Ka and Kb: Study with Video Lessons, Practice Problems & Examples

Weak acids, characterized by their ability to donate a proton (H⁺), have an acid dissociation constant (K_a) that measures their strength. The relationship between K_a and pK_a is inverse; a higher K_a indicates a stronger acid, while pK_a is the negative logarithm of K_a. For weak acids, K_a is typically less than 1, and pK_a is greater than 1. The equation K_w = K_a × K_b connects acid and base dissociation constants, with K_w representing the ion-product constant for water.

Ka and Kb Concept 1

Hey, guys. In this new video, we're going to take a look at the acid and base constants. So, as you guys can know from looking at the rules for identifying compounds as either acids or bases, you should realize that there's a lot more weak species out there than there are strong ones. What we need to realize is that these weak species have constants associated with them. We're going to say here, consider a weak monoprotic acid. Monoprotic just means it has 1 H positive. And here we're looking at how it ionizes in water. Basically, is the acid so it's going to give away an H positive to the water. The water accepts the H positive so that's how it becomes H3O+ The acid loses an H positive and that's how it becomes A-. Now what we're going to say here, the equilibrium expression equals products over reactants. And remember, we've talked about the equilibrium expression before. It looks at all phases of matter except for liquids and solids. So liquids and solids will not be included. And here, we have a liquid, so we're going to ignore it when we do the equilibrium expression. It's simply going to become A-∙H3O+ over

Ka and Kb Concept 2

Now we're going to say that \( K_a \) represents our acid dissociation constant. And it basically measures how strong our weak acids are. We're going to say weak acids use \( K_a \), weak bases don't use \( K_a \). Instead, they use \( K_b \). So this is our base dissociation constant. And what we're going to say here is their relationship to each other \( K_a \) and \( K_b \) can be expressed by this formula. \( K_w = K_a \times K_b \). And as you realize, this \( K_w \) is the same \( K_w \) we saw earlier. In the earlier times, we saw it as \( K_w = [\text{H}^+] \times [\text{OH}^-] \). It's the same exact \( K_w \). And we're going to say in general, the higher the \( K_a \) value and the stronger the acid. The stronger the acid, the greater the concentration of \( [\text{H}^+] \). Now we're going to say related to \( K_a \) is \( pK_a \). And remember, we've talked about what \( p \) means. \( P \) means negative log. \( pK_a \) means negative log of \( K_a \). Here we're going to say there's an inverse relationship. It's actually the lower the \( pK_a \), the stronger the acid and the stronger the acid, the greater the \( [\text{H}^+] \) concentration. Now, we're going to say here is when it comes to a weak acid, we're going to say weak acid tends to have \( K_a \) value less than 1 and a \( pK_a \) value greater than 1. Just realize we said inverse relationship, so \( K_a \) and \( pK_a \) are opposites. If one is up, the other one is down. Strong acids though, strong acids tend to have \( K_a \)'s much greater than 1. And they tend to have \( pK_a \)'s lower than 1, \( pK_a \)'s that are negative. And remember, we should be able to establish a relationship between \( K_a \) and \( pK_a \) in the same way we've been able to establish a relationship between \( [\text{H}^+] \) and \( pH \). Because here, we can just simply say \( K_a = 10^{-pK_a} \). We could also say the same thing for \( pK_b \). \( pK_b = \text{negative log of } K_b \) and therefore, \( K_b = 10^{-pK_b} \). Just remember these relationships and how they affect the acidity of our compound. As long as you can remember these few quick easy calculations, you'll be able to go from one to the other. And one last thing, we can say here that the relationship from \( p \) to \( pK_a \) and \( pK_b \) can be established by looking at this equation here. By taking the negative log of \( K_w \), \( K_a \) and \( K_b \), we say that the equation becomes \( 14 = pK_a + pK_b \). Now, that we've seen all these types of new variables and new types of equations, attempt to do the practice question on the bottom. Here I say if the \( K_b \) of \( \text{NH}_3 \) is \( 1.76 \times 10^{-5} \), what is the acid dissociation constant of the conjugate acid? Conjugate acid is a term we learned earlier a few videos back. But here we're given \( K_b \), we're asked to find the acid dissociation constant. So it's a simple conversion from one unit to another. So, once you're done with that, click back on the explanation button and see how I approach this problem. Good luck, guys.

Ka and Kb Example 1

Hey, guys. In this new video, we're going to put to practice some of the concepts we learned about Ka and Kb. So the first example says, knowing that HF has a larger or higher Ka value than CH₃COOH which is acetic acid, determine if possible in which direction the following equilibrium lies. We learned earlier that the higher your Ka value, the stronger you are as an acid. HF has a higher Ka value, so it's a stronger acid than acetic acid is. We're going to say HF is the stronger acid. And again, it's stronger because it has a higher Ka value. And it's the stronger acid, so the acetic acid on the product side would be the weaker acid. Now, we have to say on which side does the equilibrium lie. All you have to realize here is weaker means more stable. In chemistry, weaker just means less energy. Less energy means you're more stable. And the equilibrium will always lie on the side with the weaker acid because the weaker acid is the more stable acid. Our weaker acid is on the right side here. We're going to say that equilibrium lies to the right. It's as simple as that. First, you have to know that higher Ka means stronger acid and then just figure out which side the weaker acid would be on. Wherever the weaker acid is, that's where your equilibrium will lie.

If the Kb of NH₃ is 1.76 x 10^-5, determine the acid dissociation constant of its conjugate acid. 

• A. 1.08 x 10^-10
• B. 5.68 x 10^-10
• C. 5.68 x 10^-9
• D. 1.0 x 10^-14

Which Bronsted-Lowry base has the greatest concentration of hydroxide ions? 

• A. C₂H₈N₂(Kb = 8.3 x 10^-5)
• B. C₅H₅N (Kb = 1.7 x 10^-9)
• C. (CH₃)₃N (Kb = 1.0 x 10^-6)
• D. C₃H₇NH₂(Kb = 3.5 x 10^-4)
• E. C₆H₅NH₂(Kb = 3.9 x 10^-10)

Which Bronsted-Lowry acid has the weakest conjugate base?

• A. HCNO (K_a = 2.0 x 10^-4)
• B. HF (K_a = 3.5 x 10^-4)
• C. HN₃ (K_a = 2.5 x 10^-5)
• D. H₂CO₃ (K_a = 4.3 x 10^-7)

Here’s what students ask on this topic:

What is the relationship between Ka and Kb?

The relationship between the acid dissociation constant (Ka) and the base dissociation constant (Kb) is given by the equation:

$K_w=K_a\times K_b$

Here, Kw is the ion-product constant for water, which is 1.0 × 10⁻¹⁴ at 25°C. This equation shows that if you know either Ka or Kb, you can calculate the other. This relationship is crucial for understanding the behavior of weak acids and bases in aqueous solutions.

How do you calculate pKa from Ka?

To calculate pKa from Ka, you use the following formula:

$p{K}_a=-\log \left(K_a\right)$

This means you take the negative logarithm (base 10) of the Ka value. For example, if Ka = 1.0 × 10⁻⁵, then:

$p{K}_a=-\log (1.0\times {10}^{-})$=5

This calculation helps in understanding the strength of the acid; a lower pKa indicates a stronger acid.

What is the significance of the pKa value in acid-base chemistry?

The pKa value is significant in acid-base chemistry because it indicates the strength of an acid. It is the negative logarithm of the acid dissociation constant (Ka). A lower pKa value means a stronger acid, as it implies a higher Ka and thus a greater tendency to donate protons (H⁺). Conversely, a higher pKa value indicates a weaker acid. Understanding pKa is crucial for predicting the behavior of acids in different chemical environments and for calculating the pH of solutions.

How do you find the Ka of a weak acid if you know its pKa?

To find the Ka of a weak acid if you know its pKa, you use the following formula:

$K_a={10}^{-}$

For example, if the pKa of an acid is 4.75, then:

$K_a={10}^{-}$=1.78×10−5

This calculation helps in understanding the dissociation behavior of the acid in solution.

What is the equation that relates pKa and pKb?

The equation that relates pKa and pKb is:

$14=p_K+p_K$

This equation is derived from the relationship between Ka and Kb through the ion-product constant for water (Kw). It shows that the sum of pKa and pKb for a conjugate acid-base pair is always 14 at 25°C. This relationship is useful for converting between pKa and pKb values and understanding the acid-base properties of conjugate pairs.