Question

Which of the following solutions has the same concentration of H+ ions as \(0.1\) N HCl? (a) \(0.1 \mathrm{~N} \mathrm{H}_{2} \mathrm{SO}_{4}\) (b) \(0.3 \mathrm{~N} \mathrm{H}_{3} \mathrm{PO}_{4}\) (c) \(0.2 \mathrm{~N} \mathrm{HNO}_{3}\) (d) All of these

Short answer

(a) 0.1 N H2SO4 (b) 0.3 N H3PO4 (c) 0.2 N HNO3 Answer: None of the given options have the same H+ ion concentration as 0.1 N HCl.

Step-by-step solution

Calculate the concentration of H+ ions in 0.1 N HCl solution

As HCl is a strong monoprotic acid, it dissociates completely into one H+ ion and one Cl- ion in water. Hence, in a 0.1 N HCl solution, the concentration of H+ ions is also 0.1 M.

Calculate the concentration of H+ ions in 0.1 N H2SO4 solution

H2SO4 is a strong diprotic acid, which means it dissociates in two steps, first providing 1 H+ ion, and then providing another H+ ion. \[ \textrm{H}_2 \textrm{SO}_4 \rightarrow \textrm{H}^{+} + \textrm{HSO}_4^{-} \] \[ \textrm{HSO}_4^{-} \rightarrow \textrm{H}^{+} + \textrm{SO}_4^{2-} \] Therefore, in a 0.1 N H2SO4 solution, the concentration of H+ ions is 2 * 0.1 M = 0.2 M.

Calculate the concentration of H+ ions in 0.3 N H3PO4 solution

H3PO4 is a weak triprotic acid, but we will assume complete dissociation for this problem as it simplifies the analysis. \[ \textrm{H}_3 \textrm{PO}_4 \rightarrow \textrm{H}^{+} + \textrm{H}_2 \textrm{PO}_4^{-} \] \[ \textrm{H}_2 \textrm{PO}_4^{-} \rightarrow \textrm{H}^{+} + \textrm{HPO}_4^{2-} \] \[ \textrm{HPO}_4^{2-} \rightarrow \textrm{H}^{+} + \textrm{PO}_4^{3-} \] Therefore, in a 0.3 N H3PO4 solution, the concentration of H+ ions is 3 * 0.3 M = 0.9 M.

Calculate the concentration of H+ ions in 0.2 N HNO3 solution

HNO3 is a strong monoprotic acid, which means it dissociates completely into one H+ ion and one NO3- ion in water. \[ \textrm{HNO}_3 \rightarrow \textrm{H}^{+} + \textrm{NO}_3^{-} \] Hence, in a 0.2 N HNO3 solution, the concentration of H+ ions is 0.2 M.

Compare H+ ion concentrations to 0.1 N HCl solution

Compared to the 0.1 M concentration of H+ ions in 0.1 N HCl solution, we can see that the H+ ion concentrations in the given solutions are as follows: (a) 0.2 M (0.1 N H2SO4) (b) 0.9 M (0.3 N H3PO4) (c) 0.2 M (0.2 N HNO3) Based on these values, none of the given solutions have the same H+ ion concentration as 0.1 N HCl. Therefore, none of the given options are correct.

Key concepts

Monoprotic Acids

Acids that release one hydrogen ion (H\(^+\)) when dissolved in water are called monoprotic acids. A classic example is hydrochloric acid (HCl). When HCl gas is dissolved in water, it dissociates completely, yielding one H\(^+\) ion and one Cl\(^-\) ion per molecule:

• Reaction: \( \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \)

This characteristic makes them relatively simple to understand, as the normality (N) and molarity (M) in these acids are often equal under conditions of complete dissociation.
For instance, a 0.1 N solution of HCl also has an H\(^+\) ion concentration of 0.1 M because it is a strong acid that fully dissociates in water. Understanding monoprotic acids is crucial because they serve as the foundation for comparing more complex acids.

Diprotic Acids

Diprotic acids, like sulfuric acid (H\(_2\)SO\(_4\)), can release two hydrogen ions per molecule. This occurs in a two-step dissociation process, with each step contributing to the total concentration of H\(^+\) ions in solution:

• First Step: \( \text{H}_2\text{SO}_4 \rightarrow \text{H}^+ + \text{HSO}_4^- \)
• Second Step: \( \text{HSO}_4^- \rightarrow \text{H}^+ + \text{SO}_4^{2-} \)

For a 0.1 N solution of H\(_2\)SO\(_4\), complete dissociation results in a 0.2 M concentration of H\(^+\) ions, since each molecule contributes two H\(^+\) ions.
The dual release of hydrogen ions can affect reactions differently compared to monoprotic acids, making diprotic acids an interesting study in multi-proton donation and its impact on acidity and strength.

Triprotic Acids

Triprotic acids, such as phosphoric acid (H\(_3\)PO\(_4\)), have the ability to release three hydrogen ions. They dissociate in a sequential manner with three stages of hydrogen ion liberation:

• First Ionization: \( \text{H}_3\text{PO}_4 \rightarrow \text{H}^+ + \text{H}_2\text{PO}_4^- \)
• Second Ionization: \( \text{H}_2\text{PO}_4^- \rightarrow \text{H}^+ + \text{HPO}_4^{2-} \)
• Third Ionization: \( \text{HPO}_4^{2-} \rightarrow \text{H}^+ + \text{PO}_4^{3-} \)

While in real scenarios the ionization is often incomplete, if we assume full dissociation for calculation purposes, like in a 0.3 N H\(_3\)PO\(_4\) solution, it would produce a 0.9 M concentration of H\(^+\) ions.
Understanding triprotic acids is essential as they provide insights into complex acid behaviors and the intricate balance of reaction equilibria.

Normality and Molarity

Normality (N) and molarity (M) are two important concepts when dealing with solutions.Normality is a measure of concentration equivalent to molarity but considers the number of reactive units (such as ions) a substance provides. It's defined as the number of equivalents of solute per liter of solution.
Molarity is simply the number of moles of solute per liter of solution, without considering the specific reaction involved.

• For monoprotic acids, N = M because they release one H\(^+\) ion.
• For diprotic acids, N equals half the molarity when considering complete dissociation (e.g., 0.1 N H\(_2\)SO\(_4\) is actually 0.2 M in terms of equivalent H\(^+\) contribution).
• For triprotic acids, like H\(_3\)PO\(_4\), N may be a third of the total molarity if assuming complete dissociation since three H\(^+\) ions are released.

Grasping these concepts simplifies the predictable outcomes of acid reactions in various concentrations.

Strong and Weak Acids

Acids are categorized based on their ability to donate hydrogen ions into strong and weak acids. Strong acids such as HCl and HNO\(_3\) dissociate completely in water, meaning they give off all their available hydrogen ions. Their behavior makes it easy to predict H\(^+\) concentration directly from the solution's normality or molarity.
On the other hand, weak acids only dissociate partially. An example is H\(_3\)PO\(_4\), which, although assumed fully dissociated in this context, in reality, may not completely ionize in a regular solution.

• Strong acids: Full H\(^+\) ion release, easy calculation of concentration.
• Weak acids: Partial dissociation, requiring equilibrium calculations for accurate H\(^+\) listing.

Knowing the strength aids in anticipating chemical behavior, critical for applications and experiments.