Question

The exposed electrodes of a light bulb are placed in a solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in an electrical circuit such that the light bulb is glowing. You add a dilute salt solution, and the bulb dims. Which of the following could be the salt in the solution? a. \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) c. \(\mathrm{K}_{2} \mathrm{SO}_{4}\) b. \(\mathrm{NaNO}_{3}\) d. \(\mathrm{Ca}(\mathrm{NO}_{3})_{2}\) Justify your choices. For those you did not choose, explain why they are incorrect

Short answer

The correct salt solutions that could dim the light bulb are \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) (option a) and \(\mathrm{Ca}(\mathrm{NO}_{3})_{2}\) (option d) as they form precipitates with sulfate ions, reducing the concentration of ions available to conduct electricity. Options \(\mathrm{NaNO}_3\) (option b) and \(\mathrm{K}_{2}\mathrm{SO}_{4}\) (option c) do not form any precipitates, and thus, they are incorrect choices for this question.

Step-by-step solution

Understanding the initial condition

The exposed electrodes of a light bulb are placed in a solution of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), which is a strong electrolyte and dissociates completely into ions (\(2\,\mathrm{H}^{+}\) and \(1\,\mathrm{SO}_{4}^{-2}\)) in water. The bulb is glowing due to the flow of current through the \(\mathrm{H}_{2}\mathrm{SO}_{4}\) solution, which is acting as a conductor.

Effect of adding salt

When a dilute salt solution is added, a change in conductivity occurs, which in turn causes a change in the brightness of the light bulb. The significant effect is caused by the presence of ions from the salt solution, which may interact with the \(\mathrm{H}_{2}\mathrm{SO}_{4}\) ions already present in the solution. If a salt solution forms a precipitate with the sulfate ion (\(\mathrm{SO}_{4}^{-2}\)), then the concentration of ions available to conduct electricity would decrease, causing the bulb to dim.

Examine each salt solution

Now let's examine each salt option and determine if it forms a precipitate with sulfate ions or not: a. \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) - Barium nitrate is soluble in water and dissociates into \(\mathrm{Ba}^{2+}\) and \(2\,\mathrm{NO}_{3}^{-}\) ions. However, \(\mathrm{Ba}^{2+}\) ions have a high affinity for sulfate ions and readily form a precipitate of barium sulfate (\(\mathrm{BaSO}_4\)). This would lead to a decrease in the ions concentration and hence, the bulb would dim. b. \(\mathrm{NaNO}_3\) - Sodium nitrate is soluble in water and dissociates into \(\mathrm{Na}^{+}\) and \(\mathrm{NO}_{3}^{-}\) ions. These ions don't form any precipitate with sulfate ions. Thus, the bulb's brightness will not be affected. c. \(\mathrm{K}_{2}\mathrm{SO}_{4}\) - Potassium sulfate is soluble in water and dissociates into \(2\,\mathrm{K}^{+}\) and \(\mathrm{SO}_{4}^{-2}\) ions. These ions don't form any precipitate with sulfate ions. Thus, the bulb's brightness will not be affected. d. \(\mathrm{Ca}(\mathrm{NO}_{3})_{2}\) - Calcium nitrate is soluble in water and dissociates into \(\mathrm{Ca}^{2+}\) and \(2\,\mathrm{NO}_{3}^{-}\) ions. \(\mathrm{Ca}^{2+}\) ions interact with sulfate ions to form a precipitate of calcium sulfate (\(\mathrm{CaSO}_4\)). This would lead to a decrease in the ions concentration and hence, the bulb would dim.

Identify the correct salt solution

The correct salt solutions that could dim the light bulb are \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) (option a) and \(\mathrm{Ca}(\mathrm{NO}_{3})_{2}\) (option d) because they form precipitates with sulfate ions, reducing the concentration of ions available to conduct electricity. The other options, \(\mathrm{NaNO}_3\) (option b) and \(\mathrm{K}_{2}\mathrm{SO}_{4}\) (option c), do not form any precipitates, and thus, they are incorrect choices for this question.

Key concepts

Ionic Reactions

Ionic reactions involve the interaction of charged particles known as ions. In the context of electrolyte conductivity, these reactions often occur in aqueous solutions where salts, acids, or bases dissociate into ions. Ionic mobility and their interactions are fundamental to conductivity in solutions.
Consider the reaction setup where \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is introduced into a solution. This compound dissociates completely into \(2\,\mathrm{H}^{+}\) and \(\mathrm{SO}_{4}^{-2}\) ions, making it a strong electrolyte. The presence and movements of these ions facilitate the conductivity that powers, for example, a glowing bulb in an electrical circuit.
When a salt solution is added to this setup, the interactions between ions from both the salt and the \(\mathrm{H}_{2}\mathrm{SO}_{4}\) solution can either maintain or alter the conductivity of the solution, depending on whether a reaction such as a precipitation occurs.

Solubility Rules

Solubility rules help determine the solubility of compounds in water, which in turn affects whether a reaction like precipitation might occur. These rules guide predictions about the behavior of ionic compounds when dissolved in water.
Certain ions like \(\text{Ba}^{2+}\) and \(\text{Ca}^{2+}\) are known to form precipitates with sulfate \(\mathrm{SO}_{4}^{-2}\) ions. According to solubility rules:

• Barium salts typically precipitate with sulfate ions to form \(\text{BaSO}_4\), an insoluble compound.
• Calcium salts can also precipitate with sulfate ions, though the solubility is somewhat higher than that of barium sulfate.

Understanding these rules allows for predicting the conductivity change upon adding different salt solutions to our initial acid solution.

Precipitation Reactions

A precipitation reaction occurs when ions in solution form an insoluble compound, resulting in a solid precipitate. This process can drastically affect the number of free-moving ions in a solution, and subsequently its conductivity.
When considering the effect of different salts in a sulfuric acid solution:

• Barium nitrate, \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_2\), reacts with \(\mathrm{SO}_{4}^{-2}\) ions to precipitate \(\mathrm{BaSO}_4\), which decreases the total ion count significantly.
• Calcium nitrate, \(\mathrm{Ca}\left(\mathrm{NO}_{3\}\right)_2\), also forms a precipitate with \(\mathrm{SO}_{4}^{-2}\) as \(\mathrm{CaSO}_4\).

These precipitation processes remove ions from the solution, reducing its conductivity and dimming a connected bulb, as fewer ions are available to carry the current.

Electrical Conductivity

Electrical conductivity in a solution depends on the concentration and mobility of ions available to carry an electric charge. A strong electrolytic solution usually exhibits high conductivity due to the presence of numerous dissociated ions.
In our exercise:

• The initial \(\mathrm{H}_{2}\mathrm{SO}_{4}\) solution allows the bulb to glow brightly because it dissociates completely, providing a high ion concentration.
• Introducing \(\mathrm{Ba}\left(\mathrm{NO}_{3\}\right)_2\) or \(\mathrm{Ca}\left(\mathrm{NO}_{3\}\right)_2\) forms precipitates that reduce the overall ion concentration, causing dimming as the ions able to conduct electricity are reduced.

Understanding ion interactions and mobility helps explain the observed changes in brightness in response to adding specific salts.

Chemical Interaction Analysis

Chemical interaction analysis looks at how different chemicals within a solution interact, determining the outcome of those combinations, such as the formation of precipitates or changes in conductivity.
In the provided scenario, this analysis involves predicting which salts react to decrease ion concentration through precipitation:

• Analyzing the interactions between barium ions and sulfate leads to understanding that \(\mathrm{BaSO}_4\) precipitate results in reduced conductivity.
• Similarly, the interaction of calcium ions with sulfate ions to form \(\mathrm{CaSO}_4\) precipitate decreases ion availability for conducting electricity.

Ultimately, understanding these interactions assists in explaining why certain salt solutions like \(\mathrm{Ba}\left(\mathrm{NO}_{3\}\right)_2\) and \(\mathrm{Ca}\left(\mathrm{NO}_{3\}\right)_2\) affect the bulb's brightness, while others like \(\mathrm{NaNO}_3\) do not. Such analysis is crucial in predicting the outcomes of ionic reactions in various chemical contexts.