Henderson Hasselbalch Equation - Online Tutor, Practice Problems & Exam Prep

The Henderson-Hasselbalch equation is essential for calculating the pH of weak acid solutions, particularly in biochemistry where most biological acids are weak. It relates pH to the pKa of the acid and the ratio of conjugate base to conjugate acid. The equation is expressed as pH1=pKa+log([A-]/[HA]). Understanding this equation is crucial for determining the equilibrium pH in biochemical contexts.

The Henderson-Hasselbalch Equation

In this video, we're going to brush up on the Henderson Hasselbalch equation. In our previous lesson videos, we covered the \(K_a\) and the \(pK_a\) of acids, and we already know that the smaller the \(pK_a\) is, the stronger the acid will be. Strong acids have really small \(pK_a\)'s and they have a tendency to completely dissociate. Whereas, weak acids, on the other hand, have really high \(pK_a\)'s, and they do not completely dissociate. And by completely dissociate here, what we really mean is that these strong acids will completely break down into their conjugate base and the hydrogen ion. But again, weak acids do not completely break down like that. Because strong acids completely dissociate, calculating the pH of strong acid solutions is a relatively easy process since the initial acid concentration is going to equal the final concentration of hydrogen ions. For example, we know that hydrochloric acid, or \(HCl\), is a strong acid. And so the initial concentration of hydrochloric ion the hydrogen ion concentration, to determine the pH of the solution. Calculating the pH of a strong acid solution is an easy process, but calculating the pH of a weak acid solution is not as easy. This is because weak acids do not completely dissociate. And this is where the Henderson Hasselbalch equation comes into play, as we'll need to use it to calculate the pH of weak acid solutions. This is an especially important point for biochemistry, because most biological acids are actually weak acids, showing why the Henderson Hasselbalch equation is important for biochemists.

Now recall from your previous chemistry courses that the Henderson Hasselbalch equation expresses the relationship between the solution pH and the \(pK_a\) of the acid. Typically, the Henderson Hasselbalch equation is used to determine one of two different things. The first is the final pH of a weak acid solution after it reaches equilibrium, and the second is the ratio of the concentration of conjugate base to the concentration of conjugate acid when the pH is given to us. Below, you can see we have an image of the Henderson Hasselbalch equation, which is expressed as the pH equaling to the \(pK_a\) of the acid, plus the log of the final concentration of conjugate base over the final concentration of conjugate acid. In our next video, we will be able to get an example of how to apply the equation. So, I'll see you guys in that example video.

Henderson-Hasselbalch Equation

Alright. So here's an example problem that wants us to determine the ratio of the concentration of conjugate base to the concentration of conjugate acid for aspirin in the blood. And it tells us that aspirin's pKa is 3.4 and the pH of blood is 7.4. And so we know that we can use the Henderson Hasselbalch equation to determine the ratio of the concentration of conjugate base to the concentration of conjugate acid. And we covered the Henderson Hasselbalch equation in our previous lesson video. So we know that it's equal to the pH, which is equal to the pKa of the acid plus the log of the final concentration of conjugate base over the final concentration of conjugate acid. And so all we need to do is plug our variables straight into this Henderson Hasselbalch equation. And so we're told that we have a pH of 7.4, so we can plug that in right down here, 7.4, which is equal to the pKa, which is given to us as 3.4, so we can plug that in here, plus the log of the concentration of conjugate base, which I'll abbreviate with CB, over the concentration of conjugate acid, which I'll abbreviate with CA. And so we're solving for this ratio here, that's really what it's asking us to determine. So we want to isolate for this ratio. What we can do is subtract 3.4 from both sides of the equation, and so 7.4 minus 3.4 is equal to 4. So we have 4 is equal to the log of the concentration of conjugate base over the concentration of conjugate acid. And so now we want to get rid of this log here so that we can continue to isolate for this ratio. The way we get rid of a log is by taking the antilog, but if we take the antilog of one side of the equation, that means that we need to take the antilog of the other side of the equation in order to make sure that it stays equal. And so the antilog of a number is literally just 10 raised to the power of the same number, So it's 10 raised to the power of 4. And so, remember taking the antilog of this side gets rid of our log here, so we're just left with the ratio of the concentration of conjugate base to the concentration of conjugate acid. And so 10 to the 4th, if you type that into your calculators, is equal to 10,000, which is essentially 10,000 over 1. So this is the ratio that we were looking for all along for the concentration of conjugate base to the concentration of conjugate acid. And so what this ratio means is that for every 10,000 conjugate base molecules, we will have 1 conjugate acid molecule. And so notice that this ratio here of 10,000 is equal to answer option B, so we can go ahead and indicate that B here is correct. And that concludes this example problem, so we'll be able to get some practice in our next practice video. I'll see you guys there.

What is the pH of a mixture of 0.02 M sodium formate & 0.0025 M formic acid (pK  _a = 3.75)

• A. pH = 4.21
• B. pH = 1.27
• C. pH = 4.65
• D. pH = 9.34

What is the ratio of of [CH ₃COO^-] / [CH₃COOH] in an acetate buffer at pH = 7? pK _a = 4.76.

• A. 122.43
• B. 173.78
• C. 39.84
• D. 96.31

Consider 100 mL of a 1M acid solution (pK _a = 7.4) at pH = 8. Calculate final pH if 30 mL of 1M HCl is added.

• A. pH = 7.4
• B. pH = 7.9
• C. pH = 7.1
• D. pH = 8.2

Here’s what students ask on this topic:

What is the Henderson-Hasselbalch equation and why is it important in biochemistry?

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of weak acid solutions. It is expressed as:

${\mathrm{pH}}_1={\mathrm{pK}}_{\mathrm{a}}+log\left(\frac{[A_{-}}{[{\mathrm{HA}}_{]}}\right)$

In biochemistry, this equation is crucial because most biological acids are weak acids. It helps determine the equilibrium pH of these solutions, which is essential for understanding various biochemical processes and reactions.

How do you use the Henderson-Hasselbalch equation to calculate the pH of a weak acid solution?

To use the Henderson-Hasselbalch equation to calculate the pH of a weak acid solution, follow these steps:

1. Identify the pKa of the weak acid.

2. Determine the concentrations of the conjugate base ([A-]) and the conjugate acid ([HA]).

3. Plug these values into the equation:

${\mathrm{pH}}_1={\mathrm{pK}}_{\mathrm{a}}+log\left(\frac{[A_{-}}{[{\mathrm{HA}}_{]}}\right)$

This will give you the pH of the weak acid solution at equilibrium.

What is the significance of pKa in the Henderson-Hasselbalch equation?

The pKa in the Henderson-Hasselbalch equation represents the acid dissociation constant, which is a measure of the strength of an acid. It is the pH at which half of the acid molecules are dissociated into their conjugate base and hydrogen ions. The smaller the pKa, the stronger the acid. In the equation:

${\mathrm{pH}}_1={\mathrm{pK}}_{\mathrm{a}}+log\left(\frac{[A_{-}}{[{\mathrm{HA}}_{]}}\right)$

pKa helps determine the pH of the solution by indicating how easily the acid donates protons, which is crucial for understanding the behavior of weak acids in biochemical systems.

How does the Henderson-Hasselbalch equation help in determining the ratio of conjugate base to conjugate acid?

The Henderson-Hasselbalch equation can be rearranged to solve for the ratio of the conjugate base ([A-]) to the conjugate acid ([HA]) when the pH and pKa are known. The equation is:

${\mathrm{pH}}_1={\mathrm{pK}}_{\mathrm{a}}+log\left(\frac{[A_{-}}{[{\mathrm{HA}}_{]}}\right)$

Rearranging this equation gives:

$\frac{[A_{-}}{[{\mathrm{HA}}_{]}}={10}^{{\mathrm{pH}}_1-{\mathrm{pK}}_{\mathrm{a}}}$

This allows you to calculate the ratio of the concentrations of the conjugate base to the conjugate acid, which is important for understanding the buffering capacity and behavior of the solution.

Why is the Henderson-Hasselbalch equation particularly useful for calculating the pH of biological systems?

The Henderson-Hasselbalch equation is particularly useful for calculating the pH of biological systems because most biological acids are weak acids. These weak acids do not completely dissociate in solution, making it challenging to determine their pH using simple methods. The equation:

${\mathrm{pH}}_1={\mathrm{pK}}_{\mathrm{a}}+log\left(\frac{[A_{-}}{[{\mathrm{HA}}_{]}}\right)$

allows for accurate pH calculations by considering the equilibrium between the weak acid and its conjugate base. This is essential for understanding and controlling the pH in various biochemical processes, such as enzyme activity, metabolic pathways, and cellular functions.