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Chapter 5: Problem 47

For each solution, identify the ions that exist in aqueous solution, and specify the concentration of each ion. (a) \(0.25 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) (b) \(0.123 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) (c) \(0.056 \mathrm{M} \mathrm{HNO}_{3}\)

Short Answer

Expert verified
(a) NH4+: 0.50 M, SO4^2-: 0.25 M; (b) Na+: 0.246 M, CO3^2-: 0.123 M; (c) H+: 0.056 M, NO3-: 0.056 M.

Step by step solution

01

Analyze the Dissociation of Compounds

To determine the ions in an aqueous solution, we need to understand how each compound dissociates in water. Dissociation refers to the breaking apart of a compound into its respective ions. We address each compound separately.
02

Determine Ions for (NH4)2SO4

The compound \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\) dissociates in water into two ammonium ions \(2 \mathrm{NH}_{4}^{+}\) and one sulfate ion \(\mathrm{SO}_{4}^{2-}\). This gives a dissolution equation: \[(\mathrm{NH}_{4})_{2} \mathrm{SO}_{4} \rightarrow 2 \mathrm{NH}_{4}^{+} + \mathrm{SO}_{4}^{2-}\] For a 0.25 M solution, the concentration of \(\mathrm{NH}_{4}^{+}\) is twice that of the original compound, which is \2 \times 0.25 = 0.50\ M. The concentration of \(\mathrm{SO}_{4}^{2-}\) remains the same as the original, which is 0.25 M.
03

Determine Ions for Na2CO3

The compound \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) dissociates in water into two sodium ions \(2 \mathrm{Na}^{+}\) and one carbonate ion \(\mathrm{CO}_{3}^{2-}\). This gives the dissolution equation:\[\mathrm{Na}_{2} \mathrm{CO}_{3} \rightarrow 2 \mathrm{Na}^{+} + \mathrm{CO}_{3}^{2-}\] For a 0.123 M solution, the concentration of \(\mathrm{Na}^{+}\) is twice that of the original compound, which is \2 \times 0.123 = 0.246\ M. The concentration of \(\mathrm{CO}_{3}^{2-}\) remains the same as the original, which is 0.123 M.
04

Determine Ions for HNO3

Nitric acid \(\mathrm{HNO}_{3}\) dissociates fully in water to give hydrogen ions \(\mathrm{H}^{+}\) and nitrate ions \(\mathrm{NO}_{3}^{-}\). This gives the dissolution equation:\[\mathrm{HNO}_{3} \rightarrow \mathrm{H}^{+} + \mathrm{NO}_{3}^{-}\] For a 0.056 M solution, the concentration of both \(\mathrm{H}^{+}\) and \(\mathrm{NO}_{3}^{-}\) is 0.056 M, matching the initial concentration of the acid.

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Key Concepts

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

Chemical Dissociation
When certain compounds dissolve in water, they break apart into ions, a process called dissociation. This is key to understanding how solutions behave at a molecular level. Let's break down chemical dissociation further:
  • Dissociation occurs as the ionic compound interacts with water molecules. These interactions overcome the electrostatic forces holding the compound together, leading to the separation of ions.
  • This process can be written as a chemical equation, showing the separation into individual ions. For instance, the compound \((\mathrm{NH}_4)_2 \mathrm{SO}_4\) breaks down into two ammonium ions \(2 \mathrm{NH}_4^+\) and one sulfate ion \(\mathrm{SO}_4^{2-}\).

    • Sometimes, chemical dissociation is complete, as in the case of strong acids or bases. Other times, it might be partial, particularly in weak acids or bases. This understanding allows us to predict the behavior of ions in solution, crucial for fields spanning chemistry, biology, and environmental science.
    Ion Concentration
    Understanding ion concentration in an aqueous solution is vital for analyzing how solutions will behave. Here's what you need to know:
    • Ion concentration is often expressed in molarity (M), which indicates the number of moles of ions per liter of solution.
    • For example, if we dissolve \(0.25 \text{ M} \ (NH_4)_2SO_4\), the resulting ions are two ammonium ions \(\mathrm{NH}_4^+\) with concentrations of \(2 \times 0.25 = 0.50 \text{ M}\) and one sulfate ion \(\mathrm{SO}_4^{2-}\) at \(0.25 \text{ M}\).
    • The concentration of ions can be impacted by dissociation, as each compound releases a specific number of ions into the solution.
    Being able to calculate these concentrations aids in predicting the chemical reactivity and properties of solutions. This information influences lab practices across various sciences and helps in industrial applications like making pharmaceuticals or water treatment.
    Aqueous Chemistry
    Aqueous chemistry revolves around reactions and processes taking place in water, which is the most common solvent. Here's what you need to understand:
    • Aqueous solutions are formed when a solute dissolves in water, resulting in a mixture where the water acts as a solvent.
    • These solutions are central to many chemical reactions, particularly those involving ions. For example, when Na_2CO_3 dissolves in water, it releases two sodium ions \(2\ \mathrm{Na}^+\) and a carbonate ion \(\mathrm{CO}_3^{2-}\).

      • The unique properties of water, such as its polarity, facilitate ion dissociation and solvation. It's this capability that makes water such an effective medium for chemical reactions.
      Additionally, understanding aqueous chemistry allows chemists to manipulate and predict outcomes in reactions critical for laboratory experiments, environmental science, and even biological functions.

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    Most popular questions from this chapter

    Write a balanced equation for the reaction of aluminum hydroxide with sulfuric acid.

    A table wine has a pH of \(3.40 .\) What is the hydrogen ion concentration of the wine? Is it acidic or basic?

    Which of the following copper(11) salts are soluble in water and which are insoluble: \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{CuCO}_{3}\) \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}, \mathrm{CuCl}_{2} ?\)

    What mass of \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) in grams, is required for complete reaction with \(50.0 \mathrm{mL}\) of \(0.125 \mathrm{M} \mathrm{HNO}_{3} ?\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})+2 \mathrm{HNO}_{3}(\mathrm{aq}) \longrightarrow\) $$2 \mathrm{NaNO}_{3}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)$$

    A saturated solution of milk of magnesia, \(\mathrm{Mg}(\mathrm{OH})_{2},\) has a pH of \(10.5 .\) What is the hydrogen ion concentration of the solution? Is the solution acidic or basic?
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