What percent of imidazole is protonated at physiological pH (7...

Question

What percent of imidazole is protonated at physiological pH (7.4)?

Accepted Answer

Welcome back, everyone, calculate the percentage of pine with a P K value of 5. present in the acidic form in a solution with a P H of 7.8. First of all, let's recall that pine is a base. It's an aromatic compound where we have nitrogen with a localized lon pair of electrons. The molecular formula is C five H five N. And we understand that Perine when it acts as a base, it will undergo hydrolysis and water. And because it's a weak base, we're going to form an equilibrium where first of all, we have a conjugate asset of Perine. So we're going to draw the proton form of Perine. And then of course, we are also producing hydroxide since we are removing a proton from water. Now, for simplicity, we are going to introduce a sho shorthand notation for Perine. So let's suppose that Perine is our base A minus. So we are going to say that A minus corresponds to the molecular formal of C five H five N. And therefore, its proton form will be H A. We want to find the percentage of the acidic form, right. So we're going to say that the percentage of the acidic form H A must be equal to the ratio, right? Whenever we find, whenever we want to find a fraction, we're taking the amount of the compound of interest in this case, that would be the concentration of the asset. And now we are going to divide it by the, the initial concentration of pine. But because we're looking at equilibrium conditions and we don't know the initial concentration of Perine, we can just state that it must be a sum of the concentration of the conjugate acid and pine at equilibrium, right? Because we are dealing with the law of mass conservation. So the total amount or the total initial amount of Burdine is just the sum of the concentration of the acid and the base at equilibrium. And if we want to express it as a percentage, we're just multiplying the fraction by 100. So now from here, our next step is to express our quantities in terms of P H and P K, right? Because we're not given any of the concentrations. And for that purpose, let's simply recall that whenever a weak ass at H A undergoes hydrolysis, we are producing a minus plus hydro num. And let's recall that the equilibrium constant K A is just the product of the concentration of base and the concentration of hydro num divided by the concentration of the acid at equilibrium. This is really important for us because Now, from this equation, we can, we can sell that the concentration of base will be just the K A value multiplied by the denominator. So that would be the concentration of H A and then divided by the concentration of hydro num. The reason why this is useful is because we are getting rid of one of our unknowns. And we're simply expressing it in sums of the same H A. And now we will also have hydro in our equation. So this is really useful and we're going to get back to our previous equation and simply rewrite it as the concentration of the acidic form divided by the concentration of the acidic form. Plus. Now, we can essentially replace the concentration of the basic form as the acid dissociation constant multiplied by the concentration of the acidic form and divided by the concentration of hydro num all multiplied by 100%. Our next step is relatively simple. We can just divide both sides by the concentration of the acid, right. So we are going to simply cross out all of our H A terms because we can simply factor them out, especially when we think about the denominator, we can factor them out. And now we arrive at a simplified equation. So in our numerator, we have one right? Because we are essentially dividing H A by H A. And I was thinking about the denominator, we will have one plus K A divided by H 30 plus from here because we have a big fraction and we have another fraction. And the denominator generally, we wouldn't want to have that sort of an expression. So we can actually multiply both both sides by the concentration of hydro num to get rid of an additional fraction. Or we can simplify a common denominator and then perform division, right? But simply speaking, because the concentration of hydro num will be nonzero. We can multiply both sides by the concentration of hydro and arrive at our final expression. So if we multiply the numerator by the concentration of hydro num, we get the concentration of hydro num. And now for our denominator, we have one multiplied by the concentration of hydro. So we will have the concentration of hydro plus K A, right. That's because we're multiplying K A over H 30 plus multiplied by H 30 plus. So K A divided by H 30 plus and multiplied by H 30 plus will essentially give us K A well done. So we have our final expression for the ratio and now we are ready to think how to get our final answer. First of all, let's recall that the concentration of hydro num can be found as 10 raised to the power of negative P H. That's really important for us to understand. And in addition to that, because we have K A in our expression, we also have to recall that K A is equal to 10 raised to the power of negative P K A. So that substituting all of these in our previous equation, we end up with a different form of it. So for H 30 plus, we are going to sense the power of negative P H. For our denominator, we will have 10 erase the power of negative P H plus 10 to the power of negative P K A. Now, the reason why we did this additional step is simply because we were given P H and P K A in our problem. So apparently we want to use that final equation in terms of P H and P K A to get our final answer. So let's go ahead and get our final result. So now if we substitute the P H and P K values given on the problem, we end up with 10 raised to the power of negative P H and we know that P H is 7.8, we're going to use exactly the same term in the denominator 10 to the power of negative 7.8. And we're going to add 10, erase the power of negative P K A and or P K A, we have 5. and that would be it. We simply want to plug all of these numbers into a calculator. There's no necessity to perform any intermediate steps to avoid the propagation of error. But it is important to make sure that you include parent C in your calculator for the denominator so that you get the right answer. And when we perform this calculation, we arrive at our final percentage, which would be 0.25%. That will be our final answer. And we can conclude that at a given P H, the percentage of the acidic form of Perine in the solution would be 0.25%. Meaning the remaining 99.75% corresponds to the basic form of Perine. Thank you for watching and I hope to see you in the next video.

What percent of imidazole is protonated at physiological pH (7.4)?

Key Concepts

Protonation and Deprotonation

pKa and pH Relationship

Imidazole Structure and Function

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