in this video we're going to focus on solving acid-base titration problems so let's start with this one 24.7 milliliters of an hdl solution is completely neutralized by 35.8 milliliters of a 0.25 molar sodium hydroxide solution what is the concentration of the original hcl solution so we're going to find the answer using two methods using an equation and by dimensional analysis so let's use the equation first the first thing you need to identify is the type of substance that we have the acid is monoprotic it only has one hydrogen and the base only has one hydroxide ion per formula unit if you see that you could simply use this formula m1 v1 which is equal to m2 v2 so we're going to say that m1v1 corresponds to the acid and m2 v2 corresponds to the base and the reason why this works is because when you multiply the molarity which is moles per liter by the volume you get the number of moles the liters cancel and in a neutralization reaction the moles of the acid must equal the moles of the base and so that's why that formula works for this type of problem so in this example we're looking for the concentration of the original hdl solution so looking for the concentration of the acid m1 v1 is 24.7 milliliters m2 is 0.25 moles per liter v2 is 35.8 milliliters so m1 is going to be 0.25 times 35.8 divided by 24.7 so the concentration of hcl is 0.362 moles per liter or simply capital m now let's talk about the other method that we can use to get the same answer this is probably the most simplest method to use just using this formula if you have a monoprotic acid and base now to use the other method you need to write a balanced chemical equation so hcl reacts with sodium hydroxide and this is a double replacement reaction so h is going to pair up with oh producing liquid water and then na is going to pair up with cl produced in sodium chloride so these two they react in a one-to-one ratio the molar ratio is what we need in the balanced chemical equation now our goal is to find the concentration of hcl so we need to start with the stuff of the other substance once we could find the moles of sodium hydroxide the base that's going to equal the moles of the acid and then using the volume of the acid we could find a concentration so i'm going to start with the molarity of sodium hydroxide instead of writing as capital m i'm going to represent it as moles per liter so we have 0.25 moles of sodium hydroxide per liter of solution now let's multiply by the volume to convert milliliters into liters we need to divide by a thousand so 35.8 milliliters is the same as point zero three five eight liters you can move the decimal point three units to left now notice that the unit liters of solution cancels so now we have moles of sodium hydroxide and we can convert it to moles of the acid using the molar ratio which is one to one so for every mole of naoh that reacts one mole of hcl reacts with it so now the unit moles of naoh cancels so now we have moles of hcl to get the molarity we need to divide the moles by the liters and we have the volume of hcl but we need to convert that to liters by dividing it by a thousand so twenty four point seven milliliters is the same as point zero two four seven liters so to get the answer it's point two five times .0358 divided by 0.0247 and you get the same answer .362 moles per liter so you could find the concentration of hdl using both techniques now what about this one what volume of a 0.15 molar barium hydroxide solution is required to completely neutralize 45 milliliters of a 0.29 molar hno3 solution so like the other problem we're going to get the answer for this problem using two techniques so notice that nitric acid is monoprotic it only has one hydrogen but barium hydroxide has two hydroxides per form the unit so therefore we need to modify the equation so i'm going to write the acid first hno3 and then the base baoh2 now keep in mind the moles of the acid must equal the moles of the base in a neutralization reaction so m1 v1 which is the moles of the acid equals m2 v2 the moles of the base but in this example barium hydroxide has two hydroxide ions per formula unit so we need to incorporate that too and we could put it on the same side that barium hydrox that exists so m2 v2 has to correspond to the base we can only plug in the information of the base on this side if we plug it in on the wrong side we're not going to get the right answer nitric acid only has one hydrogen ion performing the unit so we're going to put a 1 on the left side now let's go ahead and get the answer so for the acid m1 is the concentration it's a 0.29 v1 is the volume 45 milliliters by the way if v1 is in milliliters v2 has to be in the same unit milliliters if v1 is in liters v2 has to be in liters the unit have to match then we have a 2 in front we have the molarity of the bearing hydroxide solution that's 0.15 all we need to find is v2 so now we just got to do some math.29 times 45 is 13.05 two times point fifteen is point thirty so to find v2 all we need to do is take 13.05 and divided by point three so v2 is 43.5 milliliters so that's the answer to the problem which i'm going to rewrite it here for reference so let's see if we can get the same answer using stoichiometry feel free to attempt it if you want to the first thing we need to do is write a balanced chemical equation so barium hydroxide reacts with nitric acid now when h and oh gets together it's going to produce water as always now what about when barium pairs up with nitrate what's the chemical formula between those two uh ions barium has a positive two charge it's in group two of the periodic table plus it has two hydroxide ions attached to it and you know each hydroxide ion has a charge of negative one so barium has to be plus two nitrate has a negative one charge so the chemical form of fibrium nitrate is ba1 and two now we need to balance it we have two nitrate ions on the right side so we need a two in front of a channel 3 and we have 2 hydrogens here 2 hydrogens there so there's a total of 4 hydrogens on the left so we need to put a 2 in front of water so we can have 4 hydrogen atoms on the right so now the chemical equation is balanced but what's important is the molar ratio between barium hydroxide and nitric acid it's a one to two ratio that's why we need to write the balanced chemical equation to get that molar ratio so now let's go ahead and calculate the volume of barium hydroxide so let's start with the other substance nitric acid let's get the moles of the acid first so instead of writing 0.29 m i'm going to write 0.29 moles of nitric acid per liter of solution next let's multiply by the volume of nitric acid so we have 45 milliliters and if we divide that by a thousand that's point zero four five liters so now we have the moles of the acid now let's convert it to the moles of the base using a mole ratio so for every two moles of nitric acid that participates in a reaction one mole of barium hydroxide will react with it so now we can get rid of the unit moles of nitric acid now the last thing we need is the volume let's get the volume in milliliters now we have the concentration of barium hydroxide the molarity connects moles and liters together so a point 15 molar solution means that there's point 15 moles of solute per one liter of solution so since we have moles of barium hydroxide on the top we need to put moles of bare hydroxide on the bottom so one liter of barium hydroxide solution contains 0.15 moles of ba oh2 and i'm running out of space here so we can cancel these two units now the last thing we need to do is convert liters into milliliters and one liter is equal to a thousand milliliters so now we can cross out the unit liters so this should give us our answer so it's 0.29 times .045 divided by 2 and then take that result divided by 0.15 and then multiply it by a thousand and this will give you the same answer 43.5 milliliters number three what mass of khp potassium hydrogen phthalate will be completely neutralized by 32.57 milliliters of a 0.175 molar standard sodium hydroxide solution so what do you think we need to do in this problem need to understand that khp is a monoprotic acid and we can't use the formula m1v1 equals m2v2 because that formula doesn't correspond to mass so the best way to get the answer is by stoichiometry this might be bad news for those of you who really like those formulas but let's start with a balanced chemical equation so khp reacts with sodium hydroxide if you want to you can use this but i'm just going to use khp what you need to understand is that this hydrogen will combine with the hydroxyl ion produced in water and once you take away the hydrogen what's left over will have a negative charge and that's going to pair up with the sodium so this is going to be n a k p if you want to you can replace the p part with c8 h4o4 i'm going to write as khp because it's a lot simpler so now notice that in a balanced chemical reaction khp reacts with sodium hydroxide and a one-to-one molar ratio and that's what we need as you can see there's only one acidic hydrogen in khp the other hydrogens are not acidic only the one that's lifted excuse me listed to the left is the one that's acidic so what we're going to do is start with the information of sodium hydroxide we're going to get the moles of naoh then use that to get the moles of khp and then use the molar mass of khp to get the grams so if you understand how to do it feel free to pause the video and try if not sit back and watch let's start with 0.175 moles of naoh per liter as we've been doing before and let's multiply that by the volume of the naoh solution but we need this in liters so if we divide that by a thousand that's going to be 0.03257 liters now let's convert from moles of naoh to moles of khp so it's a one-to-one ratio for every mole of sodium hydroxide that reacts one mole of khp will react as well now the last thing we need to do is we need to convert the moles of khp into grams using the molar mass so one mole of khp has a mass of 204.22 grams and so now all we got to do is just get the answer so let's multiply 0.175 by .03257 and then multiply that result by 204.22 so the mass is equal to 1.164 grams of khp so this is the answer number four 42.6 milliliters of koh was required to completely titrate 0.137 grams of khp what is the concentration of the koh solution well let's begin so khp is going to react with koh and every time h and oh gets together they're going to produce water after that we're going to combine k with kp so that's going to be k2p and keep in mind p is c8h4o4 so once again we have a one-to-one molar ratio which is what we're looking for in this example so we want to find the concentration of koh therefore start with the other substance khp so we have 0.137 grams of khb and let's convert it to moles using the molar mass so one mole of khp has a mass of 204.22 grams now let's change it to the moles of koh using the molar ratio so for every mole of khp that is consumed in reaction one mole of koh is also consumed now the last thing that we need to do to find the concentration is we need to divide the moles of koh by the liters of the solution and it's 42.6 milliliters which is .0426 liters so the answer is going to be 0.137 divided by 204.22 and then divide that by 0.0426 so it's 0.01 moles per liter or simply capital m so that's the concentration of koh in this problem so this is the answer you