Here it states that sulfuric acid, which is H_{2}SO_{4}, is a major component in the creation of commercial fertilizers. Here it asks, what is the buffer component concentration ratio of a buffer that has a pH of 1.15? Alright. We have a buffer here, so we know we're dealing with the Henderson-Hasselbalch equation: pH equals pKa plus log of our conjugate base over our weak acid. When it asks for the component concentration ratio, it's really asking what is the ratio of conjugate base to weak acid. What is that value there? We run into the problem, though. We're dealing with a diprotic acid here, and that's illustrated by it having 2 Ka values as well. We don't know, are we dealing with pKa_{1} or pKa_{2} within this question? How do we determine that? Well, we can take a look at all the forms that sulfuric acid takes when we begin to remove its H^{+} ions. Here we have sulfuric acid which is the acid form. We remove the first acidic hydrogen so that means we're dealing with Ka_{1}. That's HSO_{4}^{−}. Then we'll remove the last acidic hydrogen so we're dealing with Ka_{2} to give us SO_{4}^{2−}. Now, we're going to say here that the relationship between the acid form and the intermediate form, we're going to say we have this imaginary line here. We're going to say this imaginary line here, we're going to say this represents the line for pKa_{1}. Here if we took the negative log of Ka_{1} which is this number right here, take the negative log of it, we'll get pKa_{1} equals 1.86. Then we're going to say there's an imaginary line here which separates the intermediate form from the base form. We take the negative log of this Ka_{2} to give me pKa_{2}. That comes out to 7.17. These pKa values are important because we're gonna say here, we can relate them in terms of pH. Basically, if our pH is equal to 1.86. So let's say pH equals pKa_{1}. What would that mean? That would mean that my acid form would be equal to my intermediate form. How do we know that? If we're dealing with a buffer, if my acid form which would be this form is equal to my intermediate form which is this form. All of this would just equal 1. Log of 1 would equal 0. So that would just all drop out and so pH would equal pKa_{1}. And we're gonna say here if my pH equaled pKa_{2}, that would mean that my intermediate form equals my basic form for the same exact reason. Now, if your pH is less than, your pKa_{1}, what does that mean? That means you're dealing with a give and take between the acid form and the intermediate form. Our pH here is 1.15 which means we fall somewhere in here which means we're talking about removing that first acidic hydrogen in order to create this intermediate form. If your pH happened to be a number that was greater than 1.86 and less than 7.17, then you would fall somewhere within here. Remember, this goes all the way back to our principal species when we're talking about the form that predominates depending on the pH and when we compare it to our pKa value. And if we had a pH greater than this pKa_{2}, then this would be the dominant form. Now, going back, we said that pH is 1.15, so we know we're dealing with, the acid form as the predominant form. We're talking about removing its first acidic hydrogen to make the intermediate form. That would mean our equation now is pH equals pKa_{1} plus log of my intermediate form divided by my acid form. So pH 1 is 1.15. Then we're going to say here, so let me take myself out of this. Let me try this. pH equals 1.15, pKa_{1} equals 1.86 plus log of HSO_{4}^{−} divided by H_{2}SO_{4}. Subtract both sides by 1.86. So when we do that, we're gonna get initially negative 0.71 equals log of the intermediate form divided by the acid form. Then all we do now is we take the inverse log which just means here 10^{-0.71} equals the ratio of my intermediate form divided by my acid form. So when we punch that number into our calculators, that's gonna give us 0.195 over H_{2}SO_{4}. So what is this number telling me? Well, this number here is telling me since it's a ratio, whatever number I get is always equal is always gonna be over 1. So what this ratio was telling me is that for every one, weak acid form, we have 0.195 of the intermediate form. That's the ratio. This ratio is telling me that I have more of the acid, weak acid form than I do of the intermediate form. So our ratio here would be 0.195 to 1 to represent the ratio of my conjugate base or intermediate to my weak acid form. Just remember, remember with polyprotic acids and diprotic acids, we have to be aware of which Ka are we dealing with. That will determine which pKa we're gonna deal with within our Henderson-Hasselbalch equation to find either the pH, the ratio of the conjugate base to the weak acid, or possibly just the amount of the conjugate base by itself or the weak acid by itself.

So now that we've seen these two examples, attempt the practice question that's left on the bottom of the page. Attempt it on your own. Come back and take a look and see how I approach that same question.