Ka and Kb of compounds - Online Tutor, Practice Problems & Exam Prep

Weak acids and bases are characterized by their acid dissociation constant (Ka) and base dissociation constant (Kb), both of which are less than 1, indicating limited product formation in solution. The relationship between Ka and Kb is defined by the ion product constant for water (Kw = Ka × Kb). Understanding these constants is essential for calculating pH and pOH in weak acid-base equilibria. The equilibrium expressions for weak acids and bases exclude solids and liquids, focusing on the concentrations of ions produced in solution.

Ka and Kb

We're going to say here that associated with any weak acid or any weak base, we have our Ka and our Kb values. These are equilibrium constants for weak acids and weak bases respectively. We're going to say Ka represents the acid dissociation constant for a weak acid and it measures the strength of weak acids. And we're going to say here that the Kb is representative of our base dissociation constant and it measures the strength of weak bases.

We're going to say in general, the higher your K value is, then the lower your pKa value is. This translates to a stronger acid. That means that you'll produce more H⁺ concentration. It's going to increase the concentration of H⁺. We're going to say here that generally speaking, weak acids have Ka values less than 1.

Weak bases use Kb instead. Their Kb values are less than 1. Now, because their Ka and Kb values are less than one, that means we do not make an appreciable amount of products. Very little product would be made when our weak acid dissolves in solution or when our weak base dissolves in solution. If we're talking about weak acids and weak bases, we're going to say that they establish equilibriums because they're weak.

For a weak acid, here it's the acid. Water here will act as the base. Based on the Bronston-Lowry theory, weak acids donate H⁺ to the base creating A^- and H₃O⁺ as our products. Here, we establish an equilibrium which is the reason for the double arrows. Now, weak acids use Ka.

  
    Ka
    =
    
      
        [A−]
        [H3O+]
      
      
        [Acid]
      
    
  

For weak bases, here it's the base.

Water now acts as the acid. It's going to donate an H⁺ over to the base according to Bronston-Lowry, therefore creating OH^- as the product. Weak bases use Kb as their equilibrium constant.

  
    Kb
    =
    
      
        [OH−]
      
      
        [Base]
      
    
  

Later on, we'll learn that through these equilibrium expressions, we're able to set up an ice chart to determine the pH or pOH of a weak acid and a weak base respectively. Now Ka and Kb are connected to each other by the formula Kw = Ka × Kb. We've seen Kw in the past before.

Remember, this represents our ion product constant for water. At 25 degrees Celsius it equals 1.0 × 10^-14. This means that at 25 degrees Celsius, if I know Ka, I can determine Kb because we'll know what Kw is and vice versa. If I know Ka, I can find Kb because we again know what Kw is. Keep in mind this equation here to help you convert from either Ka to Kb or vice versa.

Now that we’ve looked at our descriptions of Ka and Kb, try to attempt this example question here on the bottom of the page. If you get stuck, don't worry. Just click on to the next video and see how I approach that same question, which relates acid strength between these two acids given in an example on the bottom of the page.

Ka and Kb

Here it says to consider two aqueous solutions of equal concentration. Which statement is true? We have chlorous acid, which has a Ka=1.1×10-2 and phenol, which has a Ka=1.3×10-10. Alright. So, both of these acids here would react with water.

They both would donate an H⁺ to water. So we'd have ClO2− and H3O⁺ being created here. And then here, this phenol would also react with water, donates an H⁺ to water to produce C6H5O− plus H3O⁺. Now remember, the higher your Ka value, the stronger the acid. What does that mean?

Well, the higher the Ka, the stronger the acid, the more it dissociates into these ions as products. So basically, the higher your Ka, the more of these you'll produce, the more products you'll produce. And since chlorous acid has a higher Ka value, that means we're going to produce a higher amount of these products. Alright, so now looking at that, let's look and see which statement is true. So, chlorous acid produces more H3O⁺ than phenol.

That is true because it has a higher Ka value. So, is chloric acid basic compared to phenol? No, it's more acidic because its Ka is larger. Does chlorous acid produce less H3O⁺ than phenol? No, again it produces more H3O⁺ because its Ka is larger, making it more acidic.

Is chlorous acid a strong acid? No, we said earlier that weak acids have Ka values less than 1, so this would be a weak acid. And then here, our chloride ion produces more OH⁻ than our phenoxide ion. Alright. So these are the conjugate base forms of those acids.

So let's think about this. So you have ClO2 as a stronger acid than phenol. If you're stronger as an acid, that means you're going to be weaker as a base. So ClO2− is a weaker base than C6H5 O−. Because remember, if you're strong as an acid, you're weaker as a base.

If you're weaker as a base, that means you produce less OH⁻. So chloride wouldn't produce more OH⁻, it would produce less because it is the weaker base of the two. So out of all the choices, only option A would be true. So just remember, the higher the Ka, the stronger the acid will be, the more it will produce the desired ions as products. But the stronger you are as an acid, the weaker you will be as a base.

Remember, you can't be incredibly strong both ways. Pick a side, you're weaker on the opposite. So the stronger the acid, the weaker the base form would be.

Ka and Kb Calculations 1

So here it asks, which of the following compounds has the strongest conjugate acid? Now realize that there is give and take. If you exist as one of the strongest acids, that means you're going to exist as also one of the weakest bases. The strongest conjugate acid here is really saying the weakest base. We're looking at the weakest base because all of these compounds here are nitrogenous compounds, so nitrogen-containing compounds which makes them amines which is the reason they have kb values associated with them.

Remember, kb values are associated with weak bases. Since we're looking for the strongest conjugate acid, that really means that we're looking at the weakest base. The weakest base would have the smallest Kb value. If we look at all the choices, the one with the smallest Kb value would be the last option here. Option D would be our correct choice.

Remember, if you're incredibly strong one way, you're incredibly weak the opposite. The strongest acid would give us the weakest conjugate base. Then we'd say here, the strongest base would give me the weakest conjugate acid. Just remember, the opposite duality that exists between acids and bases in order to answer a question like this.

Ka and Kb Calculations 1

Here for this example, it says, at 0 degrees Celsius, the ion product constant of water is 1.2×10-15. Now the pH of pure water at this temperature is discussed. So, they're talking about the ion product constant of water, or KW. Remember KW=H3O+∙OH-.

Here, they tell me that I'm dealing with pure water. When they say pure water, that just means that the concentration of H3O+ is equal to the concentration of OH-. Since we don't know what the value will be, we'll say that they're both equal to x. So now our equation is x∙x, which is equal to x2. We know what our KW is at this temperature.

It's 1.2×10-15. Now remember, you might be accustomed to seeing KW as being equal to 1.0×10-14. But that's only true when the temperature is at 25 degrees Celsius. Like any equilibrium constant, KW has its value changed if the temperature changes. So now we say that x2=1.2×10-15.

We need to find the pH. pH equals the negative log of H3O+. So if I can solve for x, which represents H3O+, I can find my pH. So take the square root of both sides. When we do that, x=3.464×10-18.

Again, this would equal the concentration of both H3O+ and OH- since they're both equal to x. But since we're looking for the pH, we only care about the H3O+. So take that and plug it into my formula. When we do that, we get 7.46 as my answer. So here, this would be my final answer.

We're not worrying about significant figures here because we're trying to match it with the correct answer. Option C would be the best answer here. Now technically, since it's a 7.46, technically, we should have had only 2 significant figures here. But again, we're not really concerned with significant figures here. We're just more concerned with, do we know how to solve a question like this?

Here water means that H3O+ and OH- are equal to each other, so set them both equal to x. And again, remember if your temperature changes from 25 degrees Celsius, KW will be a new value. You don't have to memorize all these values. They will tell you what the new value for KW would be. Use it to solve for x.

(CH₃)₂NH is a weak base. Which equilibrium corresponds to the acid dissociation constant K_a for (CH₃)₂NH₂⁺? 

• A. (CH₃)₂NH (aq) + H₂O (l) ⇌ (CH₃)₂N⁺ (aq) + H₃O⁺ (aq)
• B. (CH₃)₂NH₂⁺ (aq) + H₃O⁺ (aq) ⇌ (CH₃)₂NH (aq) + H₂O (aq)
• C. (CH₃)₂NH₂⁺ (aq) + H₂O (l) ⇌ (CH₃)₂NH (aq) + H₃O⁺ (aq)
• D. (CH₃)₂NH₂⁺ (aq) + OH⁻ (aq) ⇌ (CH₃)₂NH (aq) + H₂O (aq)
• E. (CH₃)₂NH₂⁺ (aq) ⇌ (CH₃)₂NH (aq) + H⁺ (aq)