Consider a weak acid with a dissociation constant of 1.0 times 10^-5. Evaluate t
ID: 500624 • Letter: C
Question
Consider a weak acid with a dissociation constant of 1.0 times 10^-5. Evaluate the assumption that the change in concentration of the weak acid can be ignored in an equilibrium calculation by calculating the hydronium ion concentration [H_3O^+] at equilibrium with and without the assumption for initial concentrations of the weak acid [HA] listed below. (For the percent error calculation use the value obtained from the quadratic equation as the 'correct' answer) After filling out the table, identify a reasonable value for the ratio of acid concentration to equilibrium constant for the assumption to be valid.Explanation / Answer
HA Ratio of HA/ Ka H3O+ without assumption H3O+ with assumption % age error 1 100000 0.0031 0.0031 0 0.1 10000 0.00099 0.001 -1.0101 0.01 1000 0.00031 0.00031 0 0.001 100 0.000099 0.0001 -1.0101 0.0001 10 0.000031 0.000031 0 0.00001 1 0.0000099 0.00001 -1.0101 0.000001 0.1 0.0000031 0.0000032 -3.22581 HA + H2O = A- + H3O+ HA A- H3O+ I 1 0 0 C - x +X +X E 1-x x x 0.00001 = x2/ 1-x 0.00001 -0.00001x -x2 =0 x2 + 0.00001x-0.00001 =0 If we ignore 0.00001 = x2/ 1-x 0.00001 = X2