Problem 128 - General Chemistry

Question

Providing no reaction occurs, a solid will float on any liquid that is more dense than it is. The volume of a piece of calcite weighing \(35.6 \mathrm{~g}\) is \(12.9 \mathrm{~cm}^{3} .\) On which of the following liquids will the calcite float: carbon tetrachloride (density \(=1.60 \mathrm{~g} / \mathrm{cm}^{3}\) ), methylene bromide (density = \(\left.2.50 \mathrm{~g} / \mathrm{cm}^{3}\right),\) tetrabromoethane (density \(\left.=2.96 \mathrm{~g} / \mathrm{cm}^{3}\right),\) or methylene iodide (density \(\left.=3.33 \mathrm{~g} / \mathrm{cm}^{3}\right) ?\)

Step-by-Step Solution

Answer

Calcite will float in tetrabromoethane and methylene iodide.

Step 1: Calculate Density of Calcite

First, we need to calculate the density of the calcite. Density is given by the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). The mass of the calcite is 35.6 g and its volume is 12.9 cm³. Thus, the density is calculated as: \[ \text{Density of Calcite} = \frac{35.6 \text{ g}}{12.9 \text{ cm}^3} \approx 2.76 \text{ g/cm}^3 \]

Step 2: Compare Densities

Now compare the density of calcite (2.76 g/cm³) with the densities of the given liquids. The calcite will float in any liquid that has a density greater than 2.76 g/cm³.

Step 3: Analyze Each Liquid

- **Carbon tetrachloride**: Density = 1.60 g/cm³, which is less than 2.76 g/cm³. Calcite will not float. - **Methylene bromide**: Density = 2.50 g/cm³, which is less than 2.76 g/cm³. Calcite will not float. - **Tetrabromoethane**: Density = 2.96 g/cm³, which is greater than 2.76 g/cm³. Calcite will float. - **Methylene iodide**: Density = 3.33 g/cm³, which is greater than 2.76 g/cm³. Calcite will float.

Step 4: Conclusion

From the comparison, calcite will float in tetrabromoethane and methylene iodide since their densities are greater than the density of calcite.

Key Concepts

Floating and Sinking

When it comes to understanding why objects float or sink, it's all tied to the concept of density. An object will float in a fluid if its density is less than the density of the fluid. Conversely, it will sink if its density is greater. This principle applies not just to solids and liquids, but also to gases. Let's think about floating and sinking in terms of buoyancy, which is the force that allows objects to float. The buoyant force is equal to the weight of the fluid displaced by the object. If this buoyant force is greater than the weight of the object, it will float. If it's less, the object will sink. Understanding this balance helps us predict which objects will float or sink in a given fluid. It's why we see boats floating on water or balloons rising in the air.

Density Calculation

The calculation of density is crucial in determining whether an object will float or sink. Density is defined as mass per unit volume. It is calculated using the formula:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]Every material has a unique density that can help us identify it. For example, in the exercise, calcite has a mass of 35.6 grams and a volume of 12.9 cm³. Plugging these values into the formula gives us the density of calcite:\[\text{Density of Calcite} = \frac{35.6 \text{ g}}{12.9 \text{ cm}^3} \approx 2.76 \text{ g/cm}^3\]Knowing how to calculate density can help us address many real-world problems, from determining if a rock will float in water, to identifying materials based on their mass and volume.

Density Comparison

After calculating the density of an object, the next step is to compare it with the density of the fluid it is immersed in. This comparison tells us whether the object will float or sink.

• If an object's density is less than that of the fluid, it will float.
• If an object's density is greater than that of the fluid, it will sink.

Let's use calcite and the given liquids as examples. The density of calcite was calculated as 2.76 g/cm³. To see if calcite will float, we must compare this value to the densities of the fluids: - **Carbon tetrachloride**: Density = 1.60 g/cm³ - **Methylene bromide**: Density = 2.50 g/cm³ - **Tetrabromoethane**: Density = 2.96 g/cm³ - **Methylene iodide**: Density = 3.33 g/cm³ From this comparison, we know calcite will float in tetrabromoethane and methylene iodide since their densities are greater than 2.76 g/cm³.

Density of Fluids

The density of a fluid is a measurement of how much mass it has in a certain volume. This characteristic can vary widely among different fluids, influencing whether an object will float or sink. Many factors can affect a fluid's density:

• Temperature: Most fluids expand when heated, which decreases their density.
• Composition: Different substances have unique molecular structures and arrangements, affecting how tightly packed molecules are.

In the context of the exercise, the fluids of concern are carbon tetrachloride, methylene bromide, tetrabromoethane, and methylene iodide. Each has a specific density, affecting how they interact with solids like calcite. Understanding fluid density is essential in fields like chemistry and engineering, helping with tasks ranging from designing buoyant vessels to predicting weather patterns.