Figure 2: Changes in buffer (McMurry &Fay 2003).
Figure 3: Graphical representation of changes in buffer (Wiley 2010).
The pH of solution of buffer containing acetic acid and sodium acetate is calculated as by first identifying the acid-base properties of the various species in solution, and then consider the possible proton transfer reaction these species can undergo.
Since acetic acid is largely undissociated in aqueous solution and since the salt sodium acetate is essentially 100% dissociated, the species present initially are
Figure 4: Species when dissociated (McMurry & Fay 2003).
Because we have two acids and two bases, there are four possible proton-transfer reactions. We know, however, that acetic acid is a stronger acid than water and that the principal reaction therefore involves proton transfer from CH₃CO₂H to either CH₃CO₂⁻ or H₂O:
Figure 5: Proton-transfer reactions (Mcmurry & Fay 2003)
Although the first of these reactions has the larger equilibrium constant, we cannot consider it to be the principal reaction because the reactants and products are identical. Proton transfer from acetic acid to its conjugate base is constantly occurring but the reaction doesn’t change any concentrations. Consequently, the principal reaction is dissociation of acetic acid (McMurry & Fay 2003).
The table of concentration for the species involved in the principal reaction can be set up. We define x as the concentration of acid that dissociates-here, acetic acid-but we need to remember that acetate ions come from two sources: 0.25 mol/L of acetate for buffer A and 0.125 mol/L for buffer B comes from sodium acetate present initially, and x mol/L comes from dissociation of acetic acid.
To we solve the equilibrium equation for [H₃O⁺], we obtain:
Thus, the H₃O⁺ concentration has a value close to value of Ka for the weak acid but differs by a factor equal to the concentration ratio [weak acid] / [conjugate base].
Note that in calculating this result I have set the equilibrium concentrations equal to initial concentration because x is negligible compared with initial concentrations. For commonly used buffer solutions, Ka is small and the initial concentration is relatively large. As a result, x is generally negligible compared with the initial concentrations, and we can use initial concentration in calculation.
Now suppose 0.20M of HCl is added to the buffers (A and B). The added strong acid will convert the acetate ions to acetic acid because of the neutralization reaction
Figure 6: Neutralization reaction (Wiley 2003).
Thus we can obtain equations of pH of buffer A and B through Henderson–Hasselbalch equation (Fig 7) as shown in table in page 5. The equations obtained will be useful for us to compare with the graph we have plotted from the data acquired through the experiment.
Figure 7: Henderson–Hasselbalch equation (Wiley 2003).
2.2 Water a poor buffer
One of the most important properties of water is its ability to act both as an acid and as a base. In the presence of an acid, water acts as a base, whereas in the presence of a base, water acts as an acid. It is not surprising, therefore, that in pure water one molecule can donate a proton to another in a reaction in which water acts as both acid and base at the same time.
Called the dissociation of water, this reaction is characterized by the equilibrium equation Kw=[H₃O⁺][OH⁻].
2H₂O ⇔ H₃O⁺(aq) + OH⁻(aq)
The equilibrium constant Kw is called the ion-product constant for water.
There are two important aspects of the dynamic equilibrium in the dissociation of water. First, the forward and reverse reactions are rapid; H₂O molecules, H₃O⁺ ions, and OH⁻ ions continually interconvert as protons transfer quickly from one species to another. Second, the position of the equilibrium lies far to the left; at any given instant, only a tiny fraction of the water molecules are dissociated into H₃O⁺ and OH⁻ ions. The vast majority of the molecules are undissociated.
We can calculate the extent of dissociation of the water molecules starting from the fact that the concentration of H₃O⁺ in pure water to be 1.0 X 10 ⁻⁷M at 25 ⁰C:
[H₃O⁺]=1.0 X 10 ⁻⁷M at 25 ⁰C
Since the dissociation reaction of water produces equal concentration of H₃O⁺ and OH⁻ ions, the OH⁻ concentration in pure water is also 1.0 X 10 ⁻⁷M at 25 ⁰C:
Furthermore, we know that the molar concentration of pure water, calculated from its density and molar mass, 55.4M at 25⁰C.
From these facts, we can conclude that the ratio of dissociated to undissociated water molecules is about 2 in 10 ⁹, a very small number. Hence it will definitely not be a good buffer since the amount of hydronium or hydroxide ion that will be able to neutralize and resist the counter ions from the added acid or base is almost insignificant. Therefore, we would expect drastic changes in its pH when HCl is being added in the experiment.
2.3 Instrument- Glass electrodes pH meter
Figure 8: Combined pH glass electrode (Laboratory Talk 2009).
The most common type of pH electrodes are the "glass" electrodes. They consist of a special glass membrane that is sensitive to variations in pH, as pH variation also changes the electrical potential across the glass. In order to be able to measure this potential, a second electrode, the
"reference" electrode, is required. Both electrodes can be present in a "combined" pH electrode (fig 8) which we have used during the experiment, or two physically-separate electrodes.
The glass electrode consists of a glass shaft on which a bulb of a special glass is mounted. The inner is usually filled with 3 Mol/Litre aqueous KCl and sealed. Electrical contact is provided by a silver wire immersed in the KCl.
For "combined" electrodes, the glass electrode as shown in figure 9 is surrounded by a concentric reference electrode. The reference electrode consists of a silver wire in contact with the almost-insoluble AgCl. The electrical contact with the meter is through the silver wire. Contact with the solution being measured is via a KCl filling solution. To minimize mixing of the solution to be measured and the filling solution, a porous seal, the diaphragm, is used. This is usually a small glass sinter; however other methods which allow a slow mixing contact can also be used, especially for samples with low ionic strength. Besides the "normal" KCl solutions, often solutions with an increased viscosity and hence lower mixing rate are used. A gel filling can also be used, which eliminates the necessity for slow mixing devices.
Figure 9: Labeled diagram of glass electrode
In contact with different pH solutions a typical glass electrode gives, when compared to the reference electrode, a voltage of about 0 mV at pH 7, increasing by 59 mV per pH unit above 7, or decreasing by 59 mV per pH unit below 7. Both the slopes, and the intercept of the curve between pH and generated potential, are temperature dependent. The potential of the
electrode is approximated by the Nernst equation :
E = E0 - RT log [H+] = E0 + RT pH
Where E is the generated potential, E0 is a constant, R is universal gas constant and T is the temperature in degrees Kelvin.
All pH-sensitive glasses are also susceptible to other ions, such as Na or K. This requires a correction in the above equation, so the relationship between pH and generated voltage becomes nonlinear at high pH values. The slope tends to diminish both as the electrode ages, and at high pH. As the electrode has very high impedance, typically 250 Megohms to 1 Gigohm, it is necessary to use a very high impedance measuring instrument.
The reference electrode has a fairly constant potential, but it is temperature dependent, and also varies with activity of the silver ions in the reference electrode. This occurs if a contaminant enters the reference electrode.
Calibration:
From the preceding, it is obvious that frequent calibration and adjustment of pH meters are necessary. To check the pH meter, at least two standard buffer solutions are used to cover the range of interest. The pH meter should be on for at least 30 minutes prior to calibration to ensure that all components are at thermal equilibrium, and calibration solutions should be immersed for at least a minute to ensure equilibrium.
First use the buffer at pH 7, and adjust the zero (or the intercept). Then, after thorough rinsing with water, use the other buffer to adjust the slope. This cycle in repeated at least once, or until no further adjustments are necessary. Many modern pH meters have an automatic calibration feature, which requires each buffer only once.
3. Procedure
Buffer A and B
Foremost, 100.0mL of buffer A (0.025M CH₃COOH and 0.025M CH₃COONa) was measured and poured into a 250mL beaker. Next, the pH was measured with the pH meter and recorded on the datasheet. Subsequently, 0.20M HCl solution was added in drop-wise manner from the burette and stirred constantly until the pH changes by 0.40pH units. Immediately, the pH and the volume of HCl added were recorded. Followed by that, HCl solution has been added drop-wise and stopped when pH has changed a total of 0.80, 1.20, 1.60, and 2.00 pH units. The total volume of HCl solution added and pH at each point were then recorded on datasheet. The steps as mentioned above have been repeated with 100.0mL of Buffer B (0.0125M CH₃COOH and 0.0125M CH₃COONA).
Deionised water
Afterwards, 100.0mL of deionised water was measured into 250mL beaker, and the pH has been measured with a pH meter and recorded. Later on, 0.10mL 0.20M HCl was added from a burette and stirred constantly, subsequently its pH and total volume were then recorded after each increment until the pH changes by 2 units.
4. Results and Calculation
Graph (pH against volume in mL):
White Line – Buffer A
Green Line - Buffer B
Graph (pH against volume in mL):
Blue Line- Deionised water
5. Discussion
Let us discuss about the trends observed. Both graphs for buffer A and B has a relatively flat gradient initially and as we add more hydrochloric acid to the buffers, the gradient being to be steeper and steeper and eventually the gradient become nearly vertical(exhaustion of conjugate acid or base). Moreover, we notice that greater volume (almost twice) of hydrochloric acid has to be added to Buffer A to achieve the similar gradient (steepness) and pH as Buffer B. We have to understand that steeper the gradient implies that the greater the change in pH and weaker its buffer capacity. Therefore, we may conclude that the higher the concentration of the buffer will enable a stronger buffering capacity.
This observation coincides with the theoretical results plotted in figure 10. This phenomenon occurs as Buffer A has higher concentration for both acetic acid and sodium acetate and as a given amount of hydrochloric acid is added to both buffer A and B, the similar amount (moles) of acetate anion (CH₃COO⁻) will react with hydrochloric acid and similar amount of acetic acid formed. Since the initial concentration of buffer A is higher, the amount of acetate anion reacted and of acetic acid formed will cause a smaller change in the concentration in both acetate anion and acetic acid (CH₃COOH) as compared to buffer B.
Given by Henderson–Hasselbalch equation (fig 7) that the initial pH decreases proportionately to the ratio of acetic acid over acetate anion: [CH₃COOH]/[CH₃COO⁻]. Since, the change in concentration in both acetate anion and acetic acid for Buffer A is smaller than Buffer B; the ratio will also be smaller than that of Buffer B. Eventually, this explains that Buffer A (higher concentration) has smaller change in pH as compared to buffer B(lower concentration) at any given amount of hydrochloric acid added.
Now let us consider the buffering capacity of deionised water. As mentioned in section 2.2, water has very low dissociation of hydronium and hydroxide ions (approximately 2 in 10⁹). Which implies that it has very little amount of hydronium and hydroxide ions will be able to neutralize the added acid or base. From the second graph in results and calculation section we notice that the pH of deionised water indeed decreases drastically (3 pH units) with the addition of only 0.5mL of hydrochloric acid. Therefore, we can conclusively state that deionised water has almost no buffer capacity.
We shall compare the results we have obtained from the experiment with the theoretical values that has been derived in section 2.1 (plotting the equations we have derived with Henderson–Hasselbalch equation shown below).
Equations:
Graphical Comparison (pH against volume in mL):
Figure 10: Comparison between theoretical with experimental results
Yellow line – Theoretical for Buffer B
Green line – Theoretical for Buffer B
White Line – Experimental for Buffer A
Green Line – Experimental for Buffer B
We notice that for both the experimental results we have obtained fluctuate from the theoretical results in the same sense (non-symmetrical). We may then conclude that these deviations arise from systematic errors (Instrumental errors and even human errors). The possible errors will be further discussed in section 5.1 and 5.2.
5.1 Instrumental Errors
People assume pH measurements are accurate, however many potential errors exist. There can be errors caused by the pH-sensitive glass, reference electrode, electrical components, as well as externally generated errors.
Glass Electrode Errors:
The pH-sensitive glass can be damaged. Major cracks are obvious, but minor damage can be difficult to detect. If the internal liquid of the pH-measuring electrode and the external environment are connected, a pH value close to 7 will be obtained. It will not change when the electrode is immersed in a known solution of different pH. The electrical resistance of the glass membrane will also be low, often below 1 megohm, and it must be replaced.
The glass can be dirty. A deposit on the glass will slow the response time, make the response sensitive to agitation and ionic strength, and also give the pH of the film, not the sample solution. If the deposit is known, use an appropriate solvent to remove it, and rehydrate the electrode in 3M KCl. If the deposit is not known, first immerse the electrode for a few minutes in a strongly alkaline solution, rinse thoroughly, and immerse it in a strong acid (HCl) solution for several minutes.
Reference Electrode Errors:
The diaphragm of the reference can become blocked. This is seen as unstable or wrong pH measurements. If the electrical resistivity of the diaphragm is measured, high values are reported (Most multimeters will give an over-range error). The most common reason is that AgS formed a precipitate in the diaphragm. The diaphragm will be black in this case. The electrode should be immersed in a solution of acidic thiourea until the diaphragm is white, and then replace the internal filling liquid of the reference electrode.
Errors due to fluctuation of temperature:
In a perfect pH electrode – one that is zeroed exactly pH 7 – there is no temperature effect on the electrode sensitivity at pH 7 no matter how much the temperature changes. Most pH electrodes are not perfect, but the errors from changes in temperature are still very minute when near pH 7, plus or minus one-tenths of a pH, and can be disregarded. However, the further from pH 7 the solution and the greater the temperature changes, the greater the measurement error due to changes in electrode sensitivity. To compensate for this error, the changes in electrode sensitivity due to changes in temperature can be calculated using the formula given below:
For a conventional glass electrode, the impact on temperature compensation is 0.003 pH /°C away from pH 7. For example, if the electrode is calibrated at room temperature (25 °C) and is measuring a sample around pH 4 at around 5 °C.
Temperature difference: 25°C - 5°C = 20 °C
pH away from neutral: 7pH - 4pH = 3 pH
Total error: 0.003 x 20 x 3 = 0.18 pH
This error value of 0.18 pH should be taken into consideration to derive the actual pH reading of the sample.
Selection of burette:
As with other graduated glassware, burettes are produced to both Class A and Class B specification in accordance with the appropriate standard [BS 846 (1985; ISO 385 (1984)], and Class A burettes may be purchased with BST Certificates. All Class A and some Class B burettes have graduation marks which completely encircle the burette; this is a very important feature for the avoidance of parallax errors in reading the burette. Typical values for the tolerances permitted for Class A burettes are:
For Class B, these values are approximately doubled. In addition to the volume requirements, limits are also imposed on the length of the graduated part of the burette and on the drainage time. Therefore, we should always choose a Class A burette instead of Class B burette.
Furthermore, burette must be firmly supported on a stand and various types of burette holder are available for this purpose. The use of an ordinary laboratory clamp is not recommended: the ideal type of holder permits the burette to be read without the need of removing it from the stand.
5.2 Human error
Not reading at meniscus level:
All types of volumetric glassware have a cylindrical shape in the measuring region which causes the surface of most liquids whose volumes are to be measured to be curve downwards. Take reading from the bottom of the curved surface called meniscus with your eyes at the same level.
To read the position of the meniscus, the eye must be at the same level as the meniscus, in order to avoid errors due to parallax. In the best type of burette, the graduations are carried completely round the tube for each milliliter and half way around for the other graduation marks: parallax is thus easily avoided. To aid the eye in reading the position of the meniscus a piece of white paper or cardboard, the lower half of which is blackened either by painting with dull black paint or by pasting a piece of dull black paper upon it, is employed. When this is place so that the sharp diving line is 1-2mm below the meniscus, the bottom of the meniscus appears to be darkened and is sharply outlined against the white background: the level of liquid can then be accurately read.
6. Conclusion
In conclusion, we notice that buffer with higher concentration of both the weak conjugate base and acid has greater buffer capacity as greater volume of acid is needed to swift the pH by the same units and getting a stepper gradient(greater change in pH) for curve. Moreover, deionised water has displayed almost negligible buffer capacity as it is poorly dissociated into hydronium and hydroxide ions and needed a tiny amount of HCl to change its pH drastically.
8. References
Internet:
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Stanson, 2008. How do pH electrodes work [online]. Available from: [Accessed 20 December 2010].
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University of Leeds, 1980. Common source of error in pH measurements [online]. Available from: [Accessed 20 December 2010].
Books:
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McMurry Fay, 1998. Chemistry. 4 ed. USA: Prentice Hall.
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G.H. Jeffery and J. Bassett, 1989. Vogel’s Textbook of Quantitative Chemical Analysis. 5 ed. UK: Longman Scientific & Technical.
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