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 g/cm³, and its surface area is 1242 m² per gram of material. (b) Calculate the surface area for a 10.0-mg sample of this material.

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Convert the mass of the sample from milligrams to grams by dividing by 1000, since there are 1000 milligrams in a gram.

Use the given surface area per gram of material, which is 1242 m^2/g, to find the total surface area for the sample.

Multiply the mass of the sample in grams by the surface area per gram to calculate the total surface area.

Ensure that the units are consistent and correctly cancel out to leave the final answer in square meters.

Review the calculation to ensure that all steps have been followed correctly and that the units are appropriate.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Surface Area to Mass Ratio

The surface area to mass ratio is a critical concept in material science, particularly for porous materials. It describes how much surface area is available per unit of mass, which can significantly influence the material's reactivity and absorption capabilities. In this case, the high surface area of the spongy material allows for more effective interaction with contaminants like mercury in water.

Unit Conversion

Unit conversion is essential in chemistry for ensuring that measurements are consistent and compatible. In this problem, converting the mass of the sample from milligrams to grams is necessary to align with the surface area measurement given in square meters per gram. Understanding how to convert between different units is fundamental for accurate calculations.

Calculation of Surface Area

Calculating the surface area of a sample involves multiplying the surface area per gram by the mass of the sample in grams. This straightforward mathematical operation allows us to determine how much surface area is available for interaction with substances in the environment, which is crucial for applications like water purification.

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