Problem: Quinine (C20H24N2O2) is the most important alkaloid derived from cinchona bark. It is used as an antimalarial drug. For quinine, pK b1 = 5.1 and pK b2 = 9.7 (pK b = -log K b). Only 1 g quinine will dissolve in 1900.0 mL of solution. Calculate the pH of a saturated aqueous solution of quinine. Consider only the reaction Q + H2O ⇌ QH + + OH - described by pK b1, where Q = quinine.

FREE Expert Solution

We are asked to calculate the pH of a saturated aqueous solution of quinine.


Step 1. Calculate concentration

Molar mass = 324.4 g/mol


Molarity = 1 g1900 mL×1 mL10-3 L×1 mol324.4 g

Molarity = 0.0016 M


Step 2. Set-up ICE chart



Step 3. Calculate [OH-]

Kb=[QH+][OH-][Q]10-pKb=[x][x][0.0016-x]10-5.1=[x][x][0.0016-x]7.94×10-6=[x][x][0.0016-x]


Check if x in the denominator is negligible:

0.00167.94×10-6 = 204.337 <500


Since the ratio is < 500, x is not negligible. 

7.94×10-6=[x][x][0.0016-x](7.94×10-6)[0.0016-x]=x21.27×10-8-7.94×10-6x=x20= x2  + 7.94×10-6x - 1.27×10-8


Use quadratic formula: 

From the equation, we have a = 1, b = 7.94×10–6, and c = 1.27 × 10–8. Solving for xx = -b±b2-4ac2ax = -7.94×106±(7.94×106)2-4(1)(-1.27 × 108)2(1)x = -7.94×106±5.09×1082

[OH-] = x = 1.09 x 10-4 M


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Problem Details

Quinine (C20H24N2O2) is the most important alkaloid derived from cinchona bark. It is used as an antimalarial drug. For quinine, pK b1 = 5.1 and pK b2 = 9.7 (pK b = -log K b). Only 1 g quinine will dissolve in 1900.0 mL of solution. Calculate the pH of a saturated aqueous solution of quinine. Consider only the reaction Q + H2O ⇌ QH + + OH - described by pK b1, where Q = quinine.

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