Conversion Factors and Dimensional Analysis in GOB Chemistry

Conversion Factors and Dimensional Analysis

Introduction to Conversion Factors

Conversion factors are essential tools in chemistry for converting between different units of measurement. They allow students to solve problems involving length, volume, mass, and other quantities by relating one unit to another.

• Conversion Factor: A ratio or fraction that sets together two different units.

• Example: 1 day is composed of 24 hours.

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

  • or $\frac{24\ \text{hrs}}{1\ \text{day}}$

• Given Amount: A value containing only one unit.

  • Example: We spent 3 hours studying chemistry today.

Applying Conversion Factors: Worked Example

To solve problems using conversion factors, identify the given amount and all relevant conversion factors, then set up the calculation so that units cancel appropriately.

• Example: Clutch's "Ugly but Good" chocolate chip cookie recipe is always a hit at office parties. My budget is $80. The recipe makes 18 servings for the party. Each serving requires 8 chocolate truffle chips at a cost of $0.50 per 5 chocolate truffle chips. From the information provided, determine the given amount and all conversion factors.

  • Given Amount: $80

  • Conversion Factors:

    • $\frac{1\ \text{recipe}}{18\ \text{servings}}$

    • $\frac{1\ \text{serving}}{8\ \text{ctc}}$

    • $\frac{0.50\ \$}{5\ \text{ctc}}$

Common Conversion Factors

Length, Volume, and Mass Conversion Factors

The most common conversion factors in chemistry deal with units involved with length, volume, or mass. These are used frequently in laboratory calculations and everyday measurements.

Length	Volume	Mass
1 inch = 2.54 cm 1 meter = 1.094 yards 1 mile = 5280 feet 1 km = 0.6214 miles	1 L = 1.057 quarts 1 quart = 0.946 L 1 gallon = 3.785 L	1 lb = 454 g 1 kg = 2.205 lbs

Example: Luggage Weight Conversion

While packing for a trip to Spain, a traveler wishes to weigh their luggage to make sure it doesn't exceed 23 kilograms. Unfortunately, their bathroom scale for some reason can only weigh in ounces. What conversion factors could they use to determine the mass of their luggage?

• Given Amount: 1 oz

• Conversion Factors:

  • $\frac{1\ \text{kg}}{2.205\ \text{lb}}$

  • $\frac{1\ \text{lb}}{16\ \text{oz}}$

Practice Problems: Identifying Given Amounts and Conversion Factors

Practice 1: Heart Rate Calculation

A pulse of 75 beats per minute. It is calculated that the patient pumps $8,964 \times 10^3$ mL in one day. Identify the given amount and all conversion factors.

• Given Amount: 1,108,184

Practice 2: Intravenous Medication Delivery

For 7 hours, an intravenous bag delivers medication to a patient at a rate of 2.75 drops a second with a mass of 42 mg per drop. Identify the given amount and all conversion factors.

• Given Amount: 44.75

Practice 3: Prescription Drug Dosage

The dispensing of prescription drugs are usually prescribed in units of mg per kg of body weight. A new prescription drug has a recommended dosage of 11 mg/kg. A 75 lb child requires three tablets each weighing 125 mg for their recommended dosage. Identify the given amount and all conversion factors.

• Given Amount: 211

Summary Table: Conversion Factors Used in Practice Problems

Practice Problem	Given Amount	Conversion Factors
Heart Rate Calculation	1,108,184	75 beats/min, $8,964 \times 10^3$ mL/day
IV Medication Delivery	44.75	2.75 drops/sec, 42 mg/drop, 7 hours
Prescription Drug Dosage	211	11 mg/kg, 75 lb, 125 mg/tablet

Additional info:

• Dimensional analysis is the systematic approach to converting between units using conversion factors. It is a foundational skill in GOB Chemistry for solving quantitative problems.

• Always arrange conversion factors so that unwanted units cancel, leaving the desired unit.