High school students should probably be familiar with titration curves for monoprotic strong acid-strong base, weak acid-strong base, strong acid-weak base and possibly weak acid-weak base, all at concentrations around 0.1 M. These are presented in Fig. 1-4 below (generated with the wonderful CurTiPot<\/a>).<\/p>\n Fig. 1: 0.1 M HCl vs 0.1 M NaOH<\/strong><\/p>\n Features:<\/p>\n Fig. 2: 0.1 M CH3<\/sub>COOH vs 0.1 M NaOH<\/strong><\/p>\n Features:<\/p>\n Fig 3: 0.1 M HCl vs 0.1 M NH3<\/sub><\/strong><\/p>\n Features:<\/p>\n Fig. 4: 0.1 M CH3<\/sub>COOH vs 0.1 M NH3<\/sub><\/strong><\/p>\n Features:<\/p>\n Acid\/base strength effects: monoprotic acids and monobasic bases<\/strong><\/p>\n As can be seen by comparing fig. 1 and 2 above, acid\/base strength\u00a0is one variable that affects the shape of titration curves.<\/p>\n The following graph shows the effect of acid strength on the shape of the titration curve. Acid strength can be\u00a0measured by the acid’s pKa<\/a>:\u00a0smaller pKa = stronger acid, larger pKa = weaker acid.\u00a0\u00a0All concentrations are 0.1 M (the effect of concentration will be investigated later).<\/p>\n Fig. 5: 0.1 M monoprotic acids vs 0.1 M NaOH, pKa variation<\/strong><\/p>\n Features:<\/p>\n A similar range of curves is found for the titration of the conjugate bases of these acids with hydrochloric acid (the pKa values indicated are for the parent acids, in the same order as in Fig. 5). Again,\u00a0all concentrations are 0.1 M.<\/p>\n Fig. 6: 0.1 M monobasic conjugate bases vs 0.1 M HCl,<\/strong>\u00a0parent acid pKa variation<\/strong><\/p>\n Features:<\/p>\n Diprotic acids can give rise to quite different titration curves, depending on the absolute and relative strengths of each dissociation.<\/p>\n The following graph shows the different titration curves from acids with<\/p>\n Again, all concentrations are 0.1 M.<\/p>\n Fig. 7: 0.1 M diprotic acid (pKa1 = -3, pKa2 = 2, 7 or 12)\u00a0vs 0.1 M NaOH<\/strong><\/strong><\/p>\n Features:<\/p>\n The following is a similar graph with smaller pKa2 spacing:<\/p>\n Fig. 8: 0.1 M diprotic acid (pKa1 = -3, pKa2 = 2-12)\u00a0vs 0.1 M NaOH<\/strong><\/strong><\/p>\n Features are similar to Fig. 7:<\/p>\n A similar effect is seen when the first pKa is weaker (e.g. pKa1 = 4):<\/p>\n Fig. 9: 0.1 M diprotic acid (pKa1 = 4, pKa2 = 5-12)\u00a0vs 0.1 M NaOH<\/strong><\/strong><\/p>\n Fig. 10: monoprotic strong acid, X M (pX = -1 – 5)\u00a0vs X M NaOH<\/strong><\/strong><\/p>\n Features:<\/p>\n For a weak acid similar features are observed, except that a higher concentration of acid and base is required to give an equivalent change in pH either side of the equivalence point. This makes sense given that the pH change either side of the equivalence point is already less pronounced for a weak acid than it is for a strong acid (compare Figs. 1 and 2).<\/p>\n Fig. 11: monoprotic weak acid (pKa 4.76), X M (pX = -1 – 5)\u00a0vs X M NaOH<\/strong><\/strong><\/p>\n Fig. 12: X M diprotic acid\u00a0(pX = -1 – 5,\u00a0<\/strong>pKa1 = -3, pKa2 = 2)\u00a0vs X M NaOH<\/strong><\/strong><\/p>\n Features:<\/p>\n Consider again Fig. 7 (0.1 M, reproduced immediately below) and compare with Fig. 13 below it (0.001 M):<\/p>\n Fig. 7: 0.1 M diprotic acid (pKa1 = -3, pKa2 = 2, 7 or 12)\u00a0vs 0.1 M NaOH<\/strong><\/strong><\/p>\n Fig. 13: 0.001 M diprotic acid (pKa1 = -3, pKa2 = 2, 7 or 12)\u00a0vs 0.001 M NaOH<\/strong><\/strong><\/p>\n Features:<\/p>\n As we have seen through the examples above, the pH and thus the shape of a titration curve, is a function of:<\/p>\n For polyprotic acids, the relative strength of each acid dissociation as well as the strength of these in comparison to the base strength further complicates matters.<\/p>\n Putting all of this together, the titration of X M phosphoric acid (pKas 2.15, 7.20 and 12.35) with X M sodium hydroxide (for pX between -1 and 5) shows only two equivalence points, neither of which is particularly sharp even at high concentrations:<\/p>\n Fig. 14: X M phosphoric acid vs X M NaOH\u00a0(pX = -1 – 5)<\/strong><\/strong><\/p>\n As a final example, consider the titration of X M\u00a0citric acid<\/a>\u00a0(a triprotic acid with pKas of 3.14, 4.75 and 5.41) with 3X M sodium hydroxide, for pX between 0 and 5. You can do this titration at home,\u00a0as I outlined in a previous post<\/a>. Given the proximity of its three pKa values (and their relative strength), it should not be surprising that only one equivalence point is detectable for all of these concentrations.<\/p>\n Fig. 15: X M citric acid vs 3X M NaOH\u00a0(pX = 0 – 5)<\/strong><\/strong><\/p>\n I hope you have found these examples useful; any comments are greatly appreciated!<\/p>\n Introduction After a recent discussion with a colleague I decided to investigate and write a post about the factors that influence the shape of titration curves. Acid-base titration curves (graphs of solution pH against volume of titrant added) will be … Continue reading ![\"monoprotic](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/monoprotic-strong-acid-strong-base-BTB-600x373.jpg\")
<\/a><\/p>\n\n
![\"monoprotic](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/monoprotic-weak-acid-strong-base-PT-600x373.jpg\")
<\/a><\/p>\n\n
![\"monoprotic](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/monoprotic-strong-acid-weak-base-MR-600x373.jpg\")
<\/a><\/p>\n\n
![\"monoprotic](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/monoprotic-weak-acid-weak-base-BTB-600x373.jpg\")
<\/a><\/p>\n\n
![\"pKa](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/pKa-monoprotic-acid-600x372.jpg\")
<\/a><\/p>\n\n
![\"pKa](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/pKa-monobasic-base-600x372.jpg\")
<\/a><\/p>\n\n
Acid strength effects: diprotic acids<\/strong><\/h2>\n
\n
![\"pKa](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/pKa-diprotic-acid-pKa1_-3_pKa2-7-or-12-0.1-M-600x372.jpg\")
<\/a><\/p>\n\n
![\"pKa](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/pKa-diprotic-acid-pKa1_-3_pKa22-12-600x372.jpg\")
<\/a><\/p>\n\n
![\"pKa](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/pKa-diprotic-acid-pKa14_pKa25-12-600x372.jpg\")
<\/a><\/p>\nConcentration effects: monoprotic acids<\/strong><\/strong><\/h2>\n
![\"concentration](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/concentration-monoprotic-strong-acid-600x373.jpg\")
<\/a><\/p>\n\n
![\"concentration](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/06\/concentration-monoprotic-weak-acid-600x373.jpg\")
<\/a><\/p>\nConcentration effects: diprotic acids<\/strong><\/h2>\n
![\"concentration](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/concentration-diprotic-acid-pKa1_-3_pKa22-600x372.jpg\")
<\/a><\/p>\n\n
<\/a><\/p>\n![\"pKa](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/05\/pKa-diprotic-acid-pKa1_-3_pKa2-7-or-12-000.1-M-600x372.jpg\")
<\/a><\/p>\n\n
Summary<\/h2>\n
\n
![\"concentration](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/06\/concentration-phosphoric-acid-600x373.jpg\")
<\/a><\/p>\n![\"concentration](\"http:\/\/www.trentwallis.com\/chemblog\/wp-content\/uploads\/2013\/06\/concentration-citric-acid-600x373.jpg\")
<\/a><\/p>\n![\"Creative](\"http:\/\/i.creativecommons.org\/l\/by-nc-sa\/3.0\/au\/88x31.png\")
<\/a>
\nThis work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Australia License<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"