Problem 27 - Chemistry and Chemical Reactivity

Question

Carbon tetrachloride, \(\mathrm{CCl}_{4},\) a common 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 \(\left(d=2.70 \mathrm{g} / \mathrm{cm}^{3}\right)\) in liquid \(\mathrm{CCl}_{4},\) will the plastic and aluminum float or sink?

Step-by-Step Solution

Answer

The plastic will float, and the aluminum will sink.

Step 1: Understand Density and Buoyancy

When an object is placed in a liquid, its tendency to float or sink depends on its density compared to the liquid's density. If the object's density is less than the liquid's density, it will float. Conversely, if the object's density is greater, it will sink.

Step 2: Compare the Densities

First, compare the density of the plastic with the density of carbon tetrachloride (CCl extsubscript{4}). The plastic has a density of 1.37 g/cm extsuperscript{3}, while CCl extsubscript{4} has a density of 1.58 g/cm extsuperscript{3}. Since 1.37 g/cm extsuperscript{3} is less than 1.58 g/cm extsuperscript{3}, the plastic will float.

Step 3: Compare the Densities Again

Next, compare the density of aluminum with the density of carbon tetrachloride (CCl extsubscript{4}). The aluminum has a density of 2.70 g/cm extsuperscript{3}, while CCl extsubscript{4} has a density of 1.58 g/cm extsuperscript{3}. Since 2.70 g/cm extsuperscript{3} is greater than 1.58 g/cm extsuperscript{3}, the aluminum will sink.

Key Concepts

Understanding Carbon Tetrachloride

Carbon tetrachloride is a chemical compound with the formula \(\mathrm{CCl}_{4}\). It is commonly used as a solvent in chemistry and has been employed for various industrial purposes. This liquid is quite dense, with a density of \(1.58 \mathrm{g/cm}^{3}\). Because of this density, carbon tetrachloride is often heavier than many common substances, making it a useful example when studying properties like density and buoyancy.

• Formula: \(\mathrm{CCl}_{4}\)
• Common use: Solvent
• Density: \(1.58 \mathrm{g/cm}^{3}\)

Although it has valuable applications, carbon tetrachloride is also an environmental concern due to its ozone-depleting characteristics, so usage and disposal need to be managed carefully.

Determining Float or Sink

When determining whether an object will float or sink in a liquid like carbon tetrachloride, it is key to understand the concept of buoyancy. Buoyancy refers to the upward force exerted by a fluid that opposes the weight of an object immersed in it. The crux of floating or sinking lies in comparing the density of the object with that of the fluid.

• Float: Object's density is less than fluid's density.
• Sink: Object's density is greater than fluid's density.

For instance, in our exercise, a piece of plastic with a density of \(1.37 \mathrm{g/cm}^{3}\) when placed in carbon tetrachloride will float, as its density is less than that of the liquid. Conversely, aluminum, with a density of \(2.70 \mathrm{g/cm}^{3}\), will sink because it's denser than carbon tetrachloride.

How Density Comparison Works

Density comparison is a simple but powerful method for predicting the behavior of objects in a fluid. To compare densities, check the values of the substance and the fluid it is placed in. If the object’s density is less (\(d_{object} < d_{fluid}\)), it will float, as the fluid can support its weight through buoyancy. When the object's density is greater than the fluid (\(d_{object} > d_{fluid}\)), the object is too heavy for the fluid to support, so it sinks.

• Density of carbon tetrachloride: \(1.58 \mathrm{g/cm}^{3}\)
• Density of plastic: \(1.37 \mathrm{g/cm}^{3}\) (Floats in carbon tetrachloride)
• Density of aluminum: \(2.70 \mathrm{g/cm}^{3}\) (Sinks in carbon tetrachloride)

This technique is foundational in physics and chemistry for solving real-world problems and understanding fluid interactions. Knowing this, you can predict how various materials will behave when they interact with different liquids.