Caffeine (C8H10N4O2) is a weak base with a pKb of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.
Ch.17 - Acids and Bases

Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Capitolo 17, Problema 98
A 0.135 M solution of a weak base has a pH of 11.23. Determine Kb for the base.
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Identify the relationship between pH and pOH: \( \text{pH} + \text{pOH} = 14 \). Use this to find pOH from the given pH.
Calculate the hydroxide ion concentration \([\text{OH}^-]\) using the formula \([\text{OH}^-] = 10^{-\text{pOH}}\).
Set up the expression for the base dissociation constant \(K_b\) using the formula \(K_b = \frac{[\text{OH}^-]^2}{[\text{Base}] - [\text{OH}^-]}\).
Assume that \([\text{Base}] - [\text{OH}^-] \approx [\text{Base}]\) if \([\text{OH}^-]\) is much smaller than the initial concentration of the base.
Substitute the values into the \(K_b\) expression and solve for \(K_b\).
Concetti chiave
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Weak Base and pH
A weak base is a substance that partially ionizes in solution, establishing an equilibrium between the base and its ions. The pH of a solution indicates its acidity or basicity, with values above 7 being basic. In this case, a pH of 11.23 suggests that the solution is basic, and the concentration of hydroxide ions can be derived from the pH to help calculate the base's dissociation constant.
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Calculating pH of Weak Bases Example
Equilibrium Constant (Kb)
The base dissociation constant (Kb) quantifies the strength of a weak base in solution. It is defined as the ratio of the concentration of the products (the ions formed) to the concentration of the reactants (the un-ionized base) at equilibrium. For a weak base, Kb can be calculated using the concentrations of the base and its ions at equilibrium, which can be derived from the pH and initial concentration.
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Equilibrium Constant K
Relationship Between pH and pOH
The pH and pOH of a solution are related through the equation pH + pOH = 14 at 25°C. This relationship allows us to convert pH values into pOH values, which can then be used to find the concentration of hydroxide ions (OH-) in the solution. Knowing the concentration of OH- is essential for calculating Kb, as it directly relates to the degree of ionization of the weak base.
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pH and pOH Calculations
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