A 30.0-mL sample of 0.165 M propanoic acid is titrated with 0.300 M KOH. Calculate the pH at each volume of added base: 0 mL, 5 mL, 10 mL, equivalence point, one-half equivalence point, 20 mL, 25 mL. Sketch the titration curve.

Video transcript

Welcome back everyone. A 25 mL sample of 250.1 50 molar but no acid is titrate using a 500.2 50 molar sodium hydroxide. Tyrine mark the points with 19 mL and 22.50 mL of 0. 50 molar sodium hydroxide and trace the titration curve. Our titration curve given below has our five p points listed where we have on our Y axis. A ph range from 0 to 14. And then on our X axis, we have our volume of 0.2 50 molar sodium hydroxide, which is our tyrant added in milliliters ranging from 0 to 40 mL. Our first step is to write out our reaction. So we begin with button no acid which is C H three C H two C H two coo h this is aqueous and it's a weak acid which reacts with sodium hydroxide, which is one of our memorized strong bases. So we have a acid based reaction where our acid will donate a proton to our base. And our base being a strong base will fully dissociate. So that we have one of our products being a sodium ion, we would be left with O H where once we gain that proton, our second product form would be liquid water. And note that our base will be donating an electron pair to our weak acid. Meaning that our third product is going to be our propo eight anion C H three C H two C H two coo one minus. And recognize that this propo anion is the conjugate base of our weak acid. We're going to begin by determining what our equivalence point will be. We want to recall that at the equivalence point, our moles of our base should equal our moles of acid. Currently based on our pump, we know that our volume of acid is mL. I'm sorry, this is 25 mL. Now we want volume here to be in liters. So we're going to multiply to go from one mL in the denominator to 10 to the negative third liters in the numerator canceling out millis. We have leaders and we want to multiply by our molar concentration because we understand that polarity is interpreted as moles per liter. We can get moles by multiplying our volume by our molar concentration. So our molar concentration of button acid is given us 0.1 50 molar, which we will interpret as 500.1 50 moles per liter. So that we can then cancel out our units of liters leaving us with moles of our acid, we'll say of our weak acid. And this is going to be set equal to our moles of our base. Now, we need to figure out the volume of our base at the equivalence point. But we do know it's molar concentration given in our prompt as 0.0.2 50 molar, which we will interpret as 500.2 50 moles per liter of strong base. So we need to solve for the volume of our base. Meaning on both sides of our equation, we want to divide by 500.2 50 moles per liter. So canceling out that term on the right, we would be left with our volume of our base equal to 0.15 liters. Because notice we can cancel out our units of moles leaving us with liters as our final unit for volume. Now we're going to need to convert this back to milliliters to match with our unit of volume for our but no acid which is given in millis from the prompt. So we're going to multiply to go from 10 to the negative third liters in the denominator to one mL in the numerator, canceling out liters. We're left with milliliters and we would have our volume of our base in milliliters now equal to 15 mL of our sodium hydroxide at the equivalence point. So this is our volume at the equivalence point. And so therefore, at the half equivalence point, our volume of we'll say sodium hydroxide, our base is equal to half of that, which would be 7.5 mL. And so that is written below here, our volume of sodium hydroxide is equal to 7.5 millis at the half equivalence point. Now, looking at our given volumes from the prompt, we would be past the equivalence point since we're given volumes of and 22 mL. So beginning with figuring out our first or rather, since we know our equivalence point is at 15 mL, which would be at this P H point where we have a P H of or sorry, a 15 millis would be at this P H point where we have a P H of around four, then we would determine that we are finding our third or correction. So our equivalence point for 15 millis should actually be around here at a P H of around maybe 4.5 to 5 where we would be finding. Since we know our first volume is 19 millis, we are our first P H point. We're finding is going to be our fourth P H point. And at the volume of 22.50 millilitres, we would be finding our P H point which is our fifth P H point. So right now, we need to determine our P H value at the fourth point of our titration curve or P H curve, which is upon the addition of 19 mL of sodium hydroxide or tyrant. So we're going to begin by calculating our initial moles of acid and our initial moles of bases. Beginning with our initial moles of acid. We understand from its molar concentration that we have 0.1 50 moles per liter of our weak acid proano acid, which is multiplied by its volume. Given from our prompt as 25 milit, which we need to convert to liters by multiplying by one milli in denominator to 10 to the negative third liters in the numerator canceling out milliliters as well as liters. We have moles as our final unit. And our initial moles of weak acid we'll find is equal to 0.375 moles of weak acid. Initially. Now for our initial moles of weak base or strong base rather, since we have sodium hydroxide, we begin with its molar concentration given from the prompt as 0.2 50 molar, which we will interpret in terms of moles per liter and multiply by the volume used for the fourth phh point on our curve given in our prompt as 19 millis which we need to convert to liters by again, multiplying by 10 to the negative third liters and the numerator equivalent to one mL in the denominator. So canceling out milit as well as liters were left with moles. And we would find that our initial moles of base is equal to a value of 0.475 moles. So now between our two initial amounts of acid and base, we can understand that because our amount of acid being 0.375 moles is less than our initial amount of base. We would determine our acid, which is our button acid as our limiting reagent. We also want to recall that specifically when we have a reaction between a weak acid and a strong base after the equivalence point, which is what we have here. This 19 mL is after our equivalence point, which we determined was 15 mL after the equivalence point in a reaction between a weak asset and a strong base, only the strong base will influence the P H. Now, we can include our IC F table to show our initial change and final conditions of our reaction. We're beginning with proano acid C H three C H two C H two coo H we have initially, as we stated, 0.375 moles then reacting with sodium hydroxide. Initially, we just determined that we have 0. moles of sodium hydroxide. And on our product side, we only want to include our aqueous product, which is our propo eight anion C H three C two C H two coo one minus which we stated is our conjugate base of our proano acid. And initially, we would have zero since that is a product and has not formed yet, our change is going to be based on our limiting reagent. So we would have minus that amount for our reactants minus 0.375 moles for both of our reactants. And we would have plus that amount for our products. So at the final conditions of our reaction, we have zero moles of our acid left, we have 0.1 zero moles of our base remaining. And then we have 0.3, 75 moles of our conjugate base, which is a weak base remaining in solution. So our weak base is not going to influence our P H only our strong base sodium hydroxide will influence P H. And so therefore, we want to consider our moles of sodium hydroxide that remain after our reaction, which we determined from our IC F table is 0.10 moles. And now we are going to recall that we're going to need to get this as a molar concentration in order to utilize our P O H formula, which we recall is calculated by taking the negative log of our concentration of our strong base. And then from our P H formula, we can calculate our Ph where we would take minus our P H since we should recall that our P plus our P is equal to 14. So we just rearranged that formula to solve for PH. So going back to finding our molar concentration of sodium hydroxide, we're going to take our amount of moles of solute. So for moles of N A O H. We need our moles of our solute that remain divided by our volume of our solution. So plugging in our moles remaining being 0.10 moles of sodium hydroxide and dividing by our volume of our solution, which based on our acid where we have according to our prompt, we have a volume of 25 mL of but no acid. So we would have 25 milit, we'll just say of our weak acid. So just to erase 25 mL of a weak acid, which is then added to our volume. 4.4, our fourth point on our P H curve which is 19 millis of our base sodium hydroxide. That's our strong base. We need to convert to liters in our denominators. So we're going to multiplied by our conversion factor where for one mL in our denominator, we have an equivalent of 10 to negative third liters in our numerator canceling out milliliters. We're left with units of moles per liter, which is what we want for molar. And we'll find that our molar concentration, our molar concentration of sodium hydroxide that remains after it reacts with our acid is equal to the value of 1.643452 molar. So this should be capital m for molar. So now that we have this molar concentration and actually just to make a quick correction to our molar concentration calculation, it should actually be the value 0.22727 molar of our strong base sodium hydroxide. So going into our calculation for P O H, we would set this equal to the negative log of our concentration which we just found as 0.22727 molar. In which when we take the negative log of this, we have a P O H equal to the value of about 1.64, which means that now we can find our P H by taking 14 minus 1.64. And that would result in our P H equal to the value 12.36. And so now going back to our P H curve for the volume for the volume at 19 millis of base added, which would be looking at our curve. That would be around this point here we'll say is millis. We have a P H of, as we stated, 12.36. So we should actually draw in our P H points a bit over 12.36. So here at least, so we can fill in our P H point for 19 millis at this location. And so now we're going to continue on to find our second P H point at 22.50 mL. So that's going to be past this point. We just drew in for 19 mL of base. And so we're going to get our sixth P H point now, and this is upon the addition of 22. mL of our strong base sodium hydroxide. Now, our initial moles of base are the only thing we're going to need to calculate since our volume of acid has not changed. So for our initial moles of base, we take its molar which we will interpret as 0.2 50 moles per liter. And we're going to multiply to go from or to go to our volume, which is 22.5 millis and now multiplying to go from millis in the denominator to 10 to the negative third liters in the numerator, we're going to cancel out millis as well as liters leaving us with moles. And our initial moles of base for sodium hydroxide is now going to be 0. moles. Initially, this amount of initial moles of base is greater than our initial moles of acid that we determined earlier. So our acid is still limiting and therefore our amount of base that remains after the reaction occurs would be the difference where we take our initial moles of base, 0.5625 moles of base minus the amount reacted, which is going to be based on our limiting reactant being the initial amount of acid, which is smaller. And we determined that that was minus 0.375 moles, which we'll say is reacted And from this difference, we'll find our moles of base which remains equal to zero 0.1875 moles of sodium hydroxide that are left over after the reaction. And now we just need to convert this to a molar concentration for sodium hydroxide in which we take our moles of our solute 0. moles of sodium hydroxide and divide by the total volume of our solution. Where for sodium hydroxide, we have a volume for the sixth P H point being 22.5 milit of strong base. We'll say added to our volume of weak acid which we determined from the prompt was given as again 25 mil liter. So plus 25 millis of weak acid and then multiplying by our conversion factor to go from one mL in the denominator to 10 to the negative third liters in the numerator. And then canceling out our units of milliliters. We're left with moles per liter for our molar concentration of base. And this will simplify so that we have a concentration equal to the value as 0. molar of our sodium hydroxide base. And now we're just going to use this molar to then calculate our P O H first in which we take the negative log of our concentration of sodium hydroxide as 0.3. This is a three molar and that will result in our P O H equal to the value of one 0.40. Now, with this P O H, we can move into calculating our P H to get our fifth point on our P H curve where we have 14 subtracted from our P O H in which we would take 14 minus 1.40, which would result in our P equal to the value of 12.6 approximately. So we can say that that's 12.60. And so going back to our PH curve above, we have for 22 mL of base added to our solution, which we'll say is around this point for 22 millis of base, we have a P H of about 12.60. So we'll say that that point is around this location. So now our last step is to trace our P H curve. So we're going or our titration curve. So we're going to connect all of our PH points, including the ones that were already listed and the one, the two points that we added. And this will actually complete our PHH curve for a total of seven P H points in the titration of button acid are weak acid with our strong base sodium hydroxide. So our final answer is our complete P curve as well as our two P H points that we determined where for millis of strong base, we had a P H of about 12.36. And then for 22.5 mL of strong base, we calculated A P H of about 12.60. So I hope that everything we went through is clear. If you have any questions, please leave them down below and I'll see everyone in the next video.