Maybe simple buffer question- BR Example 5.6 Gen Chem

[anon1480526]

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If 1.0 moles of a weak acid in 1.0 liters of water are treated with 0.4 moles of strong base, what is the pH of the solution? (Ka for the weak acid is 2.0 x 10^-4)
A) pH<3.7
B) pH=3.7
C) 3.7<pH<7
D) pH>7

 

[quicheduty]

The answer should be A, yes? Do you have a more specific question?
Calculating the pKa to be 3.7, from buffer rules you should know that to make a buffer from weak acid you usually add a half-equiv of strong base (I believe TBR says this too). So you'd need 0.5 moles NaOH for the pH = pKa = 3.7. Since you have less than that, think of it as having more H+ than OH- needed for pH of 3.7. More H+ means lower pH. Let me know if that helps...

 

[Lunasly]

We can estimate the pH of the solution as being less than 4. To be more precise, the pH according the pKa of the solution is 3.7 (4 - log 2 = 4 - 0.3 = 3.7). Now we would need to add 1 mole of NaOH to completely neutralize the weak acid. Therefore, we need to add 0.5 moles of NaOH to get to the half-equivelence point, where pH = pKa and moles of weak acid = moles of conjugate base. Since we added less than 0.5 moles (0.4 moles were added), pH does not equal pKa. In fact, pH is less than PKa. Therefore, the pH of the solution must be less than 3.7.