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The little-known rare earth element nauseum (atomic weight \(=172\) ) has the interesting property of being completely insoluble in everything but 25 -year- old single-malt Scotch. This curious fact was discovered in the laboratory of Professor Ludwig von Schlimazel, the eminent German chemist whose invention of the bathtub ring won him the Nobel Prize. Having unsuccessfully tried to dissolve nauseum in 7642 different solvents over a 10 -year period, Schlimazel finally came to the \(30 \mathrm{mL}\) of The Macsporran that was the only remaining liquid in his laboratory. Always willing to suffer personal loss in the name of science, Schlimazel calculated the amount of nauseum needed to make up a 0.03 molar solution, put the Macsporran bottle on the desk of his faithful technician Edgar P. Settera, weighed out the calculated amount of nauseum and put it next to the bottle, and then wrote the message that has become part of history: "Ed Settera. Add nauseum/" How many grams of nauseum did he weigh out? (Neglect the change in liquid volume resulting from the nauseum addition.)

Step by step solution

01

Calculation of number of moles needed

Since Molarity is defined as the number of moles of solute divided by volume of the solution in liters, we can rearrange the formula to find the number of moles. Thus, Moles = \(Molarity \times Volume\). Here, Molarity is 0.03 M and Volume is \(30 mL = 0.03 L\). Plugging the numbers: Moles = \(0.03 M \times 0.03 L = 9 \times 10^{-4} moles\)

02

Calculation of the mass of nauseum needed

Since we know the number of moles we require, and we’re given the atomic weight of nauseum, we can calculate the mass - \(Mass = Moles \times Atomic \space weight\). Here, Atomic weight = 172 g/mol let's plug the values: Mass = \(9 \times 10^{-4} moles \times 172 g/mol = 0.1548 g\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rare Earth Elements

Rare Earth Elements are a group of 17 elements on the periodic table. They include the 15 lanthanides, as well as scandium and yttrium. These elements are often found together in nature and are difficult to separate from one another. Despite their name, rare earth elements are relatively plentiful in the Earth's crust. However, they are not typically concentrated in ore deposits in amounts economically viable for extraction.

Rare earth elements have many critical uses and are essential in the production of many high-tech products. For instance:

• They play a vital role in the production of magnets used in wind turbines and electric vehicles.
• They are used in catalysts for petroleum refining and vehicle emission control systems.
• These elements are also crucial for manufacturing smartphones and other consumer electronics.

While the term 'rare earth' might seem to imply scarcity, it's their dispersion that makes these elements "rare" from a commercial extraction perspective.

Solubility

Solubility is a property that describes how well a solute can dissolve in a solvent. It is typically expressed in terms of the maximum amount of the solute that can dissolve in a given quantity of solvent at a specific temperature.

Factors that can influence solubility include:

• Temperature: Generally, solubility increases with temperature, though there are exceptions depending on the solute and solvent involved.
• Pressure: For gases, increasing pressure often increases solubility in liquids.
• Nature of the solute and solvent: Polar solutes typically dissolve well in polar solvents; non-polar solutes dissolve better in non-polar solvents.

In the story of "nauseum", an element perfectly insoluble in all but a very peculiar solvent (25-year-old single-malt Scotch), we see the intersection of chemistry and curiosity fascinate the scientific world. It underscores the importance of exploring a wide range of conditions and materials when conducting solubility experiments.

Atomic Weight

Atomic Weight, also known as relative atomic mass, is the average mass of an atom of an element, expressed in atomic mass units (amu). This value is weighted according to the abundance of the element's isotopes, and it allows chemists to calculate quantities in chemical reactions.

Understanding atomic weight is crucial for various calculations, including:

• Determining the mass of a substance needed to achieve a desired molarity in solution.
• Calculating the amounts of reactants and products in a chemical reaction.
• Identifying and understanding the properties of elements.

For the rare earth element nauseum, with an atomic weight of 172 amu, atomic weight enables accurate calculation of the necessary mass for a specified solution molarity. Such calculations are essential for conducting precise scientific experiments and obtaining reliable results.