Problem 88 - Chemistry: The Central Science

Question

In 2009, a team from Northwestern University and Western Washington University reported the preparation of a new "spongy" material composed of nickel, molybdenum, and sulfur that excels at removing mercury from water. The density of this new material is \(0.20 \mathrm{~g} / \mathrm{cm}^{3}\), and its surface area is \(1242 \mathrm{~m}^{2}\) per gram of material. (a) Calculate the volume of a 10.0-mg sample of this material. (b) Calculate the surface area for a \(10.0\)-mg sample of this material. (c) A \(10.0\)-mL sample of contaminated water had \(7.748 \mathrm{mg}\) of mercury in it. After treatment with \(10.0 \mathrm{mg}\) of the new spongy material, \(0.001 \mathrm{mg}\) of mercury remained in the contaminated water. What percentage of the mercury was removed from the water? (d) What is the final mass of the spongy material after the exposure to mercury?

Step-by-Step Solution

Answer

The volume of the 10.0-mg sample is 0.05 cm³. The surface area of the 10.0-mg sample is 12.42 m². The percentage of mercury removed from the water is approximately 99.987%. The final mass of the spongy material after exposure to mercury is 17.747 mg.

Step 1: Formula

To calculate the volume of the sample, we use the formula: \[Volume = \frac{Mass}{Density}\]

Step 2: Values

Here, Mass = 10.0 mg = 0.010 g and Density = 0.20 g/cm³

Step 3: Calculation

Substitute the values into the formula: \[Volume = \frac{0.010 g}{0.20 g/cm³} = 0.05 cm³\] The volume of the 10.0-mg sample is 0.05 cm³. #b) Surface Area Calculation#

Step 4: Formula

To calculate the surface area, we use the formula: \[Surface\: Area = Mass × Surface\: Area\: per\: gram\]

Step 5: Values

Here, Mass = 10.0 mg = 0.010 g and its surface area per gram = 1242 m²/g

Step 6: Calculation

Substitute the values into the formula: \[Surface\: Area = 0.010 g × 1242 m²/g = 12.42 m²\] The surface area of the 10.0-mg sample is 12.42 m². #c) Percentage of Mercury Removed#

Step 7: Formula

To determine the percentage of mercury removed from the water, we use the formula: \[Percentage = 100 \times \frac{Initial\: mercury - Final\: mercury}{Initial\: mercury}\]

Step 8: Values

Here, Initial mercury = 7.748 mg and Final mercury = 0.001 mg

Step 9: Calculation

Substitute the values into the formula: \[Percentage = 100 \times \frac{7.748 mg - 0.001 mg}{7.748 mg} = 99.987\%\] The percentage of mercury removed from the water is approximately 99.987%. #d) Final Mass Calculation#

Step 10: Values

The initial mass of spongy material is 10.0 mg. The mass of mercury absorbed is (Initial mercury - Final mercury) = (7.748 mg - 0.001 mg) = 7.747 mg.

Step 11: Calculation

Adding the mass of mercury absorbed to the initial mass of the spongy material: \[Final\: Mass = 10.0 mg + 7.747 mg = 17.747 mg\] The final mass of the spongy material after exposure to mercury is 17.747 mg.

Key Concepts

Spongy Material

Imagine a sponge but made from metal. A "spongy" material used for mercury removal is crafted from a combination of nickel, molybdenum, and sulfur. This unique creation is not like your everyday kitchen sponge, though it shares the quality of porosity and ability to absorb substances. The term "spongy" here refers to its porous structure that allows it to interact with waterborne contaminants like mercury. These pores tremendously increase the material's ability to trap mercury particles, making it an excellent choice for cleaning contaminated water. The spongy material's lightweight nature, with a density of just 0.20 g/cm³, means it doesn't require much to do a lot. Its structure bestows it with unique physical properties such as high surface area, enabling effective adsorption, which makes it perfect for making a cleaner environment.

Surface Area Calculation

The surface area of a material plays a critical role in chemical processes, especially those involving adsorption, like mercury removal. For the spongy material, the surface area is extraordinarily high—1242 m² per gram. To find the surface area of a 10 mg sample, we multiply the sample's mass by the surface area per gram, knowing that 10 mg is equivalent to 0.010 g. Using the formula:\[Surface\, Area = Mass \times Surface\, Area \ per\, gram\]Plugging in the values:\[Surface\, Area = 0.010 \times 1242 = 12.42\, \mathrm{m}^2\]Thus, a tiny 10 mg sample of this material has an enormous surface area of 12.42 m², which facilitates its mercury-trapping prowess.

Density and Volume Calculation

When considering how much space a sample of this spongy material will take up, density and volume calculations are indispensable. Volume tells us how much physical space the material occupies, here determined using the mass and density of the material.With a density of 0.20 g/cm³ and a mass of 10 mg (or 0.010 g), you can determine the volume via:\[Volume = \frac{Mass}{Density}\]Fill in the numbers:\[Volume = \frac{0.010\, \mathrm{g}}{0.20\, \mathrm{g/cm^3}} = 0.05\, \mathrm{cm^3}\]This tells us that even a small 10 mg sample of the material occupies just 0.05 cm³ of space. Hence, you can have a lot of these spongy particles in a small volume, enhancing the material's efficiency in absorbing mercury.

Chemical Adsorption

Chemical adsorption is key in removing pollutants like mercury from water using the spongy material. Adsorption involves the adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface. In this process, the surface of this spongy material plays a fundamental role. The large surface area enables more mercury molecules to contact the surface, allowing the mercury to be captured by the material. The pores on the material provide nooks and crannies for mercury to attach to, effectively pulling mercury out of the contaminated water. This remarkable capacity of adsorption was showcased when a 10 mL sample of contaminated water containing 7.748 mg of mercury was treated with 10 mg of the spongy material, resulting in 99.987% removal efficiency. Such high efficiency illustrates how chemical adsorption can aggressively detoxify hazardous elements from water, offering a cleaner, safer solution.