The Systematic Approach

1

concept

## Systematic Approach

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recall that strong acids and strong bases are considered to be strong electrolytes. That means that when we place them in solution they will completely ionized within the solvent. Now we're gonna say in general remember we also said that the larger the K. A. Value for an acid than the stronger the acid will be and the greater the concentration of H plus ions, we could also say the larger the KB value, the stronger the base and therefore the larger the O. H minus concentration. Now here for example, we have hydrochloric acid as an example here when it's thrown into water are solvent, it completely ionizing into H plus ion and cl minus ion because it is a strong acid, there's 100% ionization. So the initial concentration of my acid represents the final concentrations of the ions form because again it's 100% ionization. Now strong acids and strong bases are both strong species. Of course if we're taking a look at acids, the fact that these acids are all strong, they're gonna have K. Values that are greater than one. So we can easily see that when we look at each of them, all of them give me a value greater than one or equal to one in the case of caloric acid. Now we would normally say that if we take a look at the concentration of my strong acid or strong base we can just take the negative log of that concentration to find P. H. Or P. O. H. Respectively. Now that's not entirely true. And even with the strong species we have to be mindful of the initial concentration given to us based on the initial concentration will have to take different approaches and understand different methods to find the correct ph and P. O. H. So take a look at the next video and see how we break down the different concentrations of strong acids and strong bases to help us determine the best course of action in order to find our P. H. Or R P O. H, respectively.

2

concept

## Systematic Approach

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we've been under the assumption that whenever we're given the concentration of a strong acid or strong base, we could take the negative log of those concentrations to find P. H. Or P. O. H. Respectively. Now, in actuality when calculating the ph of a solution, we must take into consideration the concentration of the strong acid or the strong base because depending on the concentrations given, we'll have to use different methods to find the correct ph and P. O. H. Respectively. Now here we split it up into three categories here for the first one when the concentration of your strong acid or strong base is equal to or greater than 10 to the negative six molar, that means that there's a significant amount of those two species that we can just simply look at their concentrations and take the negative log. So for example here we have nitric acid, it completely lionizes into H plus ion and nitrate ion because the concentration of 1.5 times 10 to negative three moller is greater than 10 to the negative six. We can just simply take the negative log of this concentration because remember, nitric acid being a strong acid completely breaks up into H plus ion. So this would be 100% generation of this ion. I would take the negative log of that concentration And that would give me my ph which come out which comes out to 2.82. Here we have sodium hydroxide again, the concentration as long as it's equal to or greater than 10 to the negative six Mohler, we have complete ionization and here we have 100% generation of this O. H minus ion here we can just simply take the negative log of this concentration. But now it gives me P O. H. So I plug that value in That give me 3.12. And then remember at this point PH equals 14 minus that value. So we'd get 10.88 at this point. So as long as my concentration is equal to or greater than 10 to the negative six, the concentration of the strong acid and strong base are significant enough to change the ph of my solution. So I can simply look at their concentrations and take the negative log to find P. H. Or P. O. H respectively. Now when the concentration that they have is equal to or less than 10 to the negative eight moller. And really we're going to say when it's less than 10 to the negative eight moller, then we're gonna say that the concentrations are not significant enough. Therefore the ph will be seven. That's because there isn't enough strong acid or enough strong base in order to change the ph of the solution as a whole. So here we have 10 to the negative 11 and 10 to the negative nine, they're not significant enough. So both solutions will be neutral. So again it's when concentrations are less than 10 to the negative eight moller. Finally, when you have your concentration between 10 to the negative, 6 to 10 to the negative eight moller. We're gonna take a systematic approach to finding our ph that's because at these concentrations they're not large enough but not small enough. So they will have some changing of the ph of our solution here. We have to be mindful that between these concentration values we have to take into account the auto ionization of water. Remember the auto ionization of water would produce some H Plus ion and some O. H minus ion. These concentrations would actually contribute to the overall concentrations of H plus and O H minus. Taking them into consideration is key to getting the correct ph for our strong acid and the correct P. O. H. For our strong base. So remember when it comes to strong acids and strong bases, they are strong electrolytes that completely ionized in water. But we have to be careful when looking at their concentrations depending where their concentration lies. Means we'll have to take one of three possible routes to find P. H. Or P. O. H. Respectively. So just keep in mind some of the tips that we went over here. And as we continue with this topic, keep in mind the strategies needed to find again your P. H. Or P. O. H.

Whenever the concentration of your strong acid or strong base is between 10^{-6} to 10^{-8} M a systematic approach may have to be used to determine pH or pOH.

3

example

## Systematic Approach Calculations

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So here we need to determine the ph of a 3.5 times 10 to the negative eight moller, hbr or hydro Tomic acid solution. Now remember here the concentration falls between 10 to negative 6 to 10 to the negative eight. So we have to make sure if necessary to use the systematic approach when we take the negative log of the strong acid. So we'll take the negative log of 3.5 times 10 to negative eight moller that's gonna give me a ph of 7.46. We can clearly see that this is a basic ph which makes no sense because we have a strong acid because we have a strong acid um we should get a ph that's more acidic. So this means that we definitely need to do a systematic approach to calculating are correct concentration of H plus ion. And from there determining our ph now we know that HbR is a strong electrolyte. So it's gonna break up completely into H plus ions plus b r minus ions. For remember, within this region of 10 to negative 6 to 10 to negative eight, we have to compete with the auto ionization of water. So remember in the auto ionization of water, we have two water molecules, one will act as an acid to produce a church plus and the other one will become O H minus here these are all the ions that are present within our solution. From these ions were gonna say that our charge balance remember our charge balance, We'll take a look at all the ions within solution, all the positive ions will equal the negative ions. So here are positive ion is H plus ions which comes from two sources, it comes from the HPR acid but also comes from the auto ionization of water. That's going to equal my negative ions which in this case would be my bromide ion plus my hydroxide ion. So that would be my charge balance. Next we would look at our mass balance and we're focusing on the bromide ion. We're not taking a look at H plus ion because it's found in two locations HBR and the auto ionization of water. So we're gonna say here that the mass of bromide ion comes entirely from HBR And because of that that means the bromide ion all of it would have the same concentration as HBR would be 3.5 times 10 to the -8 moller. Now this is important because this will eventually lead us to the correct concentration for Rh plus ion. Alright so now we're going to say here, B r minus equals this concentration H plus equals B R minus plus O H minus. So we can say now that H plus equals 3.5 times 10 to the negative eight moller because it equals bromide ion plus the concentration of O H minus which we don't know. So that's equal to X. So this is what H plus equals. Now we can say from this information that K. W. Which is our dissociation constant for water equals H plus times O. H minus. Plugging the values that we know K. W. Is 1.0 times 10 to the negative 14 equals. We just said H plus is equal to 3.5 times 10 to the negative eight plus X. We don't know what O H minus is. So it's also X. Right from this set of values we can figure out what X will be. So what we're gonna do now is we're going to distribute this X distribute this X. So that's gonna give me 1.0 times 10 to the negative 14 equals 3.5 times 10 to the negative eight X plus X squared that X squared has the largest power for the X. Variable. So it's our lead term. So that means we're gonna have to subtract 1.0 times 10 to the negative 14 from both sides. And rewriting our equation now gives us X squared plus 3.5 times 10 to the negative eight X minus 1.0 times 10 to the negative 14. So that is our equation. And from it we'd say that this would be A B. And C. So we're gonna use the quadratic formula. So negative B plus or minus square root of B squared minus four A. C over two A. So let's plug in the values that we know. So that'd be negative 3.5 times 10 to the negative eight plus or minus 3.5 times 10 to the negative eight squared minus four times one. Don't forget the negative sign of C. Negative 1.0 times 10 to the negative 14 Divided by two times 1. Alright so now when I saw for all of this here I'll get negative 3.5 times 10 to the negative eight plus or minus 2.3039 times 10 to the negative seven divided by two. And realize here that are we'll get two X variables one that's plus and one that's minus uh 2.3039 times 10 to negative seven. So my two possible answers for X. You'll get 8.40 times 10 to the negative eight moller. Or you'll get X equals negative 1.19 times 10 to the negative seven moller. Now remember concentrations cannot be negative at the end so this one is automatically dropped out so the concentration of X is 8.4 times 10 to the negative eight moller. Now what does this X represent? Well if we go back to our expression here, we know that O. H minus is equal to just simply X. So you could take that value and plug it in and it represents minus. You could also take that X. And just plug it into here and that will give you the concentration of H. Plus here. I'm just gonna say that this is equal to O. H minus concentration, which means that if I take the negative log of it, I'll get P. O. H. So when I take the negative log of it I get 7.08. And here if we know the p. O. H. We know ph because it's 14 minus the P. O. H. So that's equal to 6.92. So this answer makes more sense. We have a strong acid And it is a concentration that is not less than 10 to the -8. So it shouldn't be a neutral solution, definitely should not be a basic solution ever. The 6.92 is pretty high of a P. H. But that's because the concentration of Hbr is very diluted. So, remember this is the approach you need to take the systematic approach for a strong acid. Remember the key steps that we did here and apply to any strong acid that you see your best course of action should always be to take the negative log of the strong acid. To see if the ph makes sense here, because it's a strong acid, you should get an acidic ph if you get a basic ph that's a strong indication that you need to do the systematic approach to calculating the correct concentration of H. Plus and from there determining your ph now that you've seen this example, attempt to do the practice question left on bottom. But we have to use the systematic approach for calculating the ph of a strong base. Again, set it up in similar ways. Remember what is the complete ionization of the strong base going to result? What kind of ions are formed? Also take into consideration the auto ionization or self ionization of water. How do those ions contribute to the pool of ions within my solution? But first of all, just make sure you first take the negative log of the concentration and see if your ph makes sense. If it doesn't make sense, that is a strong indicator. Again, to use the systematic approach. Hopefully you guys were able to follow along with this example on calculating the ph of a strong acid using the systematic approach.

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Problem

Determine the pH of a 6.7 x 10 ^{-8} M NaOH.

A

7.17

B

7.14

C

6.82

D

7.57