# ACID-BASE TITRATIONS

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4 determines the ph of the solution i.e moles of base. The total volume of solution in the flask is L of acid L of base = L of solution. The concentration of the unreacted OH - is [OH - ] = = M Hence the ph = pkw + log[oh - ] = 14 + log[ ] = Now with this information you can create a spreadsheet for the strong acid strong base titration curve. However, you have to be careful to use the right equations to calculate the ph depending on which of the above four regions you are in, which in turn depends on how much base has been added to the acid solution. Below are the four equations you will use to create this spreadsheet. Given the information above, you will have to determine which equation should be used in creating the spreadsheet. Remember deciding which equation to use depends on the amount of base that has been added to the solution in the flask. General equations Define: Ca concentration of acid Cb concentration of base Va initial volume of acid Vi total volume of base added at a given point along the titration Va + Vi - Total volume at any point along the titration 1 Initial conditions before any base added ph = -log [Ca] 2 Before equivalence ph = log( C a C b V i

6 Copy cell B13 and paste into cells B14 down to the cell before the end point (iii At the end point In column B enter 7.00 into the cell for the end point (iv Beyond the end point In the cell after the end point enter the equation = 14 + LOG10((Cb*AX-Ca*Va/(Va+AX where X is the cell number. Copy this cell and paste into cells below. 6 Plot the titration curve You should now have a completed spreadsheet for plotting the titration curve. Select all cells for which there are entries in columns A and B. From the menu select Insert->Chart. Choose an XY scatter plot with a smooth line joining the points. Finish the plot on the same sheet. You should see a titration curve as shown in figure 1. It is also instructive to plot the titration curve but showing the points along the curve. To do this, once again select all points in columns A and B. From the menu select Insert->Chart. Choose an XY scatter plot but this time choose the chart sub-option in the middle left (scatter with data points connected by smooth lines. Finish the plot on the same sheet. This time look at the data points. Notice that close to the end point, points along the y axis (ph are spaced far apart, even though they are closely spaced in x (volume of base added. This shows that near the end point the ph changes very dramatically with very small increments of added base. The end point can be very easily determined from the graph. QUESTIONS 1 Let s say you were to repeat the above titration, but with the acid in the buret and the base in the flask. Describe how the ph of the solution in the flask would vary as more acid is added (i.e. describe the shape of the titration curve. What would be the ph of the solution at the end point? Titration of a weak acid - strong base.

7 7 For the next exercise you will create a spreadsheet for a titration between a weak acid and a strong base and plot the titration curve. The steps to do this are essentially the same as that for the strong acid strong base case but the equations for calculating the ph for the different regions of the titration curve are different. Let s first look at these equations and then go through the steps for creating the spreadsheet. A titration curve for a weak acid strong base has similar features to that for a strong acid strong base titration, namely (i a region in which the ph slowly increases with addition of base, (ii a region where the ph dramatically increase with small changes in ph and (iii beyond this a region where the ph slowly increases with addition of the base. Figure 2 shows a titration curve of a weak acid versus a strong base.

8 ph volume of base added (L Figure 2 In this exercise you will titrate L of 0.10 M CH3COOH (in flask versus 0.10 M NaOH (in buret. The net ionic equation for this reaction is : CH3OOH + OH - CH3COO - + H2O Let s look at the equations for calculating the ph of the different regions of the titration curve. i Before any base is added The ph is determined by the dissociation of the weak acid. CH3OOH + H2O CH3COO - + H3O + To calculate the ph for the solution of weak acid you have to account for the amount of CH3COOH that dissociates. Unlike a strong acid, CH3COOH does not dissociate completely in solution. The extent to which CH3COOH has dissociated is characterized by its acid dissociation constant Ka. The concentration of CH3COOH in the flask is 0.10 M. Let x be the concentration of the H3O + and CH3COO - formed at equilibrium. Hence, at equilibrium the concentration of the undissociated CH3COOH is (0.1 x in molar units.

9 The acid dissociation constant is defined as: K a = [CH 3 COO ][H 3 O + ] [CH 3 COOH] = x x 9 Usually it is safe to assume that x << 0.10, so since ph = -log[h3o + ], the ph of the solution, before any base has been added, is ph = log K a C a where Ca is the initial concentration of the acid (here 0.10 M. ii Before the end point As base is added to the solution in the flask, the acid reacts with the base: CH3COOH + OH - CH3COO - + H2O This creates a buffer solution where the ph of the solution can be determined by the dissociation of the unreacted acid: Hence, CH3COOH + H2O CH3COO - + H3O + K a = [CH 3 COO ][H 3 O + ] [CH 3 COOH] ph = log( K a[ch 3 COOH] [CH 3 COO ] So as OH - is added, we need to calculate the concentration of the unreacted CH3COOH and the concentration of CH3COO - formed. The moles of CH3COO - formed = moles of OH - added = CbVi where Cb is the concentration of the base, Vi the volume of base added. So the concentration of CH3COO - formed = C b V i where Va is volume of acid in the flask. The concentration of CH3COOH unreacted = C a C b V i

10 10 We can now calculate the solution ph at any point before the end point ph = log( K a (C a C b V i C b V i ph = pk a log( C a C b V i C b V i C ph = pk a + log( b V i C a C b V i iii At the end point when enough base has been added to react with all the acid. In this example, where a L of a 0.10 M solution of acid is being titrated against a 0.10 M solution of base, the end point is reached when L of base has been added. The ph at the end point is determined by the reaction : CH3COO - + H2O CH3COOH + OH - Note that CH3COO - is the conjugate base of CH3COOH. The concentration of the OH - ions formed in the above reaction determines the ph. As you will see when you construct the spreadsheet, the ph of the solution at the end point will be greater than 7, i.e. basic. In fact, the weaker the acid (the smaller the value of Ka, the more basic the solution at the end point (since the weaker the acid, the stronger is its conjugate base, and the above reaction goes further to the right. From the reaction of the conjugate base: K b = [CH 3 COOH][OH ] [CH 3 COO ] where Kb is the dissociation constant of the base, in this case the conjugate base CH3COO -. Hence: [OH ] = K b [CH 3 COO ] [CH 3 COOH] We need to calculate the concentration of CH3COOH and CH3COO - at the end point.

11 The number of moles of CH3COO - initially formed, before it reacts with H2O to form 11 CH3COOH and OH -, is equal to the number of moles of the base added up to the end point. Since the volume of the solution in the flask = Va+Vi the initial concentration of CH3COO - formed at the end point is [CH 3 COO ] = C b V i Since the CH3COO - further reacts with water to form CH3COOH and OH -, the final concentration of CH3COO - is [CH 3 COO ] = C b V i [CH 3 COOH] However, since [CH3COOH] << [CH3COO - ], we can approximately express the concentration of CH3COO - as [CH 3 COO ] C b V i Also since, [CH3COOH] = [OH - ], the equation [OH ] = K b [CH 3 COO ] [CH 3 COOH] can be re-written as Since [OH ] = K b [CH 3 COO ] = K b C b V i K w = [H + ][OH ] where Kw is the ion product of water (= 1 x at 25 o C Therefore,

12 12 Hence, [H + ] = K w [OH ] K w log[h + ] = log( [OH ] log[h + ] = log K w ( log[oh ] = log K w + log[oh ] ph = pk w + log[oh ] ph = 14 + log K b C b V i iv Beyond the end point the ph is determined by the excess OH - added. The ph can be calculated using the equation: ph = 14 + log( C bv i C a General equations i Before base added ph = log K a C a ii Before the end point C ph = pk a + log( b V i C a C b V i iii At the end point ph = 14 + log K b C b V i iv Beyond the end point ph = 14 + log( C bv i C a

13 13 Open the Excel spreadsheet titled wkacid_strbase and note the entries made in the spreadsheet. Save this file to your floppy disk (File -> SAVE AS. Give the file a name and save to FLOPPY DISK. Ca concentration of acid (M Va volume of acid in flask (L Vb concentration of base (M Ka dissociation constant of the acid pka - -log(ka Kb dissociation constant of the base Kw ion product of water 1 Column A enter the volume increments for the base in L. Start in cell A12 and fill down till you are past the end point. Fill this column till the maximum volume of the base added is around L. Note that within L on either side of the end point, the volume should change by L. So first determine the amount of base that must be added to reach the end point (remember the strong acid- strong base titration before entering the volume increments. 2 Column B calculate the ph for each point along the curve: (i Before base added the ph is determined by the dissociation of the acid In cell B12 enter the equation = -LOG10(POWER(Ka*Ca,0.5 (ii Before the end point the ph is determined by the dissociation of the unreacted acid. In cell B13 enter the equation : =pka+log10((cb*a13/(ca*va-cb*a13 Copy cell B13 and paste into cells B14 to the cell before the end point (iii At the end point In cell corresponding to the end point enter the equation =14+LOG10(POWER(Kb*((Cb*AX/(Va+AX,0.5 where X is the cell number of the end point. (iv Beyond the end point In the cell after the end point enter the equation =14+LOG10((Cb*AY-Ca*Va/(Va+AY, where Y is the cell number of the cell right after the end point. Copy this cell and paste into cells below.

14 14 Plot the titration curve You should now have a completed spreadsheet for plotting the titration curve. Select all cells for which there are entries in columns A and B. From the menu select Insert->Chart. Choose an XY scatter plot with a smooth line joining the points. Finish the plot on the same sheet. You should see a titration curve similar to the one shown in figure 2. Create a second scatter plot showing the data points and a line joining the points (similar to the plot you created for the strong acid strong base titration. Once again note that near the end point a very small change in the volume of base added affects the ph dramatically. So once again the end point is very well defined on the graph. Affect of the dissociation constant of the acid (Ka on the shape of the titration curve. The value of Ka affects the shape of the titration curve for a weak acid strong base titration. Increase and decrease the value of Ka and see how the shape changes. For example, change the value of Ka from 1.75 x 10-5 to 1.75 x 10-7 and then to 1.75 x Notice that the height of the curve changes as Ka changes. Also note how the ph of the solution at the end point changes as Ka changes. QUESTIONS 1 How does the ph of the solution at the end point vary with Ka and why does it vary with Ka? 2 By varying the value of Ka you can see how the shape of the titration curve is affected by Ka. Explain what the problem might be in isolating the end point if Ka were very small (e.g. if Ka = 1.75 x If you were to carry out a titration with weak base in the flask and a strong acid in the buret, how would the ph of the solution in the flask vary as acid is added to the solution? Would the ph of the solution at the end point be acidic or basic?

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