Unit Conversions

Introduction to Unit Conversions

Unit conversions are a fundamental skill in General Chemistry, as many problems require converting between different measurement systems. It is essential to convert all quantities to S.I. (International System of Units) before using them in equations to ensure consistency and accuracy in calculations.

• Unit conversion involves changing a measurement from one unit to another using appropriate conversion factors.

• Commonly encountered non-S.I. units include pounds (lbs), feet (ft), gallons (gal), and others.

• Always convert to S.I. units (such as kilograms, meters, liters) before substituting values into equations.

Conversion Factors and Ratios

Conversion factors are ratios that express how many of one unit are equal to another unit. They are used as fractions to cancel out unwanted units and introduce the desired units.

• Mass:

  • 1 kg = 2.2 lbs

  • 1 lb = 450 g

  • 1 oz = 28.4 g

• Length:

  • 1 km = 0.621 mi

  • 1 ft = 0.305 m

  • 1 in = 2.54 cm

• Volume:

  • 1 gal = 3.79 L

  • 1 mL = 1 cm3

  • 1 L = 1.06 qt

Steps for Converting Units

Follow these systematic steps to perform unit conversions:

1. Write the given and target units.

2. Write conversion factors/ratios as fractions. Arrange them so that unwanted units cancel and desired units remain.

3. Multiply all numbers in the numerator and denominator, then solve.

Unit Conversions with Exponents

When converting units with exponents (e.g., area, volume), apply the conversion factor as many times as indicated by the exponent.

• For example, to convert ft2 to m2, use the conversion factor for feet to meters twice:

Example Problems

• Convert 22 lbs into kg:

  • Use the conversion factor: 1 kg = 2.2 lbs

• Convert 67.5 mi/hr to m/s:

  • Use the conversion factors: 1 mi = 1.609 km, 1 km = 1000 m, 1 hr = 3600 s

• Convert 100 ft2 to m2:

  • Use the conversion factor: 1 ft = 0.305 m

Practice Problems

• Convert 850 ft to km:

  • Use the conversion factors: 1 ft = 0.305 m, 1 km = 1000 m

• Convert the speed of light (3.00×108 m/s) to yards/week (yd/wk):

  • Use the conversion factors: 1 m = 1.094 yd, 1 week = 604800 s

• How many gallons are in 1 cubic meter (m3)?

  • Use the conversion factors: 1 m3 = 1000 L, 1 gal = 3.79 L

Summary Table: Common Conversion Factors

The following table summarizes the most frequently used conversion factors in General Chemistry:

Additional info: Mastery of unit conversions is essential for success in all areas of General Chemistry, including stoichiometry, gas laws, and solution chemistry. Always check that units cancel appropriately and that your final answer is in the correct units.