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Chapter 14: Problem 14

Consider two solutions of the salts \(\operatorname{NaX}(a q)\) and \(\operatorname{NaY}(a q)\) at equal concentrations. What would you need to know to determine which solution has the higher pH? Explain how you would decide (perhaps even provide a sample calculation).

Short Answer

Expert verified
To determine which solution has a higher pH, we need to compare the basicity of the anions (X and Y) in each salt, which can be found using their Kb or pKb values. The solution with the higher Kb value (or lower pKb value) will have the higher pH. If needed, we can calculate the pH of each solution using the equation \(pOH = \frac{1}{2} (pKw - pKb)\) and then \(pH = pKw - pOH\). Comparing the calculated pH values will allow us to identify the solution with the higher pH.

Step by step solution

01

Identify the anions

First, we need to identify the anions in each salt. In the case of NaX, the anion is X, and for NaY, the anion is Y.
02

Determine the basicity of the anions

Next, we need to determine the basicity of the anions. We can look up the Kb values (base ionization constant) or pKb values (negative base-10 logarithm of the Kb value) of the anions in a table or other reliable source. The higher the Kb value (or lower the pKb value), the stronger the base.
03

Compare the basicity of the anions

Now, we compare the basicity of the anions X and Y. If one of the anions has a higher Kb value (or lower pKb value) than the other anion, the solution containing that anion will have a higher pH. Alternatively, we can also calculate the pH of each solution based on the Kb values, if needed.
04

Calculate the pH of each solution (if needed)

If a comparison of the Kb (or pKb) values is not sufficient to determine which solution has a higher pH, we can use the following equation to calculate the pH of each solution: \(pOH = \frac{1}{2} (pKw - pKb)\) Here, pOH is the negative base-10 logarithm of the hydroxide ion concentration, and pKw is the negative base-10 logarithm of the ion product of water (usually equal to 14 at 25°C). To find the pH of each solution, we can use the following equation: \(pH = pKw - pOH\) Thus, the pH of the NaX solution can be calculated as: \(pH_{NaX} = pKw - \frac{1}{2} (pKw - pKb_X)\) And the pH of the NaY solution can be calculated as: \(pH_{NaY} = pKw - \frac{1}{2} (pKw - pKb_Y)\)
05

Determine the solution with a higher pH

After calculating the pH of each solution, compare the values to determine which solution has a higher pH. The solution with the higher pH value will be the one with a higher concentration of hydroxide ions (OH-) and thus higher basicity. By following these steps, we can determine which solution, NaX or NaY, has a higher pH, considering their equal concentrations.

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Most popular questions from this chapter

A solution is made by adding 50.0 \(\mathrm{mL}\) of 0.200\(M\) acetic acid \(\left(K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) to 50.0 \(\mathrm{mL}\) of \(1.00 \times 10^{-3} \mathrm{M} \mathrm{HCl}\) a. Calculate the pH of the solution. b. Calculate the acetate ion concentration.

Are solutions of the following salts acidic, basic, or neutral? For those that are not neutral, write balanced chemical equations for the reactions causing the solution to be acidic or basic. The relevant \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) values are found in Tables 14.2 and \(14.3 .\) $\begin{array}{ll}{\text { a. NaNO, }} & {\text { d. } \mathrm{NH}_{4} \mathrm{NO}_{2}} \\ {\text { b. NaNO_ }_{2}} & {\text { e. } \mathrm{KOCl}} \\\ {\text { c. } \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NHClO}_{4}} & {\text { f. } \mathrm{NH}_{4} \mathrm{OCl}}\end{array}$

An unknown salt is either $\mathrm{NaCN}, \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2},$ NaF, NaCl, or NaOCl. When 0.100 mole of the salt is dissolved in 1.00 \(\mathrm{L}\) of solution, the pH of the solution is \(8.07 .\) What is the identity of the salt?

Place the species in each of the following groups in order of increasing acid strength. Explain the order you chose for each group. a. \(\mathrm{HIO}_{3}, \mathrm{HBrO}_{3}\) b. \(\mathrm{HNO}_{2}, \mathrm{HNO}_{3}\) c. HOCl, HOI d. \(\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{H}_{3} \mathrm{PO}_{3}\)

Phosphoric acid is a common ingredient in traditional cola drinks. It is added to provide the drinks with a pleasant tart taste. Assuming that in cola drinks the concentration of phosphoric acid is \(0.007 M,\) calculate the \(\mathrm{pH}\) of this solution.
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