The pH of the solution in which one normal adult dose aspirin is dissolved is : 2.7
Given data :
mass of aspirin = 640 mg = 0.640 g
volume of water = 10 ounces = 0.295735 L
molar mass of aspirin = 180.16 g/mol
moles of aspirin = mass / molar mass = 0.00355 mol
First step : calculate the concentration of aspirin
= moles of Aspirin / volume of water
= 0.00355 / 0.295735
= 0.012 M
Given that pKa of Aspirin = 3.5
pKa = -logKa
therefore ; Ka = [tex]10^{-3.5}[/tex] = [tex]3.162 * 10^{-4}[/tex]
From the Ice table
[tex]3.162 * 10^{-4}[/tex] = [tex]\frac{x + H^+}{[aspirin]}[/tex] = [tex]\frac{x^{2} }{0.012-x}[/tex]
given that the value of Ka is small we will ignore -x
x² = [tex]3.162 * 10^{-4} * 0.012[/tex]
x = [tex]1.948 * 10^{-3}[/tex]
Therefore
[ H⁺ ] = [tex]1.948 * 10^{-3}[/tex]
given that
pH = - Log [ H⁺ ]
= - ( -3 + log 1.948 )
= 2.71 ≈ 2.7
Hence we can conclude that The pH of the solution in which one normal adult dose aspirin is dissolved is : 2.7
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