A buffer contains a weak acid, HA, and its conjugate base. The weak acid has a pKa of 4.5, and the buffer has a pH of 4.3. Without doing a calculation, state which of these possibilities are correct at pH 4.3. (a) 3HA4 = 3A-4, (b) 3HA4 7 3A-4, or (c) 3HA4 6 3A-4. [Section 17.2]

Video transcript

Welcome back everyone to another video. A buffer contains a weak acid H A and its conjugate base. The weak acid has a PK A of 5.7 and the buffer has a P hr 5.2 without doing a calculation, choose which of these possibilities is correct at PH of 5.2. And we're given three answer choices. A, there's a greater concentration of the weak acid than it is for the conjugate base B. The two concentrations are equal and C there's a greater concentration of the conjugate base as compared to the acid. So let's remember the Henderson Hasselback equation which will be useful for this problem. We know that PH is equal to the PK A of the weak acid plus the logarithm of base 10 of the ratio of the conjugate base A minus and the acid H A. Now we can simply state that if we plug in the values given to us, PH is 5.2 PK is 5.7. And then we have logarithm of our ratio. Mind that we are not performing any significant calculations. We're not looking for the exact ratio. We just want to understand that if we subtract 5.7 from both sides, we end up with negative 0.5 which is equal to the logarithm. Now, this is the only calculation that we performed. And on the other hand, even if we don't perform that calculation, we can essentially notice that the PK A value is greater than PH, which essentially tells us that the logarithm of our ratio is negative. OK. So that's really important. That's what we have proved in the first step. Now, if the logarithm is negative, we can simply recall that logarithm is negative. Let's say logarithm of A is negative if A is less than one. So what does that mean? It essentially means that a minus where the concentration of the base divided by the concentration of the acid is less than one. And if we multiply both sides by the concentration of the acid, we have shown that the concentration of the base is less than the concentration of the asset. Now, we can generalize this statement without any calculations at all. We can essentially say that if our PH value is less than the PK value, right, then acid dominates essentially, we have a P value that is less than the PK value, meaning we have a more acidic medium as compared to the basic medium. This is a general statement. However, in my personal opinion, I think it's more important to understand the logic behind that. So I've also shown a small calculation of how to analytically derive this answer. So essentially we can state that the correct answer to this problem, which corresponds to a minus less than H A would be option A which states that the concentration of the acid is greater than the concentration of the conjugate base. Thank you for watching.