Problem 51 - Chemistry and Chemical Reactivity

Question

Carbon tetrachloride, \(\mathrm{CCl}_{4},\) a liquid compound, has a density of \(1.58 \mathrm{g} / \mathrm{cm}^{3} .\) If you place a piece of a plastic soda bottle \(\left(d=1.37 \mathrm{g} / \mathrm{cm}^{3}\right)\) and a piece of aluminum \((d=\) \(\left.2.70 \mathrm{g} / \mathrm{cm}^{3}\right)\) in liquid \(\mathrm{CCl}_{4},\) will the plastic and aluminum float or sink?

Step-by-Step Solution

Answer

The plastic will float; aluminum will sink in CCl4.

Step 1: Understand Density and Buoyancy

To determine if an object will float or sink in a liquid, we need to compare the density of the object to the density of the liquid. An object will float if its density is less than that of the liquid and will sink if its density is higher.

Step 2: Compare Plastic's Density to CCl4

The density of the plastic is given as \(1.37 \, \text{g/cm}^3\). Compare this to the density of carbon tetrachloride, which is \(1.58 \, \text{g/cm}^3\). Since \(1.37 \, \text{g/cm}^3 < 1.58 \, \text{g/cm}^3\), the plastic will float in CCl4.

Step 3: Compare Aluminum's Density to CCl4

The density of aluminum is \(2.70 \, \text{g/cm}^3\). Compare this with the density of carbon tetrachloride (\(1.58 \, \text{g/cm}^3\)). Since \(2.70 \, \text{g/cm}^3 > 1.58 \, \text{g/cm}^3\), the aluminum will sink in CCl4.

Key Concepts

Carbon Tetrachloride

Carbon tetrachloride, often abbreviated as \(\text{CCl}_4\), is a clear, colorless liquid that was commonly used as a cleaning agent and fire extinguishing fluid. Today, it’s primarily used in the production of refrigerants and other industrial applications. One notable property of carbon tetrachloride is its relatively high density, which is \(1.58 \, \text{g/cm}^3\).
This density allows us to explore questions of buoyancy and floatation. Liquids with higher densities can support heavier objects than liquids with lower densities. Since carbon tetrachloride is denser than water, objects that might sink in water can float in \(\text{CCl}_4\) depending on their own densities.
Always handle carbon tetrachloride carefully, as it’s toxic and can be harmful to health on exposure. Proper ventilation and safety gear are advisable when dealing with this chemical.

Density Comparison

Density is a measure of how much mass is contained in a given volume. It’s usually expressed in grams per cubic centimeter (\(\text{g/cm}^3\)). This concept is crucial in understanding why some objects float while others sink.

• Materials with high density have more mass packed into the same amount of space.
• For instance, aluminum has a density of \(2.70 \, \text{g/cm}^3\), making it much denser than carbon tetrachloride at \(1.58 \, \text{g/cm}^3\).
• Plastic soda bottles have a lower density of \(1.37 \, \text{g/cm}^3\), making them less dense than carbon tetrachloride.

By comparing these densities to that of carbon tetrachloride, we can predict their behavior in this liquid. Objects with densities lower than \(\text{CCl}_4\) will float, while those with higher densities will tend to sink.
Understanding density comparison helps predict and explain phenomena in daily life, such as why icebergs float in the ocean or why oil separates from water in a salad dressing.

Float and Sink Principle

The float and sink principle is based on Archimedes’ principle, which states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object. In simpler terms:

• If an object is less dense than the liquid it's in, it will float because the buoyant force is greater than the object's weight.
• If the object is denser than the liquid, it will sink as the object weighs more than the fluid it displaces.

Applying this to carbon tetrachloride, we can determine:

• The plastic, with a density of \(1.37 \, \text{g/cm}^3\), is less dense than carbon tetrachloride, so it floats.
• The aluminum, with a density of \(2.70 \, \text{g/cm}^3\), is denser, meaning it will sink.

This principle is a fundamental concept in physics and engineering, playing a crucial role in designing ships, submarines, and various floating devices. Understanding it can explain a wide range of natural and manmade phenomena.