Multiple Choice
Which of the following methods can be used to estimate the pH of a weak base solution if the pKa values are not provided?
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17. Acid and Base Equilibrium
pH of Weak Bases
Multiple Choice
A student claims that the pH of a aqueous solution of methylamine, , is 12.54. Given for at 25 °C, which pH is most reasonable (assuming )?
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Verified step by step guidance1
Identify the given information: concentration of methylamine \([CH_3NH_2] = 2.65\,M\), base dissociation constant \(K_b = 4.4 \times 10^{-4}\), and the claimed pH is 12.54. We need to check if this pH is reasonable.
Write the base dissociation equilibrium for methylamine in water: \(CH_3NH_2 + H_2O \rightleftharpoons CH_3NH_3^+ + OH^-\).
Set up the expression for \(K_b\):
\[
K_b = \frac{[CH_3NH_3^+][OH^-]}{[CH_3NH_2]}.
\]
Assuming \(x\) is the concentration of \(OH^-\) produced, and since \(x \ll 2.65\), the concentration of methylamine remains approximately 2.65 M.
Express \(K_b\) in terms of \(x\):
\[
K_b = \frac{x^2}{2.65}.
\]
Solve for \(x\) (the hydroxide ion concentration):
\[
x = \sqrt{K_b \times 2.65}.
\]
Calculate the pOH from \(x\):
\[
\text{pOH} = -\log(x),
\]
then find the pH using the relation:
\[
\text{pH} = 14 - \text{pOH}.
\]
Compare this pH to the claimed value of 12.54 to determine which is most reasonable.
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