Multiple Choice
What is the pH of a 7.0 × 10⁻³ M NH₃ solution? (Kb = 1.8 × 10⁻⁵ for NH₃)
17. Acid and Base Equilibrium
pH of Weak Bases
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What is the pH of a solution containing 400 mg of caffeine with a pKb of 10.4, if the solution has a 3.44% mass concentration and a density of 1.01 g/mL?
A
9.5
B
6.8
C
7.0
D
8.2
Verified step by step guidance1
First, calculate the mass of the solution using the mass concentration and the mass of caffeine. The mass concentration is given as 3.44%, which means 3.44 g of caffeine per 100 g of solution. Use the formula: \( \text{mass of solution} = \frac{\text{mass of caffeine}}{\text{mass concentration}} \).
Convert the mass of the solution to volume using the density. The density is given as 1.01 g/mL, so use the formula: \( \text{volume of solution} = \frac{\text{mass of solution}}{\text{density}} \).
Calculate the molarity of caffeine in the solution. First, convert the mass of caffeine to moles using its molar mass (approximately 194.19 g/mol for caffeine). Then, use the formula: \( \text{molarity} = \frac{\text{moles of caffeine}}{\text{volume of solution in liters}} \).
Determine the concentration of hydroxide ions \( [OH^-] \) using the pKb value. The relationship is given by \( [OH^-] = \sqrt{K_b \times [caffeine]} \), where \( K_b = 10^{-pK_b} \).
Finally, calculate the pH of the solution. First, find the pOH using \( \text{pOH} = -\log[OH^-] \), and then use the relationship \( \text{pH} = 14 - \text{pOH} \) to find the pH.
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