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Chapter 5: Problem 2

Which of the following has the highest \(\mathrm{pH}\) ? a. \(0.1 \mathrm{M} \mathrm{NaOH}\) b. \(0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) c. \(0.01 \mathrm{M} \mathrm{NaOH}\) d. \(0.1 \mathrm{M} \mathrm{HCl}\)

Short Answer

Expert verified
0.1 M NaOH has the highest pH, which is 13.

Step by step solution

01

Understanding pH and Concentration

The pH measures the acidity or basicity of a solution. Lower pH values indicate higher acidity (more H鈦� ions), while higher pH values indicate higher basicity (more OH鈦� ions). Strong bases like NaOH dissociate completely, contributing to higher pH values, while strong acids like HCl dissociate completely, contributing to lower pH values. Acetic acid (CH鈧僀OOH) is a weak acid and does not dissociate completely.
02

Calculate pH of 0.1 M NaOH

NaOH is a strong base and dissociates completely in water. The concentration of OH鈦� ions is equal to the concentration of NaOH, which is 0.1 M. The pOH is calculated as:\[\mathrm{pOH} = -\log[\mathrm{OH}^-] = -\log(0.1) = 1\]Since \(\mathrm{pH} + \mathrm{pOH} = 14\),\[\mathrm{pH} = 14 - 1 = 13\]
03

Calculate pH of 0.1 M CH鈧僀OOH

CH鈧僀OOH is a weak acid, so we must use its dissociation constant (\(K_a = 1.8 \times 10^{-5}\)). Setting up the dissociation equation:\[CH_3COOH \rightleftharpoons CH_3COO^- + H^+\]Using the approximation method for weak acids, the concentration of H鈦� is approximately \(\sqrt{0.1 \times K_a} \approx \sqrt{0.1 \times 1.8 \times 10^{-5}} = 1.34 \times 10^{-3}\). Calculating pH:\[\mathrm{pH} = -\log[H^+] = -\log(1.34 \times 10^{-3}) \approx 2.87\]
04

Calculate pH of 0.01 M NaOH

NaOH is a strong base. The concentration of OH鈦� ions is equal to the concentration of NaOH, which is 0.01 M. Calculate pOH:\[\mathrm{pOH} = -\log[\mathrm{OH}^-] = -\log(0.01) = 2\]Calculate pH:\[\mathrm{pH} = 14 - 2 = 12\]
05

Calculate pH of 0.1 M HCl

HCl is a strong acid and dissociates completely in water. The concentration of H鈦� ions is equal to the concentration of HCl, which is 0.1 M. Calculate pH:\[\mathrm{pH} = -\log[H^+] = -\log(0.1) = 1\]
06

Compare the Calculated pH Values

From the calculations, the pH values are: - 0.1 M NaOH: pH = 13 - 0.1 M CH鈧僀OOH: pH 鈮� 2.87 - 0.01 M NaOH: pH = 12 - 0.1 M HCl: pH = 1 Among these, 0.1 M NaOH has the highest pH value of 13.

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Key Concepts

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

Understanding Strong Acids and Bases
Strong acids and bases are unique in the way they dissociate in water. When we say an acid or base is "strong," this means they completely split into ions in an aqueous solution. Take hydrochloric acid (HCl) for instance. In water, it dissociates entirely to form H鈦� and Cl鈦� ions. Similarly, sodium hydroxide (NaOH), a strong base, fully separates into Na鈦� and OH鈦� ions.
  • Complete dissociation leads to strong electrolytes.
  • Strong acids have very low pH values, often nearby 1 when in high concentrations.
  • Strong bases end up with very high pH values, often close to 14 in high concentrations.
These properties make them predictable and easier to calculate quantitatively, as each molecule contributes wholly to the concentration of ions.
Weak Acids: A Complex Balance
Unlike their strong counterparts, weak acids only partially dissociate in solution. This means a significant portion of the acid remains in its original form. Acetic acid (CH鈧僀OOH) is a prime example. In water, it partially dissociates into CH鈧僀OO鈦� and H鈦� ions, but a sizable amount stays as CH鈧僀OOH.
  • This partial dissociation results in lower concentrations of H鈦� ions.
  • The pH of a weak acid solution typically revolves around 2 to 6, depending on its concentration and dissociation constant.
Due to this incomplete dissociation, calculations often require the use of an equilibrium constant, known as the dissociation constant (K鈧�). Understanding weak acids often involves handling equilibria and using approximations where possible.
The pH Scale Explained
The pH scale is a convenient way to express the acidity or basicity of a solution. It ranges from 0 to 14, where 7 is neutral鈥攍ike pure water. Values below 7 indicate an acidic solution, while those above suggest a basic solution.
The pH scale operates logarithmically, meaning each whole number change on the scale represents a tenfold change in hydrogen ion concentration. For instance, a pH of 5 has ten times more H鈦� ions than a pH of 6.
  • Neutral substances have a pH of about 7.
  • Acids typically range between 0 and 7.
  • Bases usually have a pH between 7 and 14.
This scale helps in quickly understanding the nature of a solution and is pivotal when you want to compare the strengths of acidic or basic substances.
Dissociation Constant: Key to Understanding Weak Acids
The dissociation constant (K鈧�) is crucial for weak acids. It quantifies the extent of dissociation of the acid into its ions in solution. A larger K鈧� suggests a stronger weak acid, indicating more H鈦� ions in the solution. Consider acetic acid, with a dissociation constant of about 1.8 脳 10^{-5}.
This small value reveals that only a modest amount of acetic acid dissociates in an equilibrium state.
  • A small K鈧� shows weak acid strength due to lesser ion formation.
  • Larger the K鈧�, stronger is the weak acid's tendency to dissociate.
To find the pH of a weak acid, oftentimes you turn to using the approximation formula: \[\text{[H鈦篯} \approx \sqrt{K_a \cdot \text{initial concentration}}\]This enables you to determine the concentration of hydrogen ions without solving a complex equilibrium equation.

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Most popular questions from this chapter

For the decomposition of \(\mathrm{PCl}_{5}\) (g) in a closed vessel which is the correct relation between totalpressure (P), equilibrium constant \(\left(\mathrm{K}_{\mathrm{p}}\right)\) and degree of dissociation \((\alpha)\) a. \(\alpha=\sqrt{\left(K_{p}+P\right)}\) b. \(\alpha=\sqrt{\left[1 /\left(\mathrm{K}_{\mathrm{p}}+\mathrm{P}\right)\right]}\) c. \(\alpha=\sqrt{\left[K_{p} /\left(\mathrm{K}_{\mathrm{p}}+\mathrm{P}\right)\right]}\) d. \(\left.\alpha=\sqrt{[}\left(\mathrm{K}_{\mathrm{n}}+\mathrm{P}\right) / \mathrm{K}_{\mathrm{n}}\right]\)

Which of the following statement is/are correct for a reversible reaction? a. At a given temperature both \(Q\) and \(K\) vary with the progress of the reaction. b. When \(Q>K\), the reaction proceeds in backward direction before coming to stand still. c. Reaction quotient (Q) is the ratio of the product or arbitrary molar concentrations of the products to those of the reactants. d. \(Q\) may be \(<>=K\).

The oxidation of sulphur dioxide by oxygen to sulphur trioxide has been implicated as an important step in the formation of acid rain: \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) If the equilibrium partial pressures of \(\mathrm{SO}_{2}, \mathrm{O}_{2}\) and \(\mathrm{SO}_{3}\) are \(0.564 \mathrm{~atm}, 0.102 \mathrm{~atm}\), and \(0.333 \mathrm{~atm}\) respec- tively at \(1000 \mathrm{~K}\), what is the \(\mathrm{Kp}\) at that temperature? a. \(2.24\) b. \(4.68\) c. \(3.42\) d. \(13.42\)

(A): Ice melts slowly at higher altitudes. (R): The melting of ice is favoured at high pressure because ice \(\longrightarrow\) water shows decrease in volume.

(A): The \(\mathrm{pH}\) of a buffer solution containing equal moles of acetic acid and sodium acetate is \(4.8\) (pKa of acetic acid is \(4.8\) ) \((\mathbf{R}):\) The ionic product of water at \(25^{\circ} \mathrm{C}\) is \(10^{-14}\) \(\mathrm{mol}^{2} \mathrm{lit}^{-2}\)
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