Unit Conversions

Unit Conversions Important Tips  Always write every number with its associated unit.  Always include units in your calculation.  you can do the same kind of operations on units as you can on numbers  using units as a guide to problem solving is called dimensional analysis  Conversion factors are relationships between two units  Conversion factors can be generated from equivalence statements (e.g. 1 inch = 2.54 cm)  Arrange conversion factors so the starting unit is on the bottom of the first conversion factor Conceptual Plan given unit × related unit given unit = desired unit given unit × related unit desired unit given unit × related unit = desired unit Systematic Approach to Problem Solving Convert 5.70 L to cubic inches  Sort Information  Strategize Given: Desired: Conceptual Plan 5.70 in.3 L cm3 mL 1 mL = 1 cm3, 1 mL = 10−3 L 1 in. = 2.54 cm. Relationships: 1 mL 1 cm3 1 in.  Follow the conceptual plan to solve the problem Solution: 5.70 L ×  Sig. figs. and round Round  Check units are correct; number makes sense: in.3 << L 10‐3 L × 1 mL × 3 2.54 cm 3 = 347.835 in.3 347.835 in.3 = 348 in.3 (3 sig. fig.) conversion factor Mass Density as a Conversion Factor in3 Volume Density (g/cm3, g/mL) What is the mass in kg of 173,231 L of jet fuel whose density is 0.768 g/mL?  Sort Information  Strategize Given: Desired: Conceptual Plan 173.231L, density = 0.768 g/mL Mass, kg L mL g kg 1 mL = 0.768 g (from density) 1 mL = 10−3 L, 1 kg = 1000g Relationships: 1 mL 0.768 g  Follow the conceptual plan to solve the problem Solution: 173,231L ×  Sig. figs. and round Round  Check units and number makes sense 10‐3 L × 1 mL × 1 kg 1000g =1.3304 x105 kg 1.3304 x 105 kg = 1.33 x 105 kg SI Prefix Multipliers Prefix giga mega kilo deci centi milli micro mano pico Symbol G M k d c m µ n p Multiplier 1,000,000,000 1,000,000 1,000 0.1 0.01 0.001 0.0000001 0.0000000001 0.0000000000001 Volume (1 mL = 1 cm3) solid volume (cubic centimeters, cm3) 3 6 3 1 m = 10 cm 1 cm3 = 10-6 m3 = 0.000 001 m3 Power of 10 Base x 109 Base x 106 Base x 103 Base x 10-1 Base x 10-2 Base x 10-3 Base x 10-6 Base x 10-9 Base x 10-12 liquid or gas volume (milliliters, mL) 1 mL = 0.001 L = 10-3 L 1L = 1 dm3 = 1000 mL =103 mL Practice Problems 1. Use the prefix multipliers to express each measurement without any exponents. a) 1.2 × 10-9 m b) 22 × 10-15 s c) 1.5 × 109 g d) 3.5 × 106 L 2. Perform the following conversions. a) 25.5 mg to g b) 4.0 × 10-10 m to nm c) 0. 575 mm to µm d) 68.3 cm3 to cubic meters e) 242 lb to milligrams (1lb = 453.6 g) 3. The density of platinum is 21.45 g/cm3 at 20 °C. What is the volume of 87.50 g of this metal at this temperature? 4. Mercury is the only metal that is a liquid at room temperature. Its density is 13.6 g/mL. How many grams of mercury will occupy a volume of 95.8 mL? 5. Liquid nitrogen is obtained from liquefied air and is used to prepare frozen goods and in lowtemperature research. The density of the liquid at its boiling point (-196 °C) is 0.808 g/cm3. Convert the density to units of kg/m3. References: Tro, Chemistry: A Molecular Approach 2nd ed., Pearson Brown/LeMay/Bursten, Chemistry: The Central Science, 12th ed., Pearson 1. a)1.2 nm; b) 22 fs; c) 1.5 Gg; d) 3.5 ML 2. a) 2.55 x 10-2 g; b) 0.40 nm; c) 575 µm d) 6.83 x 10-5 m3 e) 1.10 x 108 mg 3. 50.35 cm3 4. 1.30 x 103 g 5. 808 kg/m3 Answers