Morphine, , is administered medically to relieve pain. It is a naturally occurring base, or alkaloid — Ionic Equilibrium Chemistry Question
Question
Morphine, $\text{C}_{17}\text{H}_{19}\text{NO}_3$, is administered medically to relieve pain. It is a naturally occurring base, or alkaloid. What is the pH of a 0.0025 M solution of morphine at $25^\circ \text{C}$? The base-ionization constant, $K_b$, is $1.6 \times 10^{-6}$ at $25^\circ \text{C}$. (log 2 = 0.3)
Answer: B
💡 Solution & Explanation
Concentration $C = 0.0025 \text{ M} = 2.5 \times 10^{-3} \text{ M}$. For a weak base, $[OH^-] = \sqrt{K_b C} = \sqrt{(1.6 \times 10^{-6}) \times (2.5 \times 10^{-3})} = \sqrt{4.0 \times 10^{-9}} = \sqrt{40 \times 10^{-10}} = 6.32 \times 10^{-5} \text{ M}$. $pOH = -\log(6.32 \times 10^{-5}) \approx 5 - 0.8 = 4.2$. The $pH = 14 - pOH = 14 - 4.2 = 9.8$. Therefore, correct answer is B.
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