Question

A small quantity of \(\mathrm{NaCl}\) containing radioactive \(_{11}^{24} \mathrm{Na}\) is added to an aqueous solution of \(\mathrm{NaNO}_{3}\). The solution is cooled, and \(\mathrm{NaNO}_{3}\) is crystallized from the solution. Would you expect the \(\mathrm{NaNO}_{3}(\mathrm{s})\) to be radioactive? Explain.

Short answer

Yes, the resulting \(\mathrm{NaNO}_{3}(\mathrm{s})\) would be radioactive because it includes the radioactive $_{11}^{24} \mathrm{Na}$ isotope from the solution.

Step-by-step solution

Identify the radioactive isotope

In this problem, the radioactive isotope is $_{11}^{24} \mathrm{Na}$. It's important to note that this isotope of sodium behaves chemically identical to other sodium isotopes.

Analyze the crystallization process

When the sodium nitrate, \(\mathrm{NaNO}_{3}\), is cooled and crystallized from the solution, all kinds of sodium ions present in the solution (including the radioactive isotope $_{11}^{24} \mathrm{Na}$ and the common sodium isotope $_{11}^{23} \mathrm{Na}$) are included into the crystal structure of the resulting sodium nitrate.

Conclude if the resulting solid is radioactive

Since the radioactive isotope of sodium is included into the crystallized sodium nitrate along with non-radioactive isotopes, the resulting sodium nitrate solid, \(\mathrm{NaNO}_{3}(\mathrm{s})\), would be radioactive.

Key concepts

Crystallization Process

Crystallization is a fascinating chemical process used to purify substances by forming solid crystals from a solution. This process occurs when a solution becomes supersaturated, typically by cooling, and begins to solidify out of the liquid phase.
In this scenario, when sodium nitrate (\(\mathrm{NaNO}_{3}\)) is dissolved in water, it forms a homogenous liquid solution. When cooled, the sodium nitrate molecules begin to arrange themselves into a crystal lattice as they solidify. This structured pattern locks the molecules in place, producing pure crystals.

• During crystallization, the rate at which the solution cools can drastically affect the size and quality of the crystals formed.
• Slow cooling tends to produce larger, well-formed crystals, while fast cooling can lead to smaller and less defined crystals.
• Impurities from the solution can sometimes be trapped in the crystal lattice, hence affecting the purity of the resulting crystal.

Understanding crystallization helps one appreciate how substances like sodium nitrate can change from a solution to a solid state while potentially incorporating various isotopes present in the solution.

Sodium Nitrate

Sodium nitrate (\(\mathrm{NaNO}_{3}\)) is an inorganic compound consisting of sodium (Na), nitrogen (N), and oxygen (O). It is widely used in fertilizers, explosives, and in the food industry as a preservative.
This compound is highly soluble in water, which makes it ideal for processes like crystallization as discussed above. When dissolved, it dissociates into sodium ions (\(\mathrm{Na}^{+}\)) and nitrate ions (\(\mathrm{NO}_{3}^{-}\)) in the solution.

• Sodium ions interact readily with nitrate ions forming sodium nitrate crystals when the solution is cooled.
• It is critical to note that regardless of which sodium isotope—whether radioactive \(\mathrm{Na}^{24}\) or stable \(\mathrm{Na}^{23}\)—is present in the solution, they all contribute to the formation of sodium nitrate crystals.
• This property makes sodium nitrate an interesting subject of study in both chemistry and radioactivity.

Through these properties, sodium nitrate's behavior showcases both a typical ionic compound's simplicity and its nuanced interactions with various isotopes in chemical processes.

Chemical Behavior of Isotopes

Isotopes are versions of the same element that contain an equal number of protons but different numbers of neutrons. This results in isotopes having nearly identical chemical properties because chemical reactions primarily involve the electrons of an atom, and not the neutrons.
In our context, radioactive sodium (\(_{11}^{24} \mathrm{Na}\)) behaves chemically similar to its more common stable counterpart (\(_{11}^{23} \mathrm{Na}\)). The reason for this similarity is due to both isotopes having the same number of electrons and thus undergoing the same types of chemical reactions.

• During crystallization, different isotopes of sodium will equally be incorporated into sodium nitrate crystals based on their abundance and interaction with other ions.
• The isotopic nature does not significantly affect the chemical behavior during the crystallization of sodium nitrate.
• This underlines the reason why the resulting sodium nitrate is radioactive when starting with a mixture containing radioactive sodium.

Thus, understanding isotopes elucidates why despite the presence of a radioactive isotope, the chemical process remains unaffected, yet the final product retains radioactivity due to the isotopic combination.