass	1 kg = 1000 g; 1 g = 1000 mg = 1,000,000 µg
Volume	1 L = 1000 mL; 1 mL = 1 cm3
Density	$d = \frac{m}{v}$; units: g/cm3 or g/mL
Energy	1 kcal = 1000 cal = 1 Cal; 1 cal = 4.184 J
Mole	1 mol = $6.02 \times 10^{23}$ items; 1 mol gas at STP = 22.4 L
Pressure	1 atm = 760 mm Hg = 760 torr

Additional info:

• STP (Standard Temperature and Pressure) is defined as 0°C (273.15 K) and 1 atm pressure.

• Unit conversions are often performed using dimensional analysis, ensuring units cancel appropriately to yield the desired unit.