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Chapter 8: Problem 183

\(0.1 \mathrm{M}\) solution of three different sodium salts NaX, NaY and \(\mathrm{NaZ}\) have \(\mathrm{pH}\) values \(7.0,9.0\) and \(11.0\) respectively. The correct order of dissociation constant values of these acids is (a) \(\mathrm{K}_{\mathrm{HX}}<\mathrm{K}_{\mathrm{HY}}<\mathrm{K}_{\mathrm{HZ}}\) (b) \(\mathrm{K}_{\mathrm{HX}}>\mathrm{K}_{\mathrm{HY}}>\mathrm{K}_{\mathrm{Hz}}\) (c) \(\mathrm{K}_{\mathrm{HX}}>\mathrm{K}_{\mathrm{Hz}}>\mathrm{K}_{\mathrm{HY}}\) (d) \(\mathrm{K}_{\mathrm{Hx}}<\mathrm{K}_{\mathrm{HY}}<\mathrm{K}_{\mathrm{Hz}}\)

Short Answer

Expert verified
(b) \(\mathrm{K}_{\mathrm{HX}} > \mathrm{K}_{\mathrm{HY}} > \mathrm{K}_{\mathrm{Hz}}\)

Step by step solution

01

Identify Role of pH and pKa

The pH of a solution can give insights into the strength of its conjugate acid. Here we are dealing with sodium salts NaX, NaY, and NaZ, which dissociate into their respective anions X鈦�, Y鈦�, and Z鈦� that act as conjugate bases. The higher the pH of these solutions, the weaker the associated acid HX, HY, and HZ, meaning a higher pH indicates a weaker acid with a lower dissociation constant, K.
02

Analyze pH Values

The pH values given are 7.0, 9.0, and 11.0 for NaX, NaY, and NaZ respectively. Since a higher pH indicates a stronger base or weaker acid, the corresponding acids HX, HY, and HZ will have increasing acidity in the order of HZ (pH 11.0), HY (pH 9.0), and HX (pH 7.0).
03

Determine Dissociation Constant Order

Based on the pH values: HZ, with the highest pH of 11.0, has the weakest acid and hence the smallest K value; HY, with a pH of 9.0, is in the middle; and HX, with the lowest pH of 7.0, is the strongest acid. Therefore, the order of dissociation constants is K_HX > K_HY > K_HZ.
04

Select Correct Answer Choice

The calculated order of dissociation constants is K_HX > K_HY > K_HZ. Comparing this with the given options, the correct choice is (b) \(\mathrm{K}_{\mathrm{HX}} > \mathrm{K}_{\mathrm{HY}} > \mathrm{K}_{\mathrm{Hz}}\).

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Key Concepts

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

pH and pKa relationship
The relationship between pH and pKa is crucial for understanding the behavior of acids and bases in solution. The pH is a measure of the acidity or basicity of a solution, while pKa is the negative logarithm of the acid dissociation constant (K_a) of the acid, indicating its strength. When the pH equals the pKa, the acid and its conjugate base are present in equal concentrations in solution.

This relationship helps predict how an acid or base will behave in different pH environments:
  • If the pH is lower than the pKa, the environment is acidic, and the acid will remain mostly in its protonated form.
  • If the pH is higher than the pKa, the environment is basic, and the acid will mostly donate its proton, forming its conjugate base.
Understanding the pH and pKa relationship also helps in predicting the extent of dissociation of acids in solution.
This is particularly important when calculating the pH of a solution or determining the strength of an acid or base.
Sodium Salts in Aqueous Solution
Sodium salts, when dissolved in water, dissociate completely into sodium (Na^+) ions and their respective anions (such as X鈦�, Y鈦�, Z鈦�). These anions are often conjugate bases of weak acids. The pH of the solution indicates the strength of these conjugate bases. More basic solutions have anions that originate from weaker acids.

For example, a sodium salt like NaZ, which results in a higher pH of 11.0, indicates that the anion Z^- is a stronger base, implying that HZ is a weaker acid. Conversely, NaX, producing a neutral pH of 7.0, suggests that its corresponding acid, HX, is stronger.
When evaluating sodium salts in aqueous solutions, one should consider:
  • The nature of the conjugate base: Stronger bases correspond to weaker acids.
  • The resulting pH: Indicates the strength of the respective conjugate acid.
This understanding is essential for predicting and explaining chemical behavior in solutions.
Conjugate Acid-Base Pairs
Conjugate acid-base pairs play a vital role in understanding acid-base equilibrium in solutions. A conjugate acid is formed when a base gains a proton (H^+), while a conjugate base is formed when an acid donates a proton.

The strength of acids and bases in these pairs is interconnected:
  • Strong acids have weak conjugate bases, as these bases are not eager to accept protons back.
  • Weak acids have strong conjugate bases, which readily accept protons, causing the acid to dissociate less completely.
By understanding this relationship, one can predict the extent of chemical reactions in buffer solutions, where both members of a conjugate pair are present. For example, the pair HX/X^- shows that if HX is a strong acid, then X^- will be a weak base. This knowledge is particularly relevant for determining pH changes in solutions and for conducting titration calculations.

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Most popular questions from this chapter

The ionization constant of \(\left[\mathrm{NH}_{4}^{+}\right]\)in water is \(5.6 \times 10^{-10}\) at \(25^{\circ} \mathrm{C}\). The rate constant for the reaction of \(\left[\mathrm{NH}_{4}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\)to form \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}\) is \(3.4 \times 10^{10}\) litmol \(^{-1}\) \(\sec ^{-1}\) at \(25^{\circ} \mathrm{C}\). The rate constant for the proton transfer form water to \(\mathrm{NH}_{3}\) in lit \(\mathrm{mol}^{-1} \mathrm{sec}^{-1}\) is (a) \(6.07 \times 10^{5}\) (b) \(6.07 \times 10^{-5}\) (c) \(6.07 \times 10^{-3}\) (d) \(6.07 \times 10^{-4}\)

Which of the following are the correct statements (a) The \(\mathrm{pH}\) of blood is same in summer and winter (b) \(\mathrm{pH}\) of an acidic buffer increases if more salt is added (c) \(\mathrm{pH}\) of a basic buffer decreases if more salt is added (d) The term solubility product is only for sparingly soluble salts

Acetic acid and aq. \(\mathrm{NH}_{3}\) are weak monobasic acid and weak monobasic base respectively and \(\mathrm{Ka}\) of acetic acid is equal to \(\mathrm{K}_{\mathrm{b}}\) of aq. \(\mathrm{NH}_{3}\). Which of the following statements are incorrect? (1) If acetic acid is exactly neutralized by aq. \(\mathrm{NH}_{3}\) then \(\mathrm{pH}\) of resulting solution is equal to \(1 / 2\) pkw. (2) All the above mixing would result solution having \(\mathrm{pH}=7\) at \(25^{\circ} \mathrm{C}\) (3) If acetic acid is exactly half neutralized by \(\mathrm{NaOH}\), then \(\mathrm{pH}\) of resulting solution is equal to \(\mathrm{pKa}\). (4) If aq. \(\mathrm{NH}_{3}\) is exactly half neutralized by HCl, then pOH of resulting solution is equal to \(\mathrm{pK}_{\mathrm{b}}\). (a) 2 and 4 (b) 2 and 3 (c) 1 and 3 (d) 2 only

Equal volumes of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) (c M) solution of \(\mathrm{pH}=5\) is mixed with \(\mathrm{HCl}\) solution of same \(\mathrm{pH}\). Which of the following is an incorrect statement? (a) Concentration of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) will become \(\mathrm{c} / 2 \mathrm{M}\) after mixing HCl with it. (b) Concentration of \(\mathrm{H}^{+}\)after mixing the two solutions is \(10^{-5} \mathrm{M}\) (c) The degree of dissociation of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) is suppressed due to addition of \(\mathrm{HCl}\). (d) Original concentration of \(\mathrm{HCl}\) was \(10^{-5} \mathrm{M}\).

The dissociation constant of monobasic acids A, B and \(\mathrm{C}\) are \(10^{-4}, 10^{-6}\) and \(10^{-10}\) respectively. The concentration of each monobasic acid is \(0.1 \mathrm{M}\). Which of the following has been arranged in increasing order of \(\mathrm{pH}\) ? (a) \(C
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