Acid Dissociation Constant: Study with Video Lessons, Practice Problems & Examples

The acid dissociation constant (K_a) quantifies acid strength, with higher K_a values indicating stronger acids. Each acid can have multiple K_a values, especially polyprotic acids like phosphoric acid (H₃PO₄), which has three acidic hydrogens. To simplify calculations, K_a can be converted to pK_a using the equation pK_a = -log(K_a), where higher pK_a values correspond to weaker acids. Understanding these relationships is crucial for comparing acid strengths and performing related calculations.

Acid Dissociation Constant (Ka)

In this video, we're going to talk about the acid dissociation constant. So now that we've reviewed pH, we know that the pH is a measure of the hydrogen ions in a solution. In this video, we're going to discuss those molecules that donate hydrogen ions to the solution, and those are acids. Every acid has an acid dissociation constant or a K_a value. The acid dissociation constant is literally just the equilibrium constant for an acid's dissociation, and we're already familiar with the equilibrium constant from our previous lesson videos.

In our image below, you'll see a typical reaction being shown where we have reactant A being converted into 2 products, product B and product C. The equilibrium constant, which we know from our previous lesson videos, is literally just a ratio. It's the ratio of the concentration of products at equilibrium over the reactants. And so, the acid dissociation constant is really nothing new. It's literally the equilibrium constant for an acid's dissociation.

Here, we're showing the acid dissociation reaction where we have a conjugate acid dissociating to form a conjugate base and a hydrogen ion. The conjugate base is represented as A^-, and the reactant is the conjugate acid. The acid dissociation constant, K_a, is essentially the same as the equilibrium constant, but for an acid dissociation. It's a quantitative measure of the strength of an acid, also known as the ion constant. Sometimes you might hear your professor say "ion constant" instead of acid dissociation constant. It expresses the tendency of an ion to dissociate from a molecule, and in our case, the ion dissociating is the hydrogen ion. The greater the K_a value, the stronger the acid, which is important for determining which acid is the strongest and which is the weakest by comparing the K_a values.

Some acids are known as polyprotic acids, containing multiple acidic hydrogen atoms, each capable of dissociating to form a hydrogen ion. This means there is one acid dissociation constant for each acidic hydrogen. In our image, we have an example of a polyprotic acid, phosphoric acid, with the chemical formula H₃PO₄. All three of these hydrogens are acidic. Hence, there are three K_a values for this one acid. The first K_a value is for the first acidic hydrogen, the second K_a value is for the second acidic hydrogen, and the third K_a value is for the third acidic hydrogen. By comparing these K_a values, the strongest acidic hydrogen is the one with the greatest K_a value, which is the first K_a. The first acidic hydrogen is the strongest acid of the three.

We will be able to apply these concepts reviewed here in our future videos, so I'll see you guys in our next video.

Acid Dissociation Constant (Ka)

Alright, guys. So here's an example problem, and it's asking us to calculate the K_a or the acid dissociation constant of Uric acid, whose chemical formula is shown here, if the concentration of this molecule here at equilibrium is 4.07×10-3 molar, and so what we'll need to realize is this molecule over here on the left is the conjugate acid of uric acid, and we know because it has one additional hydrogen. It has 4 hydrogens. And the molecule on the right is the conjugate base of uric acid because it has one less hydrogen and one less charge, a negative charge. And so, because we're being asked to calculate the K_a, and we know from our previous lesson videos that the K_a is literally just the equilibrium constant of an acid's dissociation, I provided the acid dissociation reaction over here, where we have the conjugate acid, represented by dissociating into A^- or the conjugate base and a hydrogen ion. And so because the K_a is literally just the equilibrium constant, we know it's the ratio of the concentration of products at equilibrium over the concentration of reactants at equilibrium. And so, because we're working with uric acid here, I've also provided uric acid's dissociation, where we know that the conjugate acid, is going to dissociate into the conjugate base molecule, as well as the hydrogen ion, so we have the same ratio presented over here. And so essentially, what we'll need to realize is, we have the values for all of these concentrations. So we have the value of the concentration of conjugate base, which is 7.27×10-4, and we have the value for the conjugate acid concentration, which is 4.07×10-3. And, really, the only concentration that we're missing here is the hydrogen ion concentration. And the way that we can determine the hydrogen ion concentration is by using an ICE table, an ICE chart, which I know you guys remember from your previous chemistry courses. So, we're going to do a quick little refresher here. And so, essentially, an ICE table is where you have the initial concentration, the change in the concentration over time, and then the equilibrium concentrations. And so what that means is we were going to have some initial concentration X, some unknown initial concentration of uric acid. And at the very beginning of the reaction, we would have 0 of our products. So we would have 0 of the hydrogen ion and 0 of the conjugate base. And so we know that over time, if we have all of this uric acid, it's going to essentially dissociate, it's going to react and dissociate into conjugate base. And we're told that at equilibrium we know it's at equilibrium because of the EQ here, we have a concentration of 7.27 times 10 to the negative 4th of our conjugate base. And, what that means is the change in conjugate base must have been an increase, a positive 7.27 times 10 to the negative fourth molar increase. And so what that means is that the conjugate acid here must have decreased by the same amount, so a negative 7.27 times 10 to the negative fourth molar. And because the conjugate base is at a 1 to 1 molar ratio with the hydrogen ion, because they both have coefficients of 1, that means that the hydrogen ion change in concentration is going to be the same as the conjugate base here. So it's gonna be a positive 7.27×10-4 molar. And so what that means is that the hydrogen ion concentration at equilibrium is also going to be 7.27×10-4 molar. And of course, we're told up above that at equilibrium for the conjugate acid, we have a concentration of 4.07×10-3 molar. And so recall that with the acid dissociation constant, we're using the concentrations at equilibrium, so we want to plug in these concentrations down below. And we've already plugged in the conjugate acid and the conjugate base concentration. So now, all we need to do is plug in this number here for this hydrogen ion concentration. And so we can go ahead and erase this, and type in 7.27×10-4 here. And so now we have all of our numbers. We can go ahead and plug in all of these numbers into our calculator, and essentially, what we'll get is an answer of about 1.3×10-4, and this here is our answer. So this is the K_a or the acid dissociation constant, which matches with answer option d. So we can go ahead and indicate that d here is the correct answer. And so that concludes this example problem, and we'll be able to get some practice in our next lesson video. So I'll see you guys there.

Calculate K_a of proprionic acid (CH ₃CH₂CO₂H) if [CH₃CH₂CO₂H]_eq = 0.2 M & [CH₃CH₂CO₂^-]_eq = 1.62 x 10^-3 M.

• A. K_a = 1.3 x 10^-5
• B. K_a = 7.8 x 10^-10
• C. K_a = 3.9 x 10^-12
• D. K_a = 5.1 x 10^-4

Acid Dissociation Constant (Ka)

So in our previous lesson video, we talked about the acid dissociation constant or the Ka, which we know is a quantitative measure of the strength of an acid. And the greater the Ka value is, the stronger the acid will be. But the thing about the Ka values is that sometimes they are inconveniently large or small numbers that need to be expressed with scientific notation because of how large and small they can be, making calculations unnecessarily more complicated. However, the good news is that the Ka values can be expressed on a logarithmic scale with pKa values. And so the pKa values are also a quantitative measure of the strength of an acid, just like the Ka value is. However, the relationship is different. Recall with the Ka values, the greater the Ka, the stronger the acid, but with the pKa, it's different. The greater the pKa, the weaker the acid is, and so it's actually an inverse relationship. In our example below, we have an equation for the pKa, and just like from our previous lesson of pH, we know that the "p" here is really just representing the negative log. Therefore, pKa is just the negative log of the Ka value, which is exactly what we have here: the negative log of the Ka. The rules of logarithms say that the negative log is equal to the positive log of the reciprocal. We have both equations shown here, just in case your professor is leaning one way or the other.

So now, we'll be able to get a little bit of practice utilizing this equation as we take a look at our chart over here on the right, which has an example of a weak acid, acetic acid in this yellow column, and an example of a strong acid, HCl or hydrochloric acid in the blue column. We are given the Ka values for both of these acids, and notice that the Ka value of the weak acid is incredibly small. We know it's small because it's expressed in scientific notation with a negative exponent. The strong acid, on the other hand, has an incredibly large Ka value. Again, we know it's large because it's expressed in scientific notation with a positive exponent. These numbers, being inconveniently large and small, can unnecessarily complicate calculations, but we can pretty easily convert them into pKa values using this equation for the pKa. For the weak acid, it will be the negative log of \(1.76 \times 10^{-5}\), which is equal to 4.76. That's the pKa for the weak acid. If we do the same for the strong acid, we take the negative log of \(1.3 \times 10^{6}\), which is equal to -6.3; this is the pKa for the strong acid. What you'll notice is that the pKa for the weak acid is actually larger than the pKa for the strong acid. That's because, again, it's an inverse relationship: the greater the pKa, the weaker the acid is. Moving forward, we'll be able to get a little bit of practice utilizing these concepts. So I'll see you guys in those videos.

Which of the following is the strongest acid listed?

• A. Lactic acid, Ka = 1.38 x 10^-4
• B. Formic acid, pKa = 3.75
• C. Acetic acid, Ka = 1.76 x 10^-5
• D. Proprionic acid, pKa = 4.87

Here’s what students ask on this topic:

What is the acid dissociation constant (Ka) and how is it used to measure acid strength?

The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It is defined as the equilibrium constant for the dissociation of an acid into its conjugate base and a hydrogen ion. The equation for Ka is:

$Ka=\frac{\left[H_{+}\right]\left[A_{-}\right]}{\left[{\mathrm{HA}}_{}\right]}$

where [H⁺] is the concentration of hydrogen ions, [A^-] is the concentration of the conjugate base, and [HA] is the concentration of the acid. A higher Ka value indicates a stronger acid, as it implies a greater tendency to donate hydrogen ions.

How do you convert Ka to pKa and what is the significance of pKa values?

To convert Ka to pKa, you use the equation:

$pKa=-\log \left(Ka\right)$

The pKa value is the negative logarithm of the Ka value. It provides a more convenient way to express acid strength, especially when Ka values are very large or very small. The relationship between pKa and acid strength is inverse: a lower pKa value indicates a stronger acid, while a higher pKa value indicates a weaker acid. This inverse relationship helps in comparing the strengths of different acids more easily.

What is the difference between Ka and pKa in terms of acid strength?

Ka and pKa are both measures of acid strength, but they are used differently. Ka is the acid dissociation constant and directly measures the equilibrium concentration of products and reactants in an acid dissociation reaction. A higher Ka value indicates a stronger acid. On the other hand, pKa is the negative logarithm of Ka:

$pKa=-\log \left(Ka\right)$

pKa provides a more convenient scale for comparing acid strengths. A lower pKa value indicates a stronger acid, while a higher pKa value indicates a weaker acid. The inverse relationship between Ka and pKa helps simplify calculations and comparisons.

What are polyprotic acids and how do their Ka values differ?

Polyprotic acids are acids that contain more than one acidic hydrogen atom, capable of dissociating to form hydrogen ions. Each acidic hydrogen has its own dissociation constant, resulting in multiple Ka values for a single polyprotic acid. For example, phosphoric acid (H₃PO₄) has three acidic hydrogens, leading to three Ka values:

$K_{\mathrm{a1}}=\left[H_{+}\right]\left[H_2{\mathrm{PO}}_4\right]/\left[H_3{\mathrm{PO}}_4\right]$

Each successive Ka value is typically smaller than the previous one, indicating that it becomes progressively harder to remove additional hydrogen ions. The first Ka value (Ka1) is usually the largest, indicating the strongest acidic hydrogen, while the subsequent Ka values (Ka2, Ka3) are smaller.

How do you determine the strength of an acid using Ka and pKa values?

The strength of an acid can be determined by comparing its Ka and pKa values. A higher Ka value indicates a stronger acid, as it shows a greater tendency to donate hydrogen ions. Conversely, a lower pKa value indicates a stronger acid, due to the inverse relationship between Ka and pKa:

$pKa=-\log \left(Ka\right)$

For example, if you have two acids with Ka values of 1.0 × 10^-3 and 1.0 × 10^-5, the acid with the Ka value of 1.0 × 10^-3 is stronger. Similarly, if you convert these to pKa values (3 and 5, respectively), the acid with the pKa value of 3 is stronger.