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: The process of changing a measurement from one unit to another using conversion factors.

• Conversion Factor: A ratio or fraction that expresses how many of one unit are equal to another unit.

• Application: Used in calculations involving mass, length, volume, and other physical quantities.

Common Conversion Factors

The following table summarizes frequently used conversion factors for mass, length, and volume:

Steps for Converting Units

To convert from one unit to another, follow these systematic steps:

1. Write the given and target units.

2. Write conversion factors as fractions. Arrange them so that units cancel appropriately (the unit you want to remove should be in the denominator, and the unit you want to convert to should be in the numerator).

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

Note: When converting units with exponents (e.g., cm2 to m2), apply the conversion factor as many times as indicated by the exponent.

Example Problems

• Example 1: Convert 22 lbs into kg.

  • Given: 22 lbs

  • Target: kg

  • Conversion factor: 1 kg = 2.2 lbs

  • Calculation:

• Example 2: Convert 67.5 mi/hr to m/s.

  • Given: 67.5 mi/hr

  • Target: m/s

  • Conversion factors: 1 mi = 1.609 km, 1 km = 1000 m, 1 hr = 3600 s

  • Calculation:

• Example 3: Convert 100 ft2 to m2.

  • Given: 100 ft2

  • Target: m2

  • Conversion factor: 1 ft = 0.305 m

  • Calculation:

Practice Problems

• Convert 850 ft to km.

  • Possible answers: 259 km, 0.259 km, 2.79 × 106 km, 2.79 km

• The speed of light is approximately 3.00×108 m/s. Convert this speed to yards/week (yd/wk).

  • Possible answers: 1.84×1013 yd/wk, 1.98×1014 yd/wk, 1.78×1015 yd/wk, 1.8×107 yd/wk

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

Summary Table: Conversion Factors

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 properly and that your final answer is in the desired units.