Problem 108 - Chemistry and Chemical Reactivity

Question

A The density of a single, small crystal can be determined by the flotation method. This method is based on the idea that if a crystal and a liquid have precisely the same density, the crystal will hang suspended in the liquid. A crystal that is more dense will sink; one that is less dense will float. If the crystal neither sinks nor floats, then the density of the crystal equals the density of the liquid. Generally, mixtures of liquids are used to get the proper density. Chlorocarbons and bromocarbons (see the list below) are often the liquids of choice. If the two liquids are similar, then volumes are usually additive and the density of the mixture relates directly to composition. (An example: \(1.0 \mathrm{mL}\) of \(\mathrm{CHCl}_{3}, d=1.4832 \mathrm{g} / \mathrm{mL},\) and 1.0 mL of \(\mathrm{CCl}_{4}, d=1.5940 \mathrm{g} / \mathrm{mL},\) when mixed, give \(2.0 \mathrm{mL}\) of a mixture with a density of \(1.5386 \mathrm{g} / \mathrm{mL} .\) The density of the mixture is the average of the values of the two individual components.) The problem: A small crystal of silicon, germanium, tin, or lead (Group 4A in the periodic table) will hang suspended in a mixture made of \(61.18 \%\) (by volume) \(\mathrm{CH}\) IBr \(_{3}\) and \(38.82 \%\) (by volume) \(\mathrm{CHCl}_{3} .\) Calculate the density and identify the element. (You will have to look up the values of the density of the elements in a manual such as the The Handbook of Chemistry and Physics in the library or in a World Wide Web site such as WebElements at, www.webelements.com.) $$\begin{array}{llll} \hline \text { Liquid } & \text { Density }(\mathrm{g} / \mathrm{mL}) & \text { Liquid } & \text { Density }(\mathrm{g} / \mathrm{mL}) \\ \hline \mathrm{CH}_{2} \mathrm{Cl}_{2} & 1.3266 & \mathrm{CH}_{2} \mathrm{Br}_{2} & 2.4970 \\ \mathrm{CH} \mathrm{Cl}_{3} & 1.4832 & \mathrm{CHBr}_{3} & 2.8899 \\ \mathrm{CCl}_{4} & 1.5940 & \mathrm{CBr}_{4} & 2.9609 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

Estimate the mixture density and compare with element densities to identify the silicon crystal.

Step 1: Gather Given Information

The exercise provides the densities of the liquids used in the mixture: - CHIBr₃: not given directly in the table, it must be researched or assumed based on similar compounds. - CHCl₃: 1.4832 g/mL. The mixture consists of 61.18% CHIBr₃ and 38.82% CHCl₃ by volume.

Step 2: Research or Assume the Missing Density

Assume an estimated density for CHIBr₃ based on similar halogenated compounds. If unknown, use a density close to CHBr₃ (2.8899 g/mL) as a reference for CHIBr₃.

Step 3: Calculate the Mixture's Density

Use the formula for calculating the density of a mixture: \[ \text{Density of mixture} = (\text{Volume % of CHIBr₃} \times \text{Density of CHIBr₃}) + (\text{Volume % of CHCl₃} \times \text{Density of CHCl₃}) \]Plug in the assumed density for CHIBr₃ and the density for CHCl₃. \[ \text{Density of mixture} = (0.6118 \times X) + (0.3882 \times 1.4832) \]Solve for the mixture's density given that \(X\) is the assumed density for CHIBr₃.

Step 4: Determine the Element Using Density

Compare the calculated density of the mixture with known densities of silicon, germanium, tin, and lead. Use reference materials such as WebElements to find these densities for each element and identify the element that matches the calculated mixture density.

Key Concepts

Flotation Method

The flotation method is a valuable technique used to determine the density of small crystals. This method is based on the physical principle that if a crystal and a liquid have the same density, the crystal will neither sink nor float but will remain suspended in the liquid solution. This characteristic can be utilized to identify or confirm the density of unknown crystals.

When a crystal is denser than the liquid it's placed in, it will sink to the bottom. Conversely, if the crystal is less dense, it will float. By adjusting the density of the liquid (often using a mix of different liquids), scientists can create a situation where the crystal remains suspended, indicating the liquid's density equals that of the crystal.

This method is particularly useful for small, precious gemstones, or crystals where other methods of density determination may be difficult or impossible.

Density Determination

Density determination is essential for identifying substances and understanding their properties. Density is typically expressed in grams per milliliter (g/mL) for liquids. Mathematically, density is defined as the mass of an object divided by its volume. This can be represented as:

\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]

In the exercise, you calculate the density of a mixture by knowing the percentages and densities of the individual components. The formula used is:

\[\text{Density of mixture} = (\text{Volume \, % \, of \, Component \, 1} \times \text{Density \, of \, Component \, 1}) + (\text{Volume \, % \, of \, Component \, 2} \times \text{Density \, of \, Component \, 2})\]

This approach is straightforward and takes advantage of the additivity of volume for similar liquids, allowing the calculation of mixture densities.

Group 4A Elements

The Group 4A elements, also known as the carbon group, consist of silicon, germanium, tin, and lead, along with carbon itself. These elements are characterized by having four electrons in their outermost shell. This configuration allows them to form various types of bonds, making them versatile in chemical reactions.

In the context of this exercise, the objective is to determine which Group 4A element is represented by a small crystal based on its density. Each of these elements has distinct density characteristics:

• Silicon: Approximately 2.33 g/cm³
• Germanium: Approximately 5.32 g/cm³
• Tin: Approximately 7.31 g/cm³
• Lead: Approximately 11.34 g/cm³

By comparing the calculated density of the suspension mixture with these known values, we can identify the element.

Halogenated Compounds

Halogenated compounds are organic compounds that have halogen atoms (like fluorine, chlorine, bromine, or iodine) substituted into their molecular structure. These compounds are known for their varied applications, ranging from industrial solvents to pesticides.

The exercise involves using halogenated compounds such as chlorocarbons and bromocarbons to form a liquid mixture with a specific density. Compounds like CHCl₃ (chloroform) and CHBr₃ are typical choices due to their easily modifiable densities and miscibility.

Halogenated compounds are chosen here because their densities are generally higher than water, making them suitable for suspending the crystal of interest. The densities of these compounds are typically reliable for precise density determination tasks. Their use in laboratory scenarios, such as flotation method techniques, showcases their versatility and critical role in experimental design.