Density and Measurement in GOB Chemistry

Chapter 2: Chemistry and Measurements

Introduction to Density

Density is a fundamental property in chemistry that relates the mass of a substance to its volume. It is used to identify substances and predict their behavior in mixtures, such as whether they will sink or float in water.

• Definition: Density is the mass of a substance divided by its volume.

• Formula: $\text{Density} = \frac{\text{mass of substance}}{\text{volume of substance}}$

• Units: Common units for density are grams per cubic centimeter ($g/cm^3$) for solids, grams per milliliter ($g/mL$) for liquids, and grams per liter ($g/L$) for gases.

• Example: Water has a density of $1.00\ g/mL$ at $4^\circ$C. Substances with a density greater than water will sink, while those with a lower density will float.

Density of Common Substances

The density of various materials determines their behavior in water. The following table compares the densities of several substances:

Substance	Density ($g/mL$ or $g/cm^3$)
Cork	0.26
Ice	0.92
Water	1.00
Aluminum	2.70
Lead	11.3

Additional info: Densities are typically measured at room temperature unless otherwise specified.

Calculating Density

To calculate the density of a substance, measure its mass and volume, then apply the density formula.

• For solids and liquids: $\text{Density} = \frac{g}{cm^3}$ or $\frac{g}{mL}$

• For gases: $\text{Density} = \frac{g}{L}$

• Note: $1\ mL = 1\ cm^3$

Density of Solids: Volume Displacement Method

The density of a solid can be determined by dividing its mass by its volume, which is often measured by water displacement in a graduated cylinder.

• Step 1: Measure the initial volume of water.

• Step 2: Submerge the solid object and record the new volume.

• Step 3: The difference in volume equals the volume of the object.

• Example Calculation: Initial volume: $35.5\ mL$ Final volume: $45.0\ mL$ Volume of object: $45.0\ mL - 35.5\ mL = 9.5\ mL = 9.5\ cm^3$ Mass of zinc: $68.60\ g$ $\text{Density of zinc} = \frac{68.60\ g}{9.5\ cm^3} = 7.2\ g/cm^3$

Learning Check: Density Calculation

Practice calculating density using measured mass and volume displacement.

• Question: What is the density ($g/cm^3$) of a $48.0\ g$ sample of metal if the water level rises from $25.0\ mL$ to $33.0\ mL$ after the metal is added?

• Solution: Volume displaced: $33.0\ mL - 25.0\ mL = 8.0\ mL = 8.0\ cm^3$ Density: $\frac{48.0\ g}{8.0\ cm^3} = 6.0\ g/cm^3$

Problem Solving Using Density

Density can be used as a conversion factor to solve problems involving mass and volume.

• Given: Volume and density of a sample.

• Find: Mass in grams.

• Conversion: Use density to convert between volume and mass.

• Example: John took $2.0$ teaspoons (tsp) of cough syrup. The syrup has a density of $1.20\ g/mL$ and $1\ tsp = 5.0\ mL$. What is the mass in grams? Step 1: Convert teaspoons to milliliters: $2.0\ tsp \times 5.0\ mL/tsp = 10.0\ mL$ Step 2: Use density to find mass: $10.0\ mL \times 1.20\ g/mL = 12.0\ g$

Learning Check: Volume from Density and Mass

Calculate the volume of a liquid sample given its mass and density.

• Question: An unknown liquid has a density of $1.32\ g/mL$. What is the volume (mL) of a $14.7\ g$ sample?

• Solution: $\text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{14.7\ g}{1.32\ g/mL} = 11.1\ mL$

Specific Gravity

Specific gravity is a unitless quantity that compares the density of a substance to the density of water.

• Definition: $\text{Specific gravity} = \frac{\text{density of sample}}{\text{density of water}}$

• Density of water: $1.00\ g/mL$ at $4^\circ$C

• Interpretation: A substance with a specific gravity of $1.00$ has the same density as water.

• Application: Used in medical and industrial contexts to compare substances to water.

Concept Map: Density and Related Concepts

Density is interconnected with mass, volume, specific gravity, and measurement techniques. Understanding these relationships is essential for problem solving in chemistry.

• Mass and volume are measured quantities.

• Density is calculated from mass and volume.

• Specific gravity compares density to water.

• Volume displacement is a method for measuring the volume of irregular solids.

Additional info: These concepts are foundational for laboratory work and further study in chemistry, biology, and related sciences.