[Hemidol]

Earliar today I plotted a curve of 4 data sets. I'm faced with the following question:
Visually determine the pKa value found in the acidic pH range from the titration
curves. (Hint: There are 2 pKa values present in this titration. Determine
the pKa found in the acidic pH range only).

Here are the data sets (sorry they're a bit long)... The left column indicates mL HCl added while the right is the corresponding pH value I recorded.

How can I go about determining the pKa values from these data sets?

Thanks for reading.

0mL - 12.5
1 - 11.8
2 - 11.2
3 - 11
4 - 10.7
5 - 10.6
6 - 10.6
7 - 10.4
8 - 10.3
9 - 10.2
10 - 10.1
11 - 10.1
12 - 10
13 - 9.9
14 - 9.8
15 - 9.8
16 - 9.7
17 -9.6
18 - 9.6
19 - 9.6
20 - 9.5
21 - 9.4
22 - 9.4
23 -9.4
24 - 9.2
25 - 9.1
26 - 9.0
27 - 9.0
28 - 8.8
29 - 8.7
30 - 8.6
31 -8.6
32 - 8.6
33 - 7.5
34 -7
35 - 6.7
36 - 6.5
37 - 6.4
38 - 6.4
39 - 6.4
40 - 6.4
41 - 6.2
42 - 6.1
43 - 6.0
44 - 5.9
45 - 5.9
46 - 5.8
47 - 5.5
48 - 5.5
49 - 5.4
50 - 5.1
51 - 4.5
52 - 1.5

0mL - 12.3
1 - 11.5
2 - 11.2
3 - 11.0
4 - 10.8
5 - 10.5
6 - 10.4
7 - 10.4
8 - 10.1
9 - 10.1
10 - 10.0
11 - 9.9
12 - 9.8
13 - 9.7
14 - 9.7
15 - 9.5
16 - 9.4
17 -9.1
18 - 9.1
19 - 9.0
20 - 8.7
21 - 8.4
22 - 8.3
23 -7.8
24 - 7.2
25 - 6.8
26 - 6.5
27 - 6.5
28 - 6.4
29 - 6.3
30 - 6.1
31 - 6.1
32 - 5.9
33 - 5.9
34 - 5.6
35 - 5.4
36 - 5.0
37 - 2.9
38 - 1.3

0mL - 12.1
1 - 11.5
2 - 10.9
3 - 10.7
4 - 10.5
5 - 10.4
6 - 10.2
7 - 10.1
8 - 10.0
9 - 9.8
10 - 9.6
11 - 9.6
12 - 9.4
13 - 9.2
14 - 9.0
15 - 8.8
16 - 8.5
17 - 7.3
18 - 6.9
19 - 6.5
20 - 6.2
21 - 6.0
22 - 5.9
23 - 5.7
24 - 5.5
25 - 5.3
26 - 4.7
27 - 1.1

0mL - 11.5
1 - 10.3
2 - 9.8
3 - 9.1
4 - 6.5
5 - 5.8
6 - 5.0
7 - 1.0

[cliverlong]

I think this might  be to do with something you can calculate when the titration has reached its "half-equivalence point".
Google that, or read your textbook on interpreting titration curves, and see if you can find a relevant equation.

Clive

[Hemidol]

Is there an actual calculation I can do number wise to determine the pKa values for these data sets or will it have to be done with my minds eye?

I found this information online:
http://www.chemguide.co.uk/physical/acidbaseeqia/phcurves.html

[cliverlong]

(I have read) You read from the graph  volume of acid (M) required to reach equivalence point, take half that volume of HCl (M/2), then use graph to determine the pH_half at that "half-volume"

Then pKa = pH_half (at this half equivalence point)

I'm pretty confident there is a numerical method that could analyse the data and come up with a value - (thinking off top of my head) something along the lines of - find the steepest gradient by finding difference in vertical values (pH) divided by horizontal (voulme) values, find mid point of the horizontal (volume) range = M,  then take half that value (M/2) and go back into the dataset the find the relevant pH for this "half volume" (M/2). Really all I'm doing is to try to convert into calculations the steps I would take when reading the values from the graph.

Clive

[Borek]

or will it have to be done with my minds eye?

No, with your real eye

And while Clive is right that you can try some sophisticated method, it will be an overkill - plot & ruler will do.

[Hemidol]

or will it have to be done with my minds eye?

No, with your real eye

And while Clive is right that you can try some sophisticated method, it will be an overkill - plot & ruler will do.

It was an expression... 


But clive thus wouldn't I arrive at 4 pKa values? If I have four different lines plotted will I have four different pKa values or is there a method to arrange 1 pKa value from the 4 lines plotted.
This is what I understand on visually determining the pKa value. It will be the point were I have steep drops in pH values, so does that mean that the pKa value is where the steep drop begins?

[Borek]

Each experiment will give separate result, but these should be all close to the real pKa, if they will differ that will be just effect of experimental errors.

[Hemidol]

Yeah this is what my graph suggests. But still is that what pKa value will show as, the steep drops in pH value that I have? And I'm guessing I just take a ruler and hit the middle of these drops across all four lines and that'll give me the pKa of the titration.

Also does the starting concentration of the sodium carbonate solution affect the determination of the pKa value?

[Borek]

I am not sure what you mean.

Not half of the drops - steep part of the curve is where the titration ends, pKa is at half titration.

And if you kno why pH=pKa at half titration, you should know whether initial concentration matters.