Simple question about Ka

[MediCynical]

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The Ka for HSO4- is 1.2E-2. When 1 mole of HSO4- is added to one liter of pure water:

A. the ion completely dissociates
B. most, but not all, of the ions gain a proton
C. most, but not all, of the ions lose a proton
D. some of the ions lose a proton, but most of the ions neither gain nor lose a proton

Answer: D

OK, so I understand this question mathematically. Ka = 1.2E-2 = x^2/1
x = 1.1E-1, which is [H+] which is less than 1 so D is the answer.

But what's not working for me is the Ka being 1.2E-2, which means the pKa is just under 2. Why isn't there more dissociation?? Doesn't the low pKa mean that there should be significant dissociation?

I guess I get stuck on the fact that for buffers the pKa is the pH at which there's equal concentrations of A-/HA. Any help with getting me to process this? lol

 

[MCAT guy]

The Ka for HSO4- is 1.2E-2. When 1 mole of HSO4- is added to one liter of pure water:

A. the ion completely dissociates
B. most, but not all, of the ions gain a proton
C. most, but not all, of the ions lose a proton
D. some of the ions lose a proton, but most of the ions neither gain nor lose a proton

Answer: D

OK, so I understand this question mathematically. Ka = 1.2E-2 = x^2/1
x = 1.1E-1, which is [H+] which is less than 1 so D is the answer.

But what's not working for me is the Ka being 1.2E-2, which means the pKa is just under 2. Why isn't there more dissociation?? Doesn't the low pKa mean that there should be significant dissociation?

I guess I get stuck on the fact that for buffers the pKa is the pH at which there's equal concentrations of A-/HA. Any help with getting me to process this? lol

This isn't a super low Ka. The Ka of a weak acid is less than 1, the Ka of a strong acid is greater than 1.

Here is an excerpt from my BR acid notes:

• **Strong acids (w/ pKa)
  • Hydrochloric (HCl) -7
  • Hydrobromic (HBr) -7
  • Hydroiodic (HI) -9
  • Sulfuric acid (H2SO4) -9 (pKa1)
  • Nitric acid (HNO3) -2
  • Perchloric HClO4 -10
• Weak acid only partial dissoc, hence small Ka (< 1)
  • they define weak as pKa 0-14
  • Trichloroacetic acid Cl3CCO2H 0.64
  • Dichloroacetic acid Cl2HCCO2H 1.27
  • Sulfurous acid H2SO3 1.82 (pKa1)
  • Chlorous acid HClO2 1.9
  • Chloroacetic acid ClH2CO2H 2.82
  • Hydrofluoric acid HF 3.15
  • Nitrous acid HNO2 3.41
  • Formic acid HCO2H 3.74
  • Acetic acid H3CCO2H 4.74
  • Carbonic acid H2CO3 6.36 (pKa1)
  • 4-nitrophenol 4-O2NC6H4OH 7.15
  • Hypochlorous acid HClO 7.46
  • Hypobromous acid HBrO 8.72
  • Ammonium NH4+ 9.26
  • Hydrogen Cyanide HCN 9.32
  • Hypoiodous acid 10.66
• very weak acid, pKa > 14
• Summary:
  • Strong acid / conj very weak base
    • Ka >> 1
    • pKa < 0
    • Kb < 10 E-14
    • pKb > 14
  • Weak acid / conj very weak base
    • Ka 10 E-14 - 1
    • pKa 0-14
    • Kb 10 E-14 - 1
    • pKb 0 - 14
  • Very weak acid / conj strong base
    • Ka < 10-14
    • pKa > 14
    • Kb >> 1
    • pKb < 0

 

[MediCynical]

thanks that helps 👍

 

[PiBond]

here's a little different explanation, although it seems like you already understand the answer.

HSO4- is the conjugate base of a strong acid and thus it really doesn't have any significant basic properties (ie it's very stable). Thus we can eliminate B. Based on its pka/Ka value, HSO4- isn't a strong strong acid so we won't observe complete dissociation in solution...thus eliminate A. As mcat guy alluded to, HSO4- is a weak acid and thus we'll see some deprotonation but for the most part it's going to remain as is in solution, primarily due to its stability from resonance.

 

[Rabolisk]

Strong acids dissociate nearly completely. In calculations you assume it to be 100%. Weak acids dissociate very little, even ones with a low pKa like 2. For example, 1M solution of acid with a pKa of 2 only dissociates 9.5%.