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Piperidine, C_{5}H_{11}N (pK_{b} = 2.89), is a colorless liquid having the odor of pepper. Calculate the pH of 0.00250 M C_{5}H_{11}N.
Treat this as any equilibrium problem: write the balanced chemical reaction, write the mass action expression for K_{b}, set up a table of concentrations, and then solve for the unknown variables using the given information. Assume 25 ^{o}C.










Initial 




Change 




Equilibrium 



Approximate? 0.00250/1.3×10^{–3} = 2 < 100 No!
Solve this using the quadratic equation to give:
x = 1.3×10^{–3}, –2.6×10^{–3}
Only the positive root makes sense, so [OH^{–}] = x = 1.3×10^{–3} M
pOH = –log[OH^{–}] = –log(1.3×10^{–3}) = 2.89
pH = 14.00 – pOH = 14.00 – 2.89 = 11.11