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Multiple Choice
What is the pH of a solution when 40.00 mL of 0.1000 M HCl is added to a 50.00 mL aliquot of 0.1200 M ethylamine (CH3CH2NH2) with a Kb of 5.6 x 10^-4?
A
7.50
B
9.25
C
8.75
D
8.15
Verified step by step guidance
1
Calculate the moles of HCl added using the formula: \( \text{moles of HCl} = \text{volume (L)} \times \text{molarity (M)} \). Convert 40.00 mL to liters and multiply by 0.1000 M.
Calculate the moles of ethylamine (CH3CH2NH2) using the formula: \( \text{moles of ethylamine} = \text{volume (L)} \times \text{molarity (M)} \). Convert 50.00 mL to liters and multiply by 0.1200 M.
Determine the limiting reactant by comparing the moles of HCl and ethylamine. The reaction is: \( \text{HCl} + \text{CH3CH2NH2} \rightarrow \text{CH3CH2NH3}^+ + \text{Cl}^- \). Subtract the smaller number of moles from both reactants to find the moles of excess reactant.
Calculate the concentration of the conjugate acid (CH3CH2NH3^+) formed. Use the volume of the final solution (sum of the initial volumes) to find the concentration: \( \text{concentration} = \frac{\text{moles of CH3CH2NH3}^+}{\text{total volume (L)}} \).
Use the Henderson-Hasselbalch equation to find the pH: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right) \). First, calculate \( \text{pK}_a \) from \( \text{pK}_a = 14 - \text{pK}_b \), where \( \text{pK}_b = -\log(5.6 \times 10^{-4}) \). Then, substitute the concentrations of the base (ethylamine) and the conjugate acid (CH3CH2NH3^+) into the equation.