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Chapter 16: Problem 97

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{+}\) or \(\mathrm{Cu}^{2+},(\mathbf{b}) \mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) , (c) \(\mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+}\) .

Short Answer

Expert verified
In conclusion, the more acidic cations in each pair are: (a) \(\mathrm{Cu^{2+}}\) is more acidic than \(\mathrm{K^{+}}\), (b) \(\mathrm{Fe^{3+}}\) is more acidic than \(\mathrm{Fe^{2+}}\), and (c) \(\mathrm{Al^{3+}}\) is more acidic than \(\mathrm{Ga^{3+}}\).

Step by step solution

01

Analyze the charge of the ions

All else being equal, cations with a higher positive charge are generally stronger Lewis acids (more acidic) because of their greater attraction for electrons. In this case: a) \(\mathrm{K}^{+}\) has a +1 charge, while \(\mathrm{Cu}^{2+}\) has a +2 charge. b) Both ions are from the same element \(\mathrm{Fe}\), but they have different charges: \(\mathrm{Fe}^{2+}\) (2+ charge) and \(\mathrm{Fe}^{3+}\) (3+ charge).
02

Analyze the size of the ions

The size of the ion also plays a role in acidity. Generally, smaller ions are more acidic than larger ions with the same charge. This is because smaller ions have a higher charge density, which allows them to attract electrons more easily. We will now analyze the size of the ions in part (c): c) \(\mathrm{Al}^{3+}\) and \(\mathrm{Ga}^{3+}\) are both from Group 13 on the periodic table, but \(\mathrm{Al}\) is above \(\mathrm{Ga}\) in the same group. As we move down a group in the periodic table, the atomic size increases, making \(\mathrm{Al}^{3+}\) smaller than \(\mathrm{Ga}^{3+}\).
03

Comparing the acidity of the cations

Using the information from Steps 1 and 2, we can now determine which cation in each pair is more acidic: a) \(\mathrm{Cu^{2+}}\) is more acidic than \(\mathrm{K^{+}}\) because it has a higher positive charge (+2) compared to \(\mathrm{K^{+} }\)(+1). b) \(\mathrm{Fe^{3+}}\) is more acidic than \(\mathrm{Fe^{2+}}\) because it has a higher positive charge (+3) compared to \(\mathrm{Fe^{2+}}\) (+2). c) \(\mathrm{Al^{3+}}\) is more acidic than \(\mathrm{Ga^{3+}}\) because it is smaller in size as it's higher in the periodic table (group 13) than \(\mathrm{Ga}\). In conclusion, the more acidic cations in each pair are \(\mathrm{Cu^{2+}}\), \(\mathrm{Fe^{3+}}\), and \(\mathrm{Al^{3+}}\).

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Most popular questions from this chapter

An unknown salt is either NaF, NaCl, or NaOCl. When 0.050 mol of the salt is dissolved in water to form 0.500 L of solution, the pH of the solution is 8.08. What is the identity of the salt?

If a neutral solution of water, with \(\mathrm{pH}=7.00\) , is cooled to \(10^{\circ} \mathrm{C},\) the ph rises to \(7.27 .\) Which of the following three statements is correct for the cooled water: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right],\) (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right],\) or (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right] ?\)

Identify the Bronsted-Lowry acid and the Bronsted-Lowry base on the left side of each of the following equations, and also identify the conjugate acid and conjugate base of each on the right side: (a) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{NH}_{3}(a q)\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NH}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (c)\(\mathrm{HCOOH}(a q)+\mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons\) \(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\mathrm{HCOO}^{-}(a q)+\mathrm{HPO}_{4}^{2-}(a q)\)

(a) Given that \(K_{b}\) for ammonia is \(1.8 \times 10^{-5}\) and that for hydroxylamine is \(1.1 \times 10^{-8}\) , which is the stronger base? (b) Which is the stronger acid, the ammonium or the hydroxylammonium ion? (c) Calculate \(K_{a}\) values for \(\mathrm{NH}_{4}^{+}\) and \(\mathrm{H}_{3} \mathrm{NOH}^{+}.\)

The iodate ion is reduced by sulfite according to the following reaction: $$\mathrm{IO}_{3}^{-}(a q)+3 \mathrm{SO}_{3}^{2-}(a q) \longrightarrow \mathrm{I}^{-}(a q)+3 \mathrm{SO}_{4}^{2-}(a q)$$ The rate of this reaction is found to be first order in \(\mathrm{IO}_{3}^{-}\) , first order in \(\mathrm{SO}_{3}^{2-}\) , and first order in \(\mathrm{H}^{+}\) . (a) Write the rate law for the reaction. (b) By what factor will the rate of the reaction change if the pH is lowered from 5.00 to 3.50\(?\) Does the reaction proceed more quickly or more slowly at the lower pH? (c) By using the concepts discussed in Section 14.6, ex-plain how the reaction can be pH-dependent even though H' does not appear in the overall reaction.
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