Metric Conversions and Dimensional Analysis in GOB Chemistry

Metric Conversions and Dimensional Analysis

Introduction

Understanding how to convert between different units is a fundamental skill in General, Organic, and Biological (GOB) Chemistry. This section covers the use of metric conversion factors to solve problems involving volume and mass, which are common in laboratory and health science contexts.

Volume Conversions: Cubic Centimeters to Liters

Volumes in chemistry are often measured in cubic centimeters (cm3) or liters (L). Knowing how to convert between these units is essential for interpreting laboratory data and medication dosages.

• Key Point 1: 1 liter (L) = 1000 cubic centimeters (cm3)

• Key Point 2: To convert from cm3 to L, divide the number of cm3 by 1000.

• Formula:

$V_{(L)} = \frac{V_{(cm^3)}}{1000}$

• Example: A balloon has a volume of 3500 cm3. What is the volume in liters?

$V_{(L)} = \frac{3500\ cm^3}{1000} = 3.5\ L$

Mass Conversions: Milligrams to Grams

Mass is frequently measured in milligrams (mg) and grams (g) in both chemistry and health sciences. Converting between these units is necessary for calculating dosages and nutritional values.

• Key Point 1: 1 gram (g) = 1000 milligrams (mg)

• Key Point 2: To convert from mg to g, divide the number of mg by 1000.

• Formula:

$\text{Mass}_{(g)} = \frac{\text{Mass}_{(mg)}}{1000}$

• Example: The Daily Value (DV) for phosphorus is 800 mg. How many grams is this?

$\text{Mass}_{(g)} = \frac{800\ mg}{1000} = 0.8\ g$

Using Dimensional Analysis

Dimensional analysis is a systematic method for converting between units using conversion factors. It ensures that units cancel appropriately, leading to the correct answer.

• Key Point 1: Write the quantity to be converted as a fraction.

• Key Point 2: Multiply by the appropriate conversion factor so that units cancel.

• Key Point 3: Check that the final units are correct.

• Example: Convert 2500 mg to grams.

$2500\ mg \times \frac{1\ g}{1000\ mg} = 2.5\ g$

Common Metric Conversion Factors

Unit	Equivalent
1 L	1000 mL = 1000 cm3
1 g	1000 mg
1 kg	1000 g
1 m	100 cm = 1000 mm

Additional info: These conversion skills are foundational for later topics in GOB Chemistry, including solution preparation, stoichiometry, and interpreting nutritional labels.