Investigation on the relationship between the buffering capacity and temperature of the bicarbonate-carbonate buffer system

During the titrations, there were no colour changes seen before and after the addition of the solutions (both the titrants and the buffer solution remain colourless). Even if the solutions are hot during several trials, the pH sensor and the thermometer are still cold to the touch. With the addition of acid or base during the titration procedure, the pH changed, indicating the buffer system had been neutralized.

How does temperature impact the carbonate-bicarbonate buffer system's ability to buffer?

Based on information highlighted in the background information section, as well as the undesirable nature of increasing temperature in biological processes, such as the body reacting negatively to temperatures above 38^oC, I would be inclined to hypothesize that an increase in temperature would cause the buffering capacity of the buffer system to decrease.

Volume of buffer solution used for every trial = (30.00 ± 0.01) cm³

 \(Percentage \,uncertainty=\frac{∆volume\ of\ buffer}{volume\ of\ buffer}×100=\frac{0.01}{30.00}×100=0.03\%\)

Volume of buffer solution used for every trial = (30.00 ± 0.03%) cm³

Sample calculations for trial 1, 20^oC

The volume of HCl added (cm³)

= Final reading of burette – Initial reading of burette

= 11.4 - 0.0

= 11.4 cm³

The uncertainty for the volume of HCl added (same as NaOH)

= Uncertainty of final reading of burette + Uncertainty of initial reading of burette

= 0.05 + 0.05

= ± 0.10 cm³

We first determine the average volume of titrant added across the three trials. Then we convert the volume to the average amount of titrant added to get the buffer capacity at a specific temperature. (in mol).

The average volume of HCl added to the buffer for 20 ^oC

\(=\frac {vol \ of \ HCL\ in\ trial \ 1\ +\ vol\ of\ HCL\ in\ trial\ 2\ + \ vol\ of\ HCL\ in\ trial\ 3}{number\ of \ trials}\)

\(=\frac{(11.40\ ±\ 0.10)+\ (12.70\ ±\ 0.10)\ +\ (11 .60\ ± \ 0.10)}3\)

\(=11.9±0.1cm^3\)

The average amount of HCl added to the buffer for 20 ^oC

= Average volume of HCl added to buffer 20 ^oC concentration of HCl used

\(=\frac{11.9\ ± \ 0.10}{1000}×0.1\)

\(=(0.00119±0.00010)mol\)

\(=(0.00119±8\%)mol\)

Since the pH change of the buffer is 1, the buffer capacity expression can be rewritten as

\(\frac{Average\ amount\ of\ titrant\ added\ to\ buffer\ solution)}{𝑣𝑜𝑙𝑢𝑚𝑒\ 𝑜𝑓\ 𝑏𝑢𝑓𝑓𝑒𝑟\ 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛\ 𝑢𝑠𝑒𝑑}=(0.00119\ ± 8\%) \div\left(\frac{30.00}{1000}\pm\ 0.030\%\right)\) 

                                                                \(=(0.0397±8\%)\ mol\ dm^{-3}\)

                                                                \(=(0.0397±0.003)\ mol \ dm^{-3}\)

At first, I wanted to simulate the bicarbonate buffer system that the body uses to regulate the pH of the bloodstream. However, I discovered that carbonic acid, the weak acid that is required, is only present when it is in equilibrium with carbon dioxide and water and cannot be obtained chemically alone, making it impractical to study this buffer system because it was challenging to control. Instead of a weak acid and a salt carrying its conjugate base, I made the decision to instead investigate the carbonate-bicarbonate buffer system, which could be formed with two salts, one having the weak base and the other the weak acid. I'll be utilizing sodium carbonate and sodium bicarbonate as my two salts.

Ignoring the sodium, Na⁺ spectator cation, the following reversible reaction takes place at equilibrium when sodium carbonate is supplied (Purdue, n.d.):

CO₃^2-_(aq) + H₂O_(I) ⇌ HCO₃^- _(aq) + OH^- _(aq)

According to equation 1, the strong base fully dissociates in water during addition, resulting in the formation of OH- ions, which raises the concentration of OH- ions and consequently the concentration of products. According to Le Chatelier's principle, the equilibrium position will move to the left to offset the change in concentration, preserving the equilibrium constant and favouring reactants over products. As a result, the surplus OH- ions are transformed back into the reactants (on the left side of the equation), which initially raises pH when a strong base is added.

The following equation comes into equilibrium when sodium bicarbonate is supplied, again neglecting the sodium, Na⁺ spectator cation (Purdue, n.d.):

H₂O_(I) + HCO₃^- _(aq) ⇌ H₃O⁺_(aq) + CO₃^2-_(aq)

The protonation of water results in the formation of the hydronium (H3O⁺) ion. When a weak acid releases H⁺ ions into the water, which behave as protons and have a high charge density, they strongly attract the oxygen atom's lone pair of electrons, forming a coordinate bond with the hydrogen ion. 2017's Chemistry Libretexts

The position of equilibrium shifts to the left, favouring reactants over products when the strong acid is introduced as a titrant because it completely dissociates in water to generate hydronium and chloride ions. This causes the concentration of hydronium ions to rise. Le Chatelier's principle states that excess hydronium ions must be returned to the reactants in order to maintain the equilibrium constant and pH level since pH = -log [H3O⁺].

When their ionic salt complexes are dissolved in water, the weak acid and base, which are ions of bicarbonate (HCO₃^-) and carbonate (CO₃^2-), respectively, can be formed. According to Arrhenius' description of weak acids and bases, these ions do not entirely ionize or dissociate in an aqueous solution to give hydroxide (OH-) or hydronium ions (H3O⁺). Still, they are reversible equations where the reactants and products are in dynamic equilibrium. Common bicarbonate and carbonate salts, specifically sodium bicarbonate and sodium carbonate, were chosen to keep costs as low as feasible. When the aforementioned solid salt compounds are ionized in distilled water, the sodium ion functions as a spectator ion and has no impact on the buffer's equilibrium, hence it is disregarded in equations 1 and 2.

Because it is convenient and practical, a buffer solution that contains both HCO₃^- and CO₃^2- ions at concentrations of 0.1 mol dm^-3 is employed as a stock solution that contains both salts at equal concentrations of 1 dm³. This indicates that 0.5 dm³ of 0.1 mol dm^-3 of each salt solution will be present in the stock solution. This was done since there have been numerous trials conducted.

• The experimenter must exercise caution to ensure no spillage, such as not coming into contact with the hot solutions in the beakers, as this could result in the experimenter being burnt or scalded. The experimenter can wear heat-resistant gloves as a precautionary measure during the experiment. Any spillage of water/ solutions can come into contact with the wires of the heating plate since it uses electricity for heating, and could lead to a short circuit, electrocuting the experimenter.
• The experiment should handle the strong acid and base carefully, especially at higher temperatures, because even though solutions are fairly diluted (0.1 mol dm-3), prolonged exposure to the skin can cause irritation. Severe eye damage might occur, especially if it enters the eyes, therefore goggles and lab coats are to be worn during the experiment.
• The chemicals should be disposed of properly in the sink after the experiment.

• Independent variable
• Temperature of the bicarbonate-carbonate buffer (^oC)

This is varied by heating the buffer solution in a beaker to the different temperatures using a heating plate, except 20 ^oC, which was cooled using an ice bath. Also, to ensure minimal heat transfer to ensure accuracy for this variable between thetitrant and the buffer, the titrant is also heated up or cooled such that both the titrant and the buffer are at the equal, desired temperature before the neutralization process.

• Range 20 ^oC to 60 ^oC (divisions of 10 ^oC)

• Dependent variable
• Buffering capacity (mol)

In the expression for buffer capacity, the number of moles of H₃O⁺/ OH^- added is measured using a burette during titration, and the pH change is measured using a pH sensor.

• Controlled variables
• Concentration of HCl and NaOH solutions (0.1 mol dm^-3)

Reason: Varying concentrations of the HCl and NaOH solutions would mean there are different concentrations of [H⁺] and [OH^-] ions respectively in the same volume of solution used, which affects titration results when comparing across different temperatures.

• Concentration of NaHCO₃ and Na2CO₃ solutions (0.1 mol dm^-3)

Reason Any variations in the concentrations would shift the equilibrium of the buffer system based on Le Chatelier's principle hence a constant concentration must be maintained.

• Temperature of surroundings

The surrounding temperature is kept constant by conducting the experiment in the same environment and ensuring that the experiment takes place at a similar temperature and pressure.

Concentration changes do not alter the value of K_a, instead, the reaction's equilibrium position adjusts to preserve the K_a equilibrium constant. Since the weak acid's equilibrium constant, K_a, is temperature-dependent, a temperature rise will cause the buffer system's equilibrium to change in favour of an endothermic reaction, which eliminates heat, and vice versa. However, I could not locate the forward/backward reaction enthalpies in the literature for the buffer system, thus, I cannot determine if the reaction is endothermic or exothermic, which influences the reaction's equilibrium position. The buffer's pH will be impacted by this departure from the initial equilibrium brought on by the altered value of K_a because the concentrations of reactants and products will vary.

The formula mass of Na2CO₃ = 105.99 g mol^-1

The formula mass of NaHCO₃ = 84.00 g mol^-1

For a concentration of 0.1 mol dm^-3,

Mass of Na₂CO₃ to be added in stock solution = (10.599 ± 0.001) g

Mass of NaHCO₃ to be added in stock solution = (8.400 ± 0.001) g

[mass values are in 3 d.p. due to the electronic scale’s precis]

When modest amounts of acid or alkali are added, buffers, and aqueous acid-base systems, effectively resist pH fluctuations, allowing the pH to stay comparatively steady. Weak acid and salt that includes its conjugate base are typically used to create buffers. It may neutralize modest amounts of acid or alkali without significantly altering its pH because a buffer solution is made up of a conjugate acid-base pair that is at equilibrium and differs by one proton (H⁺), which is present in substantial numbers (Chemistry Libretexts, 2017)

• Sodium bicarbonate (0.1 mol dm^-3)
• Sodium carbonate (0.1 mol dm^-3)
• Hydrochloric acid (0.1 mol dm^-3)
• Sodium hydroxide (0.1 mol dm^-3)
• Electronic scale (precision of 0.001g; therefore uncertainty = ± 0.001 g)
• 10 cm³ volumetric pipette (±0.01 cm³)
• Heating plate
• Thermometer (± 0.5 ^oC)
• pH probe (precision of 0.01; therefore ± 0.01 g)
• 50 cm³ Burette (± 0.05 cm³)
• 50 cm³ beakers
• Glass rod
• Filter funnel

Due to the high sensitivity of the three-dimensional structures of many extracellular proteins to extracellular pH, which necessitates strict pH maintenance within very narrow limits, I have always been interested in the system underlying the homeostatic regulation of the pH of the fluids in the body. Blood includes substantial levels of carbonic acid and bicarbonate, creating a buffer system. The bicarbonate and the carbonic acid neutralize excess acids and bases, respectively, for pH maintenance. This is one crucial system. As a result, this has aroused my interest and motivated me to learn more about capacity buffer systems so that the pH stays within a specific, acceptable range.

The dependent variable I would focus on is buffer capacity, which is the quantity (mol) of strong acid or strong base added to 1m³ of a buffer to produce a pH change of 1 unit. Since the goal of this investigation is to determine how temperature would affect the buffer system, this is the dependent variable I will be focusing on. Mathematically, it can be expressed as the following equation:

 \(Buffer\ capacity=\frac{(amount\ of\ H_3O^+\ or\ {\rm OH}^-added)}{(volume\ of\ buffer\ solution)(pH\ change)}\)

Based on the average number of moles of HCl or NaOH added throughout the three trials, which is the result of the average volume of HCl or NaOH added and the concentration of the titrants, the amount of H₃O⁺ or OH- ions is estimated (0.1 mol dm^-3). The amount of acid or alkali used during the titration will consequently impact the dependent variable (buffer capacity).

Due to practicality and convenience, a buffer solution containing both HCO₃- and CO₃^2- ions at 0.1 mol dm^-3 as a stock solution containing both salts of equal concentrations of 1 dm³ is used. This indicates that 0.5 dm³ of 0.1 mol dm^-3 of each salt solution will be present in the stock solution. This was accomplished because numerous tests utilizing the buffer solution were conducted.

To ensure that the ions were distributed evenly throughout the beaker for each titration experiment, 30.0 cm³ of the buffer solution was first transferred from the 1 dm³ volumetric flask using a 10.00 cm³ volumetric pipette into a 50 cm³ beaker and swirled. Due to their easy access in the lab, sodium hydroxide and hydrochloric acid were also put into separate 50 cm³ beakers and heated or cooled alongside the buffer solution. A thermometer inserted into each beaker while they are on the heating plate is used to closely monitor the temperatures of the buffer solution and the acid/alkali. To prevent heat loss to the environment, the titrant was swiftly put into the burette for titration only when the beakers containing the acid/alkali and the buffer solution were at the exact required temperature as the independent variable. The pH sensor was then put into the beaker containing the buffer solution after being linked to the Labquest mini, which feeds pH data into the logger pro programme on a laptop.

The pH of the buffer system will theoretically be where [HA] and [A^-] indicate the concentration of the weak acid (bicarbonate) and the conjugate base (carbonate), respectively. This is according to the Henderson-Hasselbalch equation (the University of Arizona, n.d.):

\(pH=pK_A+log_{10}\frac{\left[A^-\right]}{\left[HA\right]}\Rightarrow pK_A=10.33\)

The pH of the buffer becomes equal to the pK A of the acid, the bicarbonate ion, as log₁₀ 1=0 because the concentrations of the bicarbonate and carbonate ions are equal. The pH of the buffer will begin at roughly 10.33 because the bicarbonate ion's pKa is 10.33 (Silberberg, 2009). As a result, the pH sensor reading of the buffer before the injection of the acid or alkali should start at roughly 10.33.

The pH sensor can then be calibrated in the logger pro software using a two-point calibration with a pH 7 buffer and then a primary buffer once the initial starting pH of the buffer has been determined (pH 10 is used, for precision purposes, since the bicarbonate-carbonate buffer investigated is a primary buffer). The reading seen in Logger Pro is stabilized before calibration when the pH sensor is initially submerged in the pH 7 buffer, then the pH 10 buffer. After that, the calibration is verified for accuracy by dipping the calibrated pH sensor into the pH 7 buffer solution and making sure the reading that appears on the screen is correct (pH 7).

The buffer solution beaker is then put on a heating plate with a target temperature selected, as seen in Figures 1 and 2 The thermometer and the burette are held using clamps attached to a retort stand set up in addition to the heating plate.

The pH probe was linked to LabQuest Mini, and the logger pro program shows the discovered pH values. The titrants are added to the buffer solution while the beaker is continuously spun to ensure that the ions are distributed equally throughout the solution. The process is finished when the pH drops by one unit from the original pH recorded. The amount of acid or alkali injected and subsequently the buffer capacity was determined by reading the burette's final reading and comparing it to the burette's initial reading.