Measurement and Problem Solving: Conversion Factors in Chemistry

Measurement and Problem Solving

Conversion Factors (Simplified)

Conversion factors are essential tools in chemistry for converting between different units of measurement. They allow us to express quantities in various units, facilitating calculations and comparisons.

• Conversion Factor: A ratio or fraction that relates two quantities expressed in different units.

• For example, 1 day is composed of 24 hours, so the conversion factors are:

  • $\frac{1\ \text{day}}{24\ \text{hr}}$

  • $\frac{24\ \text{hr}}{1\ \text{day}}$

• Given Amount: The value containing only one unit (the starting value in a conversion problem).

Example: If a recipe makes 18 servings but you need to serve 36 people, you can use a conversion factor to adjust the recipe accordingly.

• Key Steps:

  1. Identify the given amount.

  2. Determine the proper conversion factor(s).

  3. Multiply to convert to the desired unit.

Example: Claudia's "Ugly but Good" chocolate chip cookie recipe makes 18 servings. If the party requires 54 servings, the conversion factor is $\frac{54\ \text{servings}}{18\ \text{servings}} = 3$. Multiply all ingredient amounts by 3.

Common Conversion Factors

The most common conversion factors in chemistry involve units of length, volume, and mass. These are used to convert between metric and English units, or within the metric system itself.

Length	Volume	Mass
1 m = 100 cm 1 in = 2.54 cm	1 L = 1000 mL 1 qt = 946 mL	1 kg = 1000 g 1 lb = 454 g

Example: While packing for a trip, you need to ensure your suitcase does not exceed 23 kilograms. If your scale only reads in pounds, use the conversion factor $\frac{1\ \text{kg}}{2.2\ \text{lb}}$ to convert pounds to kilograms.

Practice Problems

• Practice 1: A patient has approximately 83 mL of blood pumped by their heart at each beat. If their pulse is 75 beats per minute, calculate the total blood pumped in one day. Identify the given amount and all conversion factors.

  • Given: 83 mL/beat

  • Conversion factors: $75\ \text{beats}/1\ \text{min}$, $60\ \text{min}/1\ \text{hr}$, $24\ \text{hr}/1\ \text{day}$

• Practice 2: For 7 hours, an intravenous bag delivers medication at a rate of 2.75 drops/second with a mass of 42 mg/drop. Identify the given amount and all conversion factors.

  • Given: 7 hr

  • Conversion factors: $60\ \text{min}/1\ \text{hr}$, $60\ \text{sec}/1\ \text{min}$, $2.75\ \text{drops}/1\ \text{sec}$, $42\ \text{mg}/1\ \text{drop}$

• Practice 3: Prescription drugs are often dosed in mg/kg of body weight. If a prescription is 10 mg/kg and a patient weighing 125 kg needs three tablets, each containing 125 mg, identify the given amount and all conversion factors.

  • Given: 10 mg/kg, 125 kg

  • Conversion factors: $1\ \text{tablet}/125\ \text{mg}$

Additional info: Conversion factors are fundamental in chemistry for unit analysis (dimensional analysis), ensuring that calculations are accurate and units are consistent throughout problem solving.