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Mobile App Chapter 16: Problem 144
A solution of 0.23 mol of the chloride salt of protonated quinine (QH+), a weak organic base, in 1.0 L of solution has pH = 4.58. Find the Kb of quinine (Q).
Short Answer
Expert verified
Kb of quinine (Q) can be calculated using the given pH and the equations Ka = [Q][H3O+] / [QH+] and Kb = Kw / Ka, where Kw is 1.0 × 10^(-14) at 25°C.
Step by step solution
01
Write down the equilibrium expression for QH+ dissociation
The chloride salt of protonated quinine (QH+) is a weak acid in this context and can be represented as QH+. In water, it dissociates according to the equilibrium: QH+ + H2O ⇌ Q + H3O+. Write the corresponding expression for its dissociation constant, Ka:
02
Calculate the concentration of H3O+
The pH of the solution is given as 4.58, which is a measure of the hydronium ion (H3O+) concentration. Use the pH to find the concentration of H3O+ using the formula: pH = -log[H3O+]. Then calculate [H3O+] as 10^{-pH}.
03
Find the concentration of Q and QH+ at equilibrium
Use the stoichiometry of the dissociation reaction to relate the concentrations of Q, QH+, and H3O+. Since QH+ is a weak acid, we can assume that [QH+] initial approximately equals [QH+] equilibrium. Calculate [Q]=[H3O+] because they are produced in a 1:1 ratio in the dissociation reaction.
04
Calculate the acid dissociation constant (Ka)
Use the formula Ka = [Q][H3O+] / [QH+]. Since [Q] and [H3O+] are equal, square the [H3O+] concentration for the numerator. Use the initial concentration of QH+ which barely changes upon dissociation for the denominator.
05
Calculate the base dissociation constant (Kb) for quinine (Q)
Use the relationship between the acid dissociation constant (Ka) of QH+ and the base dissociation constant (Kb) of Q, where Kw is the ion-product constant of water at 25°C (approximately 1.0 × 10^(-14)). The relationship is given by Kb = Kw / Ka. Calculate Kb using this formula.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Acid Dissociation Constant (Ka)
The acid dissociation constant, abbreviated as Ka, is a quantitative measurement of the strength of an acid in solution. It is the equilibrium constant for the chemical reaction in which an acid donates a proton to water, producing hydronium ions (H3O+). The generic formula for this reaction is:
HA + H2O ⇌ A− + H3O+
The Ka expression for this reaction is given by:
Ka = \( \frac{[A^{-}][H_{3}O^{+}]}{[HA]} \)
where [A−] is the concentration of the conjugate base, [H3O+] is the concentration of hydronium ions, and [HA] is the concentration of the undissociated acid. A higher Ka value indicates a stronger acid, as it signifies a greater degree of dissociation.
HA + H2O ⇌ A− + H3O+
The Ka expression for this reaction is given by:
Ka = \( \frac{[A^{-}][H_{3}O^{+}]}{[HA]} \)
where [A−] is the concentration of the conjugate base, [H3O+] is the concentration of hydronium ions, and [HA] is the concentration of the undissociated acid. A higher Ka value indicates a stronger acid, as it signifies a greater degree of dissociation.
pH Calculation
pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. To calculate the pH of a solution, you need to know the concentration of hydronium ions (H3O+) in the solution. The pH is then found using the formula:
pH = -log[H3O+]
Given the pH, the concentration of hydronium ions can be calculated as follows:
[H3O+] = \(10^{-pH}\)
Understanding this calculation helps to connect the pH value to the concentration of acids or bases in solution.
pH = -log[H3O+]
Given the pH, the concentration of hydronium ions can be calculated as follows:
[H3O+] = \(10^{-pH}\)
Understanding this calculation helps to connect the pH value to the concentration of acids or bases in solution.
Equilibrium Expression
An equilibrium expression represents the relationship between the concentrations of reactants and products in a chemical reaction at equilibrium. For the dissociation of an acid, HA, the equilibrium constant (Ka) can be written as follows:
\(Ka = \frac{[A^{-}][H_{3}O^{+}]}{[HA]}\)
This formula involves the concentrations of the species in the reaction when the rate of the forward reaction equals the rate of the reverse reaction. The equilibrium expression allows us to calculate the extent to which an acid dissociates in water and its corresponding strength.
\(Ka = \frac{[A^{-}][H_{3}O^{+}]}{[HA]}\)
This formula involves the concentrations of the species in the reaction when the rate of the forward reaction equals the rate of the reverse reaction. The equilibrium expression allows us to calculate the extent to which an acid dissociates in water and its corresponding strength.
Stoichiometry
Stoichiometry is the calculation of reactants and products in chemical reactions. It's grounded in the principle that matter is conserved in reactions, and thus the number of atoms of each element should remain unchanged. In the context of acid-base reactions, stoichiometry helps determine the relationships between the amounts of acids, bases, and ions present in solution. For instance, in the dissociation of a weak acid (HA) into its conjugate base (A−) and hydronium ion (H3O+), the stoichiometric coefficients indicate a 1:1:1 ratio. This means that each mole of HA that dissociates will produce one mole of A− and one mole of H3O+.
Hydronium Ion Concentration
The hydronium ion concentration in a solution is a key factor in determining both the pH of the solution and the position of equilibrium in acid-base reactions. Represented as [H3O+], it's directly related to the strength of the acid present. In practical terms, the pH of a solution can give a quick understanding of the hydronium ion concentration, as pH and [H3O+] are logarithmically related:
pH = -log[H3O+]
Thus, by knowing the pH, one can calculate the hydronium ion concentration. Moreover, the concentration of H3O+ also plays a pivotal role in calculating the acid dissociation constant (Ka) when equilibrium concentrations are known.
pH = -log[H3O+]
Thus, by knowing the pH, one can calculate the hydronium ion concentration. Moreover, the concentration of H3O+ also plays a pivotal role in calculating the acid dissociation constant (Ka) when equilibrium concentrations are known.
