Metric Conversions and Dimensional Analysis in GOB Chemistry

Metric Conversions and Dimensional Analysis

Introduction to Metric Conversions

Metric conversions are essential in chemistry for expressing measurements in different units. Understanding how to convert between units such as centimeters cubed (cm3) and liters (L), or milligrams (mg) and grams (g), is fundamental for solving quantitative problems in GOB Chemistry.

Volume Conversions: Cubic Centimeters to Liters

Volume is commonly measured in cubic centimeters (cm3) and liters (L) in chemistry. The conversion between these units is based on the metric relationship:

• 1 liter (L) = 1000 cubic centimeters (cm3)

To convert a volume from cm3 to L, use the following formula:

$\text{Volume in liters} = \frac{\text{Volume in cm}^3}{1000}$

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

• Calculation: $\frac{3500\ \text{cm}^3}{1000} = 3.5\ \text{L}$

Mass Conversions: Milligrams to Grams

Mass is often measured in milligrams (mg) and grams (g). The metric relationship is:

• 1 gram (g) = 1000 milligrams (mg)

To convert mass from mg to g, use the following formula:

$\text{Mass in grams} = \frac{\text{Mass in mg}}{1000}$

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

• Calculation: $\frac{800\ \text{mg}}{1000} = 0.8\ \text{g}$

Using Metric Conversion Factors

Metric conversion factors are ratios that express the relationship between two units. They are used in dimensional analysis to convert measurements:

• Conversion factor for volume: $\frac{1\ \text{L}}{1000\ \text{cm}^3}$ or $\frac{1000\ \text{cm}^3}{1\ \text{L}}$

• Conversion factor for mass: $\frac{1\ \text{g}}{1000\ \text{mg}}$ or $\frac{1000\ \text{mg}}{1\ \text{g}}$

To solve conversion problems, multiply the given value by the appropriate conversion factor so that units cancel and the desired unit remains.

Summary Table: Common Metric Conversions

Quantity	From	To	Conversion Factor
Volume	cm3	L	1 L = 1000 cm3
Mass	mg	g	1 g = 1000 mg

Additional info:

• Dimensional analysis is a systematic method for converting between units using conversion factors.

• Always check that units cancel appropriately in your calculations.