Density and Water Displacement: Measurement and Problem Solving in Chemistry

Measurement and Problem Solving

Density of Non-Geometric Objects: Water Displacement

In chemistry, the density of an object is a fundamental property that relates its mass to its volume. For non-geometric objects, determining volume can be challenging. Water displacement is a practical method used to measure the volume of irregularly shaped objects by observing the change in water level when the object is submerged.

• Water Displacement: The amount of water moved out of the way when an object is totally submerged. The difference in water level before and after submersion equals the volume of the object.

• Application: Useful for measuring the volume of non-geometric solids, which cannot be calculated using simple geometric formulas.

Example: Calculating Volume by Water Displacement

To find the volume of an object using water displacement, subtract the initial water level from the final water level after the object is submerged.

• Initial water level: 3.5 mL

• Final water level: 5.8 mL

• Volume displaced: $5.8\,\text{mL} - 3.5\,\text{mL} = 2.3\,\text{mL}$

Example Calculation:

• Initial: 5.6 mL

• Final: 7.8 mL

• Displaced volume: $7.8\,\text{mL} - 5.6\,\text{mL} = 2.2\,\text{mL}$

Practice Problem: Determining Density

Density is calculated by dividing the mass of an object by its volume. When a solid is placed in a liquid, the increase in water level gives the volume of the solid.

• Given: Mass = 0.45 g, Water level increases from 200 mL to 201.2 mL

• Volume displaced: $201.2\,\text{mL} - 200.0\,\text{mL} = 1.2\,\text{mL}$

• Density formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Calculation: $\text{Density} = \frac{0.45\,\text{g}}{1.2\,\text{mL}} = 0.375\,\text{g/mL}$

Practice Problem: Calculating Mass from Density and Volume

If the density and volume of an object are known, its mass can be calculated using the formula:

• Density: 0.96 g/cm3

• Volume displaced: 5.0 mL (from water displacement)

• Mass formula: $\text{Mass} = \text{Density} \times \text{Volume}$

• Calculation: $\text{Mass} = 0.96\,\text{g/cm}^3 \times 5.0\,\text{cm}^3 = 4.8\,\text{g}$

Summary Table: Water Displacement Calculations

Step	Calculation	Result
Initial Water Level	Measured before submersion	e.g., 3.5 mL
Final Water Level	Measured after submersion	e.g., 5.8 mL
Volume Displaced	Final - Initial	2.3 mL
Density	Mass / Volume	0.375 g/mL
Mass	Density × Volume	4.8 g

Additional info: Water displacement is a foundational technique in introductory chemistry for measuring the volume of irregular solids and is directly related to the concepts of density, mass, and volume.