Acid–base titrations

a titration is a procedure for determining the concentration of a solution and so let's say we're starting with an acidic solution so in here let's say we have some hydrochloric acid so we have some HCl and we know the volume of HCl let's say we're starting with 20 point zero milliliters of HCl but we don't know the concentration right so question mark here for the concentration of HCl we can find out that concentration by doing a titration next we need to add a few drops of an acid-base indicator so to this flask we're also going to add a few drops of an acid based indicator we're going to use phenolphthalein and a phenolphthalein is colorless an acid but turns pink in the presence of base and since we have our phenolphthalein and acid right now we have a clear solution there's no color to it up here we're going to have our standard solution right we're going to have a known concentration of sodium hydroxide so let's say we have a solution of sodium hydroxide and the concentration is 0.100 molar and we're ready to start our titration so we allow the sodium hydroxide to drip into our flask containing our HCL and our indicator and the acid and the base will react right so we get an acid-base neutralization reaction HCl plus and a o H right if we think about the products this would be H - this would be H plus h plus and o H - give us h2o and our other products we would have na+ and cl- which give us NaCl or sodium chloride so let's say we add a certain volume of base right so now now this would be higher and we see our solution turn light pink all right so let's say we see our solution turn light pink and it stays light pink that means that all of the acid has been neutralized by the base and we have a tiny a tiny amount of excess base present and that's causing the acid base indicator to remain pink so a tiny excess bass means we've neutralized all of the acid present and where the indicator changes color this is called the endpoint of a titration alright so when our solution when our solution changes color that's the endpoint of our titration and here we stop and we check and see the volume of base that we used in our titration so if we started right here or if we started with that much base let's say we end it down here all right so we still have a little bit of base left and this would be the volume of base that we used in the titration all right so we have a change in volume here and and let's say that it's forty eight point six milliliters so it took 48 point 6 milliliters of our base to completely neutralize the acid that we had present and so we can now calculate the cap the concentration of the HCL all right so let's go ahead and do that and let's start with the concentration of sodium hydroxide all right we know that we started with point one zero zero molar solution of sodium hydroxide 0.100 molar and molarity molarity is equal to moles over liters alright so this is equal to moles over liters and our goal is to figure out how many moles of base that we used to neutralize the acid that was present all right so we can take our volume here forty eight point six milliliters and we can convert that into liters alright so just move your decimal place three places to the left so one two three so that's point zero four eight six liters so this is equal to moles over zero point zero four eight six liters and so let's get some more space alright let me just rewrite this really quickly zero point one zero zero is equal to x over zero point zero four eight six so we're just solving for x and x represents the moles of sodium hydroxide that were necessary to neutralize the acid that we at present all right so when you solve for X you get zero point zero zero four eight six moles of sodium hydroxide used in our titration next you look at the balanced equation for what happened right so if I look at my balanced equation alright there's a one here right and there's a one here so we have a one to one mole ratio and the equivalence point is we're just enough of your standard solution has been added to completely react with the solution that's being titrated and at the equivalence point all of the acid has been neutralized all right so it's completely reacted and since we have a one to one mole ratio right if I have if I use this many moles of sodium hydroxide that must be how many moles of HCl that we had present in our original solution so therefore I can go ahead and write that I must have had zero point zero zero four eight six moles of HCL present in the flask before we started our titration right I knew that because of the one to one mole ratio all right remember our goal was to find the concentration of HCl right the original concentration and concentration molarity is equal to moles over liters so now I know how many moles of HCl I had and my original volume of HCl was twenty milliliters right so right up here we had 20 milliliters so I need to convert that into liters so I move my decimal place one two three so I get point zero two liters so now our final step here to calculate the concentration of HCl alright so the concentration of HCl is equal to how many moles of HCl we have which is zero point zero zero four eight six moles over liters of solution and we had 20 milliliters which is equal to zero point zero two zero zero liters all right so now we can take out our calculator and do this calculation to find the concentration of HCl that we started with Oh point zero zero four eight six all right and we're going to divide that by point zero two zero zero and we get zero point two four three for our answer so the concentration of HCl right is equal to zero point two four three molar so we've solved we've solved for the original concentration of HCl there's a shortcut way to do this problem all right and the shortcut way would be to do the molarity times the volume of the acid is equal to the molarity times the volume of the base use so MV is equal to mV so let's say we have the acid over here on the left and the base over here on the right so the molarity the molarity of the acid is what we're trying to find so I'll just make that X the volume of the acid that we started with you can just leave this in milliliters if you want 20 point zero milliliters is how much of the acid we started with and for the base we knew the concentration of the base that we used in our titration right it was 0.100 molar and we also knew the volume of base that we used to completely neutralize the acid we used forty eight point six milliliters and notice how the MLS would cancel out here all right and we can just go ahead and do the math and solve for X so we get out the calculator and we need to multiply 48 point six times point one zero zero all right and so we get four point eight six obviously and then if we divide by 20 if we divide by 20 we will get our answer of zero point two four three so X is equal to zero point two four three molar and this shortcut way works works pretty well when you're dealing with a strong acid and a strong base in a 1 to 1 molar relationship all right in the next video we'll do a problem where the mole ratio is no longer one-to-one