Question

Arrange the following \(0.1 M\) aqueous solutions in order of decreasing \(\mathrm{pH}\) (highest to lowest). \(\begin{array}{lllll}\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}, & \mathrm{HNO}_{3}, & \mathrm{NH}_{4} \mathrm{NO}_{3}, & \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}, & \mathrm{NaF}\end{array}\)

Short answer

Question: Arrange the following aqueous solutions in order of decreasing pH: Barium nitrate (\(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\)), Nitric acid (\(\mathrm{HNO}_{3}\)), Ammonium nitrate (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)), Aluminum nitrate (\(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\)), and Sodium fluoride (\(\mathrm{NaF}\)). Answer: \(\mathrm{NaF} > \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} > \mathrm{NH}_{4} \mathrm{NO}_{3} > \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3} > \mathrm{HNO}_{3}\)

Step-by-step solution

Determine the effect of each substance on the pH of the solution

First, let's determine if the given substances produce acidic, neutral, or basic solutions when dissolved in water. We will look at the ions formed and their behavior in water. 1. \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\): Barium nitrate is a salt of a strong base (barium hydroxide) and a strong acid (nitric acid), so it will dissociate completely in water and will not affect the pH of the solution significantly. Thus, it produces a neutral solution. 2. \(\mathrm{HNO}_{3}\): Nitric acid is a strong acid, so it will dissociate completely in water to produce \(\mathrm{H^{+}}\) ions, which will significantly decrease the pH of the solution. Thus, it produces an acidic solution. 3. \(\mathrm{NH}_{4} \mathrm{NO}_{3}\): Ammonium nitrate is a salt of a weak base (ammonium hydroxide) and a strong acid (nitric acid), so it will dissociate completely in water and produce \(\mathrm{NH_{4}^{+}}\) and \(\mathrm{NO_{3}^{-}}\) ions. The \(\mathrm{NH_{4}^{+}}\) ions will release \(\mathrm{H^{+}}\) ions, and thus, decrease the pH of the solution. Thus, it produces an acidic solution. 4. \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\): Aluminum nitrate is a salt of a weak base (aluminum hydroxide) and a strong acid (nitric acid), so it will dissociate completely in water and produce \(\mathrm{Al^{3+}}\) and \(\mathrm{NO_{3}^{-}}\) ions. The \(\mathrm{Al^{3+}}\) ions will react with water molecules to produce \(\mathrm{H^{+}}\) ions, and thus, decrease the pH of the solution. Thus, it produces an acidic solution. 5. \(\mathrm{NaF}\): Sodium fluoride is a salt of a strong base (sodium hydroxide) and a weak acid (hydrofluoric acid), so it will dissociate completely in water and produce \(\mathrm{Na^{+}}\) and \(\mathrm{F^{-}}\) ions. The \(\mathrm{F^{-}}\) ions will react with water molecules to produce \(\mathrm{OH^{-}}\) ions, and thus, increase the pH of the solution. Thus, it produces a basic solution.

Arrange the solutions in order of decreasing pH

Now we have the nature of the solutions for each substance, let's arrange them in order of decreasing pH (highest to lowest): 1. \(\mathrm{NaF}\): Sodium fluoride produces a basic solution with a pH greater than 7. 2. \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\): Barium nitrate produces a neutral solution with a pH of around 7. 3. \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\), and \(\mathrm{HNO}_{3}\): All of these produce acidic solutions with pH values less than 7. However, since nitric acid is a strong acid, it will have a much lower pH value compared to the other two (which include weak bases). Between ammonium nitrate and aluminum nitrate, aluminum nitrate will have a slightly lower pH value due to the higher positive charge of the aluminum ion, which causes it to have a stronger effect on decreasing the pH. Putting these together, the order of aqueous solutions in decreasing pH is: \(\mathrm{NaF} > \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} > \mathrm{NH}_{4} \mathrm{NO}_{3} > \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3} > \mathrm{HNO}_{3}\)

Key concepts

pH Scale

Understanding the pH scale is crucial when dealing with aqueous solutions, as it gives us an immediate indication of the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are basic or alkaline.

One important point to remember is that pH is a logarithmic scale. This means each unit change represents a tenfold change in concentration of \( H^+ \) ions. For instance, a solution with a pH of 3 is 10 times more acidic than one with a pH of 4. When we consider 0.1 M aqueous solutions, a strong acid like nitric acid \( HNO_3 \) will cause the solution to have a low pH, well below 7, due to the high concentration of \( H^+ \) ions. On the other hand, a base like sodium fluoride \( NaF \) will yield a pH above 7, due to the presence of \( OH^- \) ions that decrease the concentration of \( H^+ \) ions.

Acid-Base Properties of Salts

Salts can affect the pH of an aqueous solution based on the acid-base properties of their constituent ions. Understanding these properties requires an examination of the strength of the parent acid and base from which the salt is derived. A salt from a strong acid and a strong base, as in the case of barium nitrate \( Ba(NO_3)_2 \), will not significantly affect the pH and results in a neutral solution.

On the other hand, salts such as ammonium nitrate \( NH_4NO_3 \) or aluminum nitrate \( Al(NO_3)_3 \) are derived from a combination of a weak base and a strong acid. In solution, these salts tend to produce \( H^+ \) ions due to the hydrolysis of their respective cations, \( NH_4^+ \) and \( Al^{3+} \) , leading to acidic solutions. Sodium fluoride \( NaF \) is a prime example of a salt from a strong base and a weak acid, which makes the solution basic. This happens because the fluoride ion \( F^- \) captures \( H^+ \) from water, creating \( OH^- \) ions and thereby raising the pH.

Strong and Weak Electrolytes

Electrolytes are substances that dissolve in water to form a solution that can conduct electricity. They are categorized as strong or weak based on their ability to dissociate into ions. Strong electrolytes dissociate completely, resulting in a high concentration of ions; weak electrolytes only partially dissociate.

Strong acids like nitric acid \( HNO_3 \) are strong electrolytes because they completely ionize in water, contributing a high concentration of \( H^+ \) ions, which considerably lowers the pH. Similarly, strong bases are also strong electrolytes, like the sodium ion \( Na^+ \) from sodium fluoride \( NaF \) which fully dissociates in solution. Weak electrolytes, such as the ammonium ion \( NH_4^+ \) from ammonium nitrate \( NH_4NO_3 \) or the aluminum ion from aluminum nitrate \( Al(NO_3)_3 \) only partially release \( H^+ \) ions, so they produce solutions with higher pH than strong acids but still lower than 7. Hence, when arranging solutions of strong and weak electrolytes in order of decreasing pH, we need to consider their full dissociation or partial dissociation tendencies, respectively.