Problem:
For aspirin, Ka=3X 10-5 at 37 degrees C. There are 325 mg of aspirin in an aspirin tablet. If two aspirin tablets are dissolved in a volume of 1L in which the pH is 2, What percentage of the aspirin is in the form of molecules?
1) You can find the initial concentration of H+ in the solution from the pH.
pH = - log [H+]
2 = - log [H+]
[H+] = 0.01 M
2) Next you need to convert g aspirin to moles. The structure of aspirin is HC9H7O4. The molecular weight (molar mass) is 180.2 g/mol.
Convert 650 mg aspirin to moles. 650 mg = 0.650 g
0.650 g * 1 mol/180.2 g = 0.00361 moles
Since the total volume of the solution is 1 L, the concentration is also 0.00361 M
3) Write down the acid dissociation reaction for this compound.
4) Make a chart containing the initial amount, change and equilibrium amount of each substance.
HC9H7O4 ------------> H+ + C9H7O4-
initial 0.00361 M 0.01 M 0
Change - x + x + x
----------------------------------------------------------------------------------
equilibrium 0.00361 - x 0.01 + x x
The initial value of H+ came from step 1. Initial value for aspirin cam from step 2.
5) Set up equilibrium and solve for x.
[H+][C9H7O4-]
Ka = -------------------------
HC9H7O4
3 X 10-5 = (0.01 + x)(x)
--------------------
0.00361 - x
x = 1.083 X 10-5
To make this arithmetic easier you may assume that x that is added and subtracted in the expressions is negligible. That is x<<0.01 and x << .00361
The expression then becomes:
3X10-5 = (0.01)(x)
--------------
0.00361
Solving for x now is simple.
Now we know the number of moles of aspirin that dissociated.
6) Convert moles dissociated to g.
1.083X10-5 * 180.2 g/mol = .00195 g = 195 mg aspirin
650 mg - 195 mg = 455 mg not dissociated or remains in the form of molecules.
To find the percentage,
455/650 * 100 = 70%
R. H. Logan, Instructor of Chemistry, Dallas County Community College District, North Lake College.
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All textual content copyrighted (c) 1995 R.H. Logan, Instructor of Chemistry, DCCCD All Rights reserved
Revised: 4/16/97
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