Consider the titration of \(100.0 \mathrm{~mL}\) of a \(0.0500 \mathrm{M}\) solution of the hypothetical weak acid \(\mathrm{H}_{3} \mathrm{X}\left(K_{\mathrm{a}_{1}}=1.0 \timesight.\) \(10^{-3}, K_{\mathrm{a}_{2}}=1.0 \times 10^{-7}, K_{\mathrm{a}_{3}}=1.0 \times 10^{-12}\) ) with 0.100 \(M \mathrm{KOH}\). Calculate the \(\mathrm{pH}\) of the solution under the following conditions.

a. before any \(\mathrm{KOH}\) has been added

b. after \(10.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

c. after \(25.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

d. after \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

e. after \(60.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

f. after \(75.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

g. after \(100.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

h. after \(125.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

i. after \(150.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added

j. after \(200.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KOH}\) has been added