Buffer Calculations

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[00:00:01]thank you all right guys so we are going to continue looking at buffers um so remember we said any solution that contains something that can absorb hydrogen ions can act as a base and if you have something that can absorb hydroxide ions that can act as an acid and if it has both it can act as a buffer so remember buffers have something that can react with hydrogen and something that reacts with hydroxide to neutralize any additional acid or base let's refresh and look at what type of things can be considered a buffer so remember you have to look and see does it have something that can absorb hydrogen and hydroxide in the solution so our first example we have potassium nitrate and nitric acid so you're looking to see if it can absorb both so potassium nitrite or nitrate excuse me can produce Koh and hnr3 both of those are a strong base and strong acid so that cannot absorb either because it will reionize looking at the nitric acid it can react with hydroxide to make water but then it also makes nitric acid so it can react with hydroxide but not hydrogen so that is not a buffer let's look at the next one so we have sodium nitrite and nitrous acids for sodium nitrite it can make sodium hydroxide and nitrous acid the sodium hydroxide would reionize because it's a strong base but it could make nitrous acid so that can be considered a base whereas the nitrous acid is a weak acid so remember it can react to make water with hydroxide leaving behind the nitrous ion so this has a weak acid and its conjugate base so that can act as a buffer looking at the next one we have um acetic acid and potassium hydroxide acetic acid can react with hydroxide and the astray iron can produce acetic acid which is a weak acid so that's okay potassium hydroxide would produce potassium hydroxide and water when reacted so here's where the acetic acid by itself we do have a substance that can react with hydrogen from our potassium hydroxide and the acetic acid can react with the hydroxide excuse me so that because we have the weak acid and strong base can react with both I'm looking at our next one we have sodium carbonate and sodium phosphate this would produce sodium hydroxide and carbonic acid and sodium hydroxide and phosphoric acid we have a substance that can react with hydrogen in both of these but we do not have anything that will react with the hydroxide because it would produce a strong Basin either way so that cannot act as a buffer look at our next one this is where we have one substance and we want to see if it can react with both the acid and base the ammonium would lose a hydrogen to produce ammonia that hydrogen would go on to the nitrite to make nitrous acid which is a weak acid so it produces a weak base and a weak acid so that is one of those salts that does not have a spectator and can react um with both the hydrogen hydroxide for the last one sodium would make sodium hydroxide which would cancel because it would reionize however this dihydrogen phosphate could turn into h3po4 hpo4 negative 2. so that's one of those amphoteric ions that can act as both an S and a base so because that ion is present that could also act as a buffer all right so let us look at buffer calculations um this is going to utilize ice tables again and we're going to look at how much of a substance can be absorbed and what the new pH would be foreign so here we have a buffer that's made by adding 0.3 moles of acetic acid and 0.3 moles of sodium acetate to enough water to make two liters of solution so and we're going to address three different types of problems that you can do first we want to know what is the pH of the buffer solution itself then we want to know what is the pH of the solution after.02 moles of sodium hydroxide or base is added and then we also want to compare how this is different than if we had the pH from.02 moles of sodium hydroxide simply added to one liter of water of pure water instead of a buffer solution that way you can see how a buffer solution truly affects the base so looking at what is the pH of the buffer solution so we have a weak acid with acetic acid and we have its conjugate base with that acetate ion from sodium acetate so since we have both our ass weak acid and its fungiate base we can use the henderson-hasselback equation to find pH so remember it's pH is the pka of the acid plus the log of the base amount over the acid amount and remember you can use molarity for the base antacid or you can use moles so here we can use moles and we have the negative log of the KA for acetic acid is 1.8 times 10 a fifth plus the log of the base over the acid and here we get the the pH is going to be equal to 4.74 and that is of the buffer by itself to address the second problem it wants us to calculate the pH after 0.02 moles of sodium hydroxide is added so remember that this hydroxide is going to be absorbed by the acid so we have to write that the acid reacts with the hydroxide and remember we already have some of the acetate ion at the beginning we're reacting it with hydroxide the overall goal is to neutralize the hydroxide so we're wanting to subtract the hydroxide so that subtracts on our reactant side adds on our product side and it is moles canceling out moles so you don't have to worry about molarity with these but moles canceling out moles that gives us our new value for our amount of acid and our amount of Base that are left once we have both of those we have our acid amount and our base amount we can plug back oops we can plug back into that henderson-hasselbach equation so that would give us a new pH of 4.80 so notice that the pH did increase because we added a base but it only increased by like.06 so it did not increase slightly a lot all right so let's look at what happens if we were to add that same amount to Pure Water instead of the buffer so we added.02 moles of the same volume of pure water the two layers of pure water remember the concentration of hydroxide is equal to the concentration of sodium hydroxide which is moles over liters so.02 moles divided by 2 liters is a concentration of.01 molar which with hydroxide ion concentration we can find the poh which would be equal to two the pH would then be equal to 12. that is a lot higher and much more basic than the 4.80 whenever that same amount is added to a buffer solution all right let's look at another problem here we have a buffer that's made by dissolving 14 grams of sodium nitrite in 50 milliliters of a.050 molar nitrous acid first thing it wants to know is what is the pH of the buffer solution and it wants us to write a chemical reaction that would occur when a small amount of hydrochloric acid is added to the buffer solution so to find the pH we first need our molarities or moles for both sodium hydroxide and or excuse me sodium nitrite and nitrous acid because if we have the amount for both we can plug in the henderson-hasselbock so we can convert grams into moles and molarity and volume into moles plug into Henderson hospital and get that this buffer would have a pH equal to 3.61 and that leads us to the second question at one no what happens if we add acid to it what is the reaction that would occur so remember the acid is going to react with the conjugate base which is the nitrite ion excuse me so the acid which would be just hydrogen ion or more commonly the h3o Plus would react with the nitrite ion producing water so remember all buffer Solutions produce water and nitrous acid okay so let's look at another buffer problem here we have 500 milliliters of the buffer solution that has 0.5 molar ammonia and 1.8 molar ammonium chloride first wants us to calculate the pH of the buffer solution then calculate the pH after eight grams of base are added and then it wants us to calculate the pH after a 10-fold dilution of the original buffer so this looks at what happens if a buffer is diluted so first calculate pH of the solution remember we can do this using Henderson hasselbach with either molarity or moles here we do have molarity for both the acid and the base and we need Ka of the acid which is the ammonia the nh4 you cannot substitute KB for Ka using the same henderson-hasselbach equation so that would give us a buffer solution with a pH equal to 8.70 whenever we are looking at finding the pH after 8 grams of sodium hydroxide are added to the solution remember in our ice table we have to um compare moles to moles whenever we are trying to cancel them out so we need to change the 8 grams of sodium hydroxide into moles so divide by molar mass which is roughly 40.

[00:14:59]so that means that we have 0.2 moles of hydroxide from the sodium hydroxide so in our eyes table we have to write out our equations so the hydroxide is going to combine with the ammonia to produce ammonium in water we need to plug in moles for both ammonia and ammonium so remember it's molarity is moles over liters so we can multiply by liters so multiply by the.05 liters to get moles for both so that means the ammonia we have 0.9 moles ammonium we have 0.25 moles and we said there's 0.2 moles of hydroxide remember our goal is to neutralize and cancel out the hydroxide so we would have to subtract our hydroxide so subtract from our reactant side add to our product side to get our new amounts of acid in base and once we have the new amounts we can plug back into Henderson hasselbot to find the new pH so notice that because we added base the pH did increase however it did not increase by that much all right so looking at what happens whenever we dilute a buffer this we don't actually have to do math for we're going to talk about it more conceptually but if we dilute a buffer all we're doing is changing the overall volume which would change the molarity for both parts of the buffer equally so the ratio within the buffer itself would stay the same so when we plugged in that new ratio in the Henderson hospital we would actually end up with the same pH so diluting a buffer does not change the pH at all so let's look at how effective a buffer is um a good buffer should be able to neutralize moderate amounts of added acid or base so we want something that is not a super low concentration so we wouldn't want it to be like.001 molar for the different parts of our buffer because that's not going to be able to neutralize a lot of anything the effectiveness of a buffer depends on two conditions it depends on the relative amounts of acid and a base so how much of it you have initially the more acid base you have the more it will be able to neutralize and it also depends on the absolute concentrations of acid and base generally the higher the concentration of the parts of the buffer the more you're able to neutralize and a buffer is going to be most effective when the ratio to base and acid in the buffer are equal to one so when they have identical molarities it's going to be a more effective buffer because it can neutralize the same amount of acid and base and a buffer is considered effective if the base to acid ratio is between one tenth and 10 to 1.

[00:18:41]so even if we had like a 0.1 molar and then a one molar part of a buffer that is still within ratio um but if they're too far apart in ratio it's not going to be a very effective buffer so here you can see a concentrated buffer um that has a lot of ions in there and a dilute buffer they're both going to be able to neutralize acid or base but a concentrated buffer can neutralize more added acid base than a dilute buffer so the higher the concentration the more they're going to be able to dilute or dissolve all right so um here if we consider the following two solutions um we have a buffer that is sorry 0.1 molar the hydrogen phosphate and then a buffer that is 0.2 molar hydrogen phosphate so that is a one to two ratio between those and then solution B is a buffer of the same substance but it's a 0.15 molar dihydrogen phosphate and a 0.3 molar hydrogen phosphate yet again it is a one to two ratio so looking at what is true about the pH of these Solutions excuse me let it open up my new page so they are the same ratio therefore they should have the same pH so if they are the same ratio they will have the same pH looking at which solution will be able to neutralize the addition of 0.11 molar hydroxide so hydroxide is going to have to react with hydrogen so you're looking at which one can give up an additional hydrogen that would be able to neutralize 0.11 molar solution a only has 0.10 molar dihydrogen phosphate so that cannot fully neutralize the 0.11 molar hydroxide so solution B is the only one that can neutralize this whereas if we look at which solution can neutralize 0.11 molar um hydronium ion that is going to combine with the hydrogen phosphate both of them are above 0.11 molar so both solutions could neutralize that acid and looking at what's true about the buffer capacity of these well since the molarities in solution B are higher solution B is going to be able to neutralize more because it has a higher molarity so looking at how to prepare a buffer because you're going to do this as part of your lab the sweet remember we said a buffer is considered effective when the base to acid ratio is between 1 10 and 10.

[00:22:13]and the effective range of a buffer is the pka of the buffer plus or minus one so our PKA and the buffer we want to be within one of our Target pH and what most determines the PH range of a buffer is the pka of the weak acid so the pH can range up one or down one from the pka of the weak acid that is in the buffer so we would want to choose the appropriate acid that has a PKA almost equal to our desired PHR Target pH and we can use the ratio of Base to acid to adjust so if we want a pH exactly equal to five we can pick a weak acid that's PKA is close to five and then either include more base or more acid to alter that pH overall so let's look at how this could come up so here it wants to know which acid and its sodium salt would you choose to make a solution buffered at a pH of 4.25 and for your choice it says calculate the ratio of the base to the acid acid required to attain the desired pH so we would want to pick the acid that is closest to the 4.25 when we find PKA so here we have four acids and their pkas the one that is within one or closest to our pH of 4.25 it's time between nitrous acid and formic acid but the 4.25 it needs to go up one or down one so the one that's closest to 4.25 is formic acid so we would want to make a buffer with that formic acid and to figure out that ratio of Base to acid to obtain the desired pH so we said we're going to use formic acid which has the pka of 3.74 this is we're going to plug that into Henderson hospital but we don't know the acid base ratio we know that we want a pH of 4.25 our pka of formic acid is 3.74 plus the log of the base to acid ratio so you can kind of replace that base to acid ratio with x so we would subtract the 3.74 on both sides and then to get rid of log we need to do the anti-log which is that 10 raised to the power and that tells us that our base to acid ratio needs to be 3.24 so we can do the ratio base to acid we can do 3.24 milliliters of base for every one milliliter of acid and that is what we would use to make the overall buffer solution