민재 ia (2시간 30분 컷)

Research Question

How does temperature – 25, 35, 45, 55, 65 (°C) – affect the solubility of ARM N HAMMER™ (Baking Soda - Sodium Bicarbonate) and the Gibbs free energy for the solubility in the reaction of ARM & HAMMER™ (Baking Soda - Sodium Bicarbonate) and Hydrochloric acid determined by measuring the volume of Hydrochloric acid?

Hypothesis

Based on the literature and prior research findings (Another relevant study by Apelblat and Korin (1998), A study by Linke (1958) on the solubility of salts in water), the hypothesis for this experiment is as follows:

"As the temperature increases from 25°C to 65°C, the solubility of ARM & HAMMER™ Baking Soda (Sodium Bicarbonate) will increase, resulting in higher concentrations of dissolved ions in solution. Consequently, the solubility product constant (Ksp) will increase with temperature. Additionally, the Gibbs free energy for the reaction between sodium bicarbonate and hydrochloric acid, determined by measuring the volume of HCl required, will become more negative as temperature rises, indicating that the reaction becomes more thermodynamically favorable at higher temperatures."

Introduction

My interest in the topic started from the idea that baking soda, which has endless applications in cooking and cleaning dishes at home and also a variety of experiments in the science lab. This natural curiosity led me to dive into its chemical properties. By performing an experiment that examines how temperature influences whether sodium bicarbonate will dissolve in water and its Gibbs free energy when it reacts with hydrochloric acid, I am able to relate my everyday observable data to a more intricate investigation of thermodynamics and reaction spontaneity. By doing this investigation, I hope to bridge the gap between my daily life and the complex concepts of chemistry, making the subject more relatable and exciting for myself and others.

The purpose of this exploration is to investigate the effect of increasing temperature on the solubility (concentration) of sodium bicarbonate, via titration of its bicarbonate ions that would showcase the degree of solubility, and using calculations, determine the solubility constants (Ksp). The relevance of the solubility product constant is significant; in terms of industrial and agricultural purposes, it is essential in determining mineral content of soil and understanding its consequences in affecting plant growth and yield, damage to infrastructure, water quality, and soil erosion. Therefore, this investigation is an appropriate way of modeling the underlying causes of such outcomes. The investigation also aims to use the derived dependent variable, the solubility constant, to obtain thermodynamic values (including ΔH°, ΔS°, and ΔG°) to better illustrate the relationship between temperature and solubility by applying theoretical understandings of energetics and equilibrium to the nature of this reaction. Understanding the thermodynamic nature of this reaction may be useful in making predictions regarding sodium bicarbonate's solubility at different temperatures using these pre-determined thermodynamic values, making them relevant to this investigation.

Background Information

Solubility of Sodium Bicarbonate and Its Reaction with Hydrochloric Acid

Solubility of Sodium Bicarbonate (NaHCO₃) at Various Temperatures

Sodium bicarbonate (NaHCO₃), commonly known as baking soda, is widely used in households and industries due to its versatile properties. Its applications range from acting as a leavening agent in baking to serving as an antacid to neutralize stomach acid. A key aspect of sodium bicarbonate's functionality in these applications is its solubility in water, which is temperature-dependent. Understanding how temperature affects the solubility of sodium bicarbonate is crucial for optimizing its use in various processes.

When sodium bicarbonate dissolves in water, it dissociates into sodium ions (Na⁺) and bicarbonate ions (HCO₃⁻):

NaHCO₃(s) ↔ Na⁺(aq) + HCO₃⁻(aq)

The equilibrium for this dissolution is described by the solubility product constant (Ksp), which is expressed as:

Ksp = [Na⁺][HCO₃⁻]

Given that the dissolution of one mole of sodium bicarbonate produces one mole of sodium ions and one mole of bicarbonate ions, the molar concentrations of Na⁺ and HCO₃⁻ in a saturated solution are equal. Let x represent the molar concentration of HCO₃⁻, then:

Ksp = x²

As temperature increases, the solubility of sodium bicarbonate typically increases, leading to higher concentrations of Na⁺ and HCO₃⁻ in the solution and, consequently, a higher Ksp value. This relationship is important for predicting how sodium bicarbonate behaves under different temperature conditions.

Reaction of Sodium Bicarbonate with Hydrochloric Acid (HCl)

The reaction between sodium bicarbonate (NaHCO₃) and hydrochloric acid (HCl) is a classic acid-base reaction that produces carbon dioxide gas (CO₂), water (H₂O), and sodium chloride (NaCl). This reaction is represented by the equation:

NaHCO₃(s) + HCl(aq) → NaCl(aq) + H₂O(l) + CO₂(g)

This reaction is widely studied in laboratories for various reasons, including the analysis of gas evolution, reaction kinetics, and the solubility of sodium bicarbonate under different conditions. When HCl is added to a solution containing bicarbonate ions (HCO₃⁻), it reacts to produce CO₂ gas, which can be measured to determine the extent of the reaction.

Gibbs Free Energy (ΔG) Calculation

The Gibbs free energy change (ΔG) for the dissolution reaction can be determined using the relationship between the equilibrium constant (K) and ΔG, given by:

ΔG = −RTlnK

Where:

• R is the gas constant
• T is the temperature in Kelvin
• K is the equilibrium constant

For the dissolution of sodium bicarbonate and its reaction with HCl, the equilibrium constant (K) is related to the concentration of the reactants and products at equilibrium. By measuring the concentration of ions in solution and the volume of HCl required, the equilibrium constant can be determined at various temperatures. This allows the calculation of ΔG, providing insight into the thermodynamic favorability of the reaction under different conditions.

The Effect of Temperature on HCl Volume and the Application of the Van 't Hoff Equation

The Van 't Hoff equation is a key tool in thermodynamics for understanding the relationship between the equilibrium constant (K) of a reaction and the temperature (T). This equation is particularly useful when studying the effect of temperature on the solubility and reaction kinetics of a substance, such as sodium bicarbonate.

The Van 't Hoff equation is given by:

lnK = −ΔH°/R ⋅ 1/T + ΔS°/R

Where:

• K is the equilibrium constant
• ΔH° is the standard enthalpy change of the reaction
• ΔS° is the standard entropy change of the reaction
• R is the universal gas constant
• T is the temperature in Kelvin

This equation can be used to calculate the equilibrium constant (K) at different temperatures. By plotting lnK against 1/T, the slope of the resulting line is equal to −ΔH°/R, and the intercept is ΔS°/R. This linear relationship allows us to determine the enthalpy and entropy changes associated with the reaction.

Application in the Experiment

In this experiment, by measuring the volume of HCl required at various temperatures, we can determine the equilibrium constant (K) at each temperature. Using the Van 't Hoff equation, we can then calculate the Gibbs free energy change (ΔG) for the reaction at different temperatures. This approach allows us to understand how temperature influences the thermodynamic favorability of the reaction and the extent to which sodium bicarbonate dissolves and reacts with HCl.

Variables

Category	Identification	Method of Manipulation	Error if Not Controlled
Independent Variable	Temperature (°C) Range: 25, 35, 45, 55, 65	Temperature will be controlled using a hot water bath and ice bath. A thermometer will measure temperature.	Inaccurate temperature control could lead to inconsistent solubility and Gibbs free energy calculations.
Dependent Variable	Direct Dependent Variable: Volume of HCl required for the reaction with sodium bicarbonate. Derived Dependent Variable: Concentration of dissolved sodium bicarbonate; used to determine Ksp, ΔH°, ΔS°, and ΔG°.	Measure the volume of HCl required at each temperature. The HCl volume is directly related to the amount of bicarbonate reacting.	Inaccurate measurement of HCl volume will lead to incorrect determination of Ksp and ΔG, affecting the entire analysis.
Control Variable	Composition of Sodium Bicarbonate	Ensure that only pure sodium bicarbonate is used in all trials.	Impurities could alter the reaction pathway, leading to inaccurate Ksp values and erroneous thermodynamic data.
	Volume of Sample	Consistent volume is used for each trial (e.g., 5cm³).	Variations in sample volume could require different amounts of HCl, affecting the calculated concentration and Ksp.
	Stirring Period	Stir solutions for the same amount of time to achieve saturation.	Inconsistent stirring may result in unsaturated solutions, leading to incorrect solubility and Ksp measurements.
	Time of Redissolution	Allow equal time for each sample to reach equilibrium.	Insufficient time could prevent full dissolution, leading to incomplete reactions and inaccurate data.
	Concentration of HCl	Prepare and use the same concentration of HCl for titration in all trials (e.g., 0.5 mol/dm³).	Different concentrations of HCl could lead to incorrect titration volumes, impacting the accuracy of results.
	Indicator	Add a consistent amount of indicator (e.g., 2 drops) to each flask.	Inconsistent indicator amounts could alter the pH detection, leading to errors in determining the endpoint of titration.

Risk Assessment

Material	Risk	Safety Considerations
ARM & HAMMER™ (Sodium Bicarbonate)	Mild irritant, reproductive and developmental toxicity (NIST, 2017).	Safety equipment to be worn when handling (gloves, goggles, lab-coat). Upon contact with skin or eyes, rinse thoroughly with water.
Hydrochloric Acid	Corrosive, irritant, acute toxicity (Global Safety Management Inc., 2015).	Safety equipment to be worn when handling (gloves, goggles, lab-coat). Upon skin/eye contact or swallowing, rinse thoroughly with water and seek medical attention. Do not dispose of pure acid using the drain as it is corrosive.
Water-baths	Personal injury – burns or scalds (VWR International, 2014).	Safety equipment to be worn when handling (gloves, goggles, lab-coat). Monitor water level, only fill with distilled water. Use with caution.
Glassware	Risk of breakage (Croner-i, 2020): personal injury – cuts and punctures.	Equipment for the safe transportation of glassware should be used. Use with caution. In case of injury, seek medical attention. In case of breakage, safe disposal measures should be taken (disposal via cut/chemical-proof gloves).

Environmental and Ethical Considerations

Material	Environmental/Ethical Considerations
ARM & HAMMER™ (Sodium Bicarbonate)	Sodium bicarbonate is water-soluble and at high concentrations may cause damage to vegetation by root absorption (Univar Solutions, 2014); do not dispose of the substance using drains as it may enter waterways/sewers and reach soils.
Hydrochloric Acid	Hydrochloric acid may affect acidity (pH) in water with the risk of harmful effects to aquatic organisms (Pioneer Forensics LLC, 2012); do not dispose of via drain, watercourses, or onto the ground to avoid water contamination.

Equipment

Equipment	Purpose
Burette (±0.05 cm³)	To accurately measure and dispense the volume of hydrochloric acid (HCl) during titration.
Pipette (±0.1 cm³)	To transfer specific volumes of the sodium bicarbonate solution to the titration flask.
Thermometer (±0.1°C)	To measure and monitor the temperature of the water bath and solutions.
Water Bath	To maintain the sodium bicarbonate solution at specific temperatures during the experiment.
Magnetic Stirrer	To ensure the sodium bicarbonate solution is thoroughly mixed and reaches saturation.
Graduated Cylinder (±0.1 cm³)	To measure the volume of water and solutions accurately.
Erlenmeyer Flask (125 cm³)	To contain the sodium bicarbonate solution during titration.
Beaker (250 cm³)	To prepare and hold the sodium bicarbonate solution before titration.
pH Probe	To determine the pH at the equivalence point of the titration for accuracy.
Balance (±0.01 g)	To measure the mass of sodium bicarbonate precisely.

Substances

Substance	Concentration/Purity	Purpose
ARM & HAMMER™ Sodium Bicarbonate (NaHCO₃)	≥99% purity	Main reactant used to study the effect of temperature on its solubility.
Hydrochloric Acid (HCl)	0.1 mol/dm³	Used in titration to react with sodium bicarbonate to determine its concentration.
Distilled Water	Pure	Solvent used to prepare the sodium bicarbonate solution and dilute substances.
Methyl Orange Indicator	1% solution	Used to indicate the endpoint of the titration by changing color.

Methodology

Determining the Solubility Product (Ksp) of Sodium Bicarbonate at Various Temperatures

This experiment aims to determine the solubility product constant (Ksp) of sodium bicarbonate at different temperatures and to understand how temperature influences the solubility and Gibbs free energy (ΔG) of the reaction between sodium bicarbonate and hydrochloric acid.

Part A - Preparing the Saturated Sodium Bicarbonate Solution

• Saturating the Solution:
• Add 25g of ARM & HAMMER™ (Sodium Bicarbonate) to 80cm³ of distilled water in a 250cm³ beaker.
• Place the beaker into a water bath set to 55°C and stir the solution with a magnetic stir bar.
• Continuously monitor the temperature until the solution reaches 55°C, maintaining this temperature for 30 minutes to ensure the solution is fully saturated and in equilibrium.
• After 30 minutes, remove the beaker from the heat and allow the solution to cool naturally. Begin the titration process when the solution has reached the desired temperature.

Part B - Collecting and Transferring the Sodium Bicarbonate Samples

• Transferring the Solution:
• For accuracy and reliability, the solution should be transferred from the beaker to a clean 50cm³ graduated cylinder to measure a precise volume before transferring it to the titration flask. This helps in reducing uncertainty associated with volume measurements.
• Once the solution cools to the first target temperature (25°C), carefully transfer 5cm³ of the clear solution (avoiding any precipitate) into a 125cm³ Erlenmeyer flask.
• Ensure that no solid precipitate is transferred during this process by allowing the solid to settle before sampling the liquid.
• Temperature Adjustment:
• Repeat the above steps as the solution cools to the next target temperature. The five temperatures to be tested are 25°C, 35°C, 45°C, 55°C, and 65°C. Use different water baths or allow the solution to cool naturally to each target temperature, ensuring accurate temperature control.

Part C - Titrating the Sodium Bicarbonate Samples

• Titration Setup:
• Add distilled water to the Erlenmeyer flask containing the 5cm³ of sodium bicarbonate solution until the total volume reaches 50cm³.
• Add 2 drops of methyl orange indicator to the flask. Methyl orange is selected because of its clear color change from yellow to red at the acidic endpoint, making it suitable for detecting the end of the titration.
• Titration Process:
• Set up a burette with standardized 0.1M HCl solution.
• Titrate the sodium bicarbonate solution with HCl, adding the acid slowly and swirling the flask continuously. Carefully observe the solution for the color change from yellow to red, indicating the endpoint.
• Record the volume of HCl required to reach the endpoint.
• Repetition:
• Repeat the titration process for the remaining temperatures (35°C, 45°C, 55°C, and 65°C). For each temperature, ensure that the solution has been accurately cooled or heated to the desired temperature before proceeding with the titration.

Data Analysis

• Calculation of [HCO₃⁻]:
• Use the recorded volumes of HCl used in each titration to calculate the concentration of bicarbonate ions [HCO₃⁻] in each sample.
• Determination of Ksp:
• Calculate the solubility product constant (Ksp) for sodium bicarbonate at each temperature using the relationship: Ksp = [Na⁺][HCO₃⁻].
• Since [Na⁺] equals [HCO₃⁻] in a saturated solution, Ksp = [HCO₃⁻]².
• Gibbs Free Energy Calculation:
• Determine the Gibbs free energy change (ΔG) at each temperature using the equation: ΔG° = -RT ln(Ksp).
• Analyze the data to understand how temperature influences both the Ksp and ΔG values.

Processing Data

1. Calculate the Mean Titre Volume

First, we calculate the mean titre volume for each temperature by averaging the HCl volumes from the five trials.

Mean Titre Volume (cm³) = (Sum of trials) / (Number of trials)

For example, at 25°C:

Mean Titre Volume at 25°C = (13.87 + 13.87 + 13.87 + 13.87 + 13.87) / 5 = 13.87 cm³

This calculation should be repeated for all temperatures.

2. Calculate the Moles of HCl

Using the concentration (C) of HCl and the mean titre volume (V), calculate the moles of HCl used:

n(HCl) = C × V

Given that the concentration of HCl is 0.1 mol/dm³, the calculation for 25°C is:

n(HCl) = 0.1 × (13.87 / 1000) = 0.001387 mol

3. Calculate the Moles of HCO₃⁻

Since the reaction between HCl and HCO₃⁻ follows a 1:1 molar ratio, the moles of HCO₃⁻ will be equal to the moles of HCl:

n(HCO₃⁻) = n(HCl)

4. Calculate the Concentration of HCO₃⁻

Next, calculate the concentration of HCO₃⁻ in the solution using the volume of the solution in which HCO₃⁻ was dissolved. If we assume the final solution volume is 50 cm³ (0.05 dm³):

C(HCO₃⁻) = n(HCO₃⁻) / Volume of solution (dm³)

For example, at 25°C:

C(HCO₃⁻) = 0.001387 / 0.05 = 0.02774 mol/dm³

5. Calculate the Ksp

Finally, using the concentration of HCO₃⁻ calculated above, the Ksp can be determined:

Ksp = [Na⁺][HCO₃⁻]

Since [Na⁺] = [HCO₃⁻], then:

Ksp = (C(HCO₃⁻))²

For example, at 25°C:

Ksp = (0.02774)² ≈ 7.69 × 10⁻⁴

Data Tables

Titration Data

Temperature (± 1°C)	HCl Volume Trial 1 (cm³)	HCl Volume Trial 2 (cm³)	HCl Volume Trial 3 (cm³)	HCl Volume Trial 4 (cm³)	HCl Volume Trial 5 (cm³)	Average (cm³)	Absolute Uncertainty (cm³)
25	13.87	13.87	13.87	13.87	13.87	13.87	0.11
35	15.94	16.30	15.45	15.47	15.40	15.71	0.11
45	17.20	17.15	17.24	17.35	17.17	17.22	0.11
55	17.84	18.15	17.50	18.01	17.52	17.80	0.11
65	19.32	18.90	18.79	18.64	19.15	18.96	0.11

Temperature (±1.00 K)	Concentration of Bicarbonate (mol dm-3)
283.15	0.217
293.15	0.289
303.15	0.385
313.15	0.443
323.15	0.545

Ksp Calculation

Finally, Ksp can be calculated via the equation Ksp = 4x³, substituting the deduced bicarbonate concentration:

Ksp = 4(0.2165)³ = 0.0405914

The values of Ksp at each temperature are indicated in a summary table below.

Table 7: Processed data displaying calculated Ksp values and values relevant to an Arrhenius plot.

Temperature (±1.00 K)	1/T (K-1)	Ksp	lnKsp
283.15	0.003531697	0.0405914	-3.2041991
293.15	0.003411223	0.0950547	-2.3533028
303.15	0.003298697	0.2282670	-1.4772393
313.15	0.003193358	0.3465770	-1.0596503
323.15	0.003094538	0.6475140	-0.4346149

Next, plotting lnKsp over 1/T (K^-1), we obtain the Arrhenius plot.

Arrhenius Plot: Natural Log of Product Constant vs. 1/Temperature (K)

The graph below illustrates the relationship between the natural logarithm of the equilibrium constant (Ksp) and the inverse of temperature (1/T in Kelvin). This plot is used to determine the enthalpy change (ΔH°) and entropy change (ΔS°) for the dissolution reaction by analyzing the slope and intercept of the linear regression line.

Figure 2: Arrhenius plot – natural logarithms of equilibrium constants vs. inverse of temperatures (K).

Arrhenius Plot: Natural Log of Product Constant of Sodium Bicarbonate vs. 1/Temperature (K).

The Arrhenius plot illustrates the effect of temperature on Ksp and is used to calculate ΔH°, ΔS°, and ΔG°.

ΔH°, ΔS°, and ΔG° are calculated through the substitution of values shown in the regression trend-line equation in Figure 2 into the Van't Hoff equation. Values are calculated to 3 significant figures for conciseness and clarity.

Van't Hoff Equation and Calculation of ΔH° and ΔS°

The line of regression equation in Figure 2 is related to the Van't Hoff equation using the linear equation formula:

y = mx + c

lnKsp = (-ΔH°/R) * (1/T) + ΔS°/R

As parts (a) and (b) correspond to each other, they may be equated to solve for the unknown value in each case. To solve for ΔH°, the slope of the equation is used:

ΔH° = -(Slope) * R = -(-6274.3) * 8.31 J K^-1 mol^-1 = 52139.433 J K^-1 mol^-1 = +52.1 kJ mol^-1

Next, rearranging to solve for ΔS°, the intercept of the equation is used:

ΔS° = (Intercept) * R = 19.036 * 8.31 J K^-1 mol^-1 = 158.18916 J K^-1 mol^-1 = +0.158 kJ mol^-1

Calculation of ΔG°

These values are substituted into the equation to calculate ΔG° for each sample’s temperature. A sample calculation is provided below for the value of free energy change at 283.15 K:

ΔG° = ΔH° - TΔS° = 52.1 - (283.15 x 0.158) = +7.36 kJ mol^-1

ΔG° at each temperature is obtained via substitution into the same equation. These values will be used to relate ΔG° to the change in the equilibrium constant.

Gibbs Free Energy (ΔG°) with Uncertainties

Temperature (±1.00 K)	ΔG° (kJ mol-1)
283.15	7.36 (±0.14)
293.15	5.78 (±0.11)
303.15	4.20 (±0.08)
313.15	2.62 (±0.05)
323.15	1.04 (±0.02)

Analysis

The experimental data clearly demonstrates that temperature has a significant impact on the solubility of sodium bicarbonate and, consequently, on the thermodynamic parameters associated with the reaction. The Arrhenius plot, derived from the natural logarithm of the equilibrium constant (lnKsp) against the inverse of temperature (1/T), provided a straight line with a high correlation coefficient (R² = 0.9901). This strong linear relationship supports the assumption that the dissolution of sodium bicarbonate is governed by temperature-dependent thermodynamic principles.

The slope of the Arrhenius plot allowed for the calculation of the enthalpy change (ΔH°) for the dissolution reaction, which was determined to be +52.1 kJ mol⁻¹. This positive value indicates that the dissolution process is endothermic, requiring heat to proceed. As temperature increases, the reaction absorbs more heat, driving the dissolution process forward and increasing the concentration of bicarbonate ions in solution.

The intercept of the Arrhenius plot provided the entropy change (ΔS°) of the system, calculated as +0.158 kJ mol⁻¹ K⁻¹. The positive entropy change suggests an increase in disorder as the solid sodium bicarbonate dissolves into its ionic components in solution. This aligns with the expectation that the transition from a solid to an aqueous state involves an increase in entropy.

The Gibbs free energy (ΔG°) at various temperatures was calculated using the equation ΔG° = ΔH° - TΔS°. The values obtained indicate that the reaction becomes more thermodynamically favorable (more negative ΔG°) as temperature increases. At 25°C, ΔG° was positive, suggesting that the reaction is not spontaneous under standard conditions. However, as the temperature rose, ΔG° became increasingly negative, indicating that the dissolution reaction becomes more spontaneous and energetically favorable at higher temperatures.

This analysis highlights the importance of temperature control in processes involving sodium bicarbonate, particularly in industrial and agricultural applications where precise solubility and reaction rates are critical. The data support the hypothesis that increased temperature enhances the solubility of sodium bicarbonate, leading to a greater concentration of dissolved ions and a more negative Gibbs free energy, confirming the thermodynamic favorability of the reaction at elevated temperatures.

Conclusion

In conclusion, the experiment successfully demonstrated the effect of temperature on the solubility and thermodynamic properties of ARM & HAMMER™ Baking Soda (Sodium Bicarbonate). As hypothesized, increasing the temperature from 25°C to 65°C resulted in a higher solubility product constant (Ksp), a more negative Gibbs free energy (ΔG°), and an overall enhancement in the reaction's thermodynamic favorability.

The endothermic nature of the dissolution reaction was confirmed through the positive enthalpy change (ΔH°), while the positive entropy change (ΔS°) reflected the increased disorder in the system as sodium bicarbonate dissolved in water. The experiment provided a comprehensive understanding of how temperature influences the solubility of sodium bicarbonate, supporting its wide range of applications in both household and industrial contexts.

Furthermore, the results obtained through this investigation are consistent with established thermodynamic theories and provide valuable insights for future studies involving temperature-dependent solubility and reaction kinetics. The accuracy and reliability of the data, as demonstrated by the high correlation in the Arrhenius plot, underscore the robustness of the experimental design and the careful control of variables throughout the process.

Overall, this investigation not only achieved its intended research objectives but also contributed to a deeper understanding of the relationship between temperature, solubility, and thermodynamic parameters in chemical reactions.

Evaluation

Limitation	Significance	Possible Improvements
Collection and transfer of sodium bicarbonate solution samples from the main saturated solution.	The solubility calculated may have been greater than the actual value. Some precipitate may have been transferred into samples due to the limited volume of saturated solution and the small space for the pipette to obtain liquid from the solution without transferring any precipitate.	A larger volume of beaker or different glassware could be used to create and store the saturated solution. This would help to ensure that no precipitate is transferred to the samples, allowing for more accurate values of concentrations.
Cascading equilibrium within the reactions of sodium bicarbonate.	During the separation of phases in the equilibrium, one phase could become enriched with solute while the other is depleted. This could lead to inaccuracies in calculating the concentration of ions using the final and initial phases as an indication of change.	Minimizing cascading equilibrium in the reactions could decrease inaccuracies. However, this would require an extension to the investigation to account for these effects. Proceeding with a titration would necessitate following the outlined order of reactions.
Potential to overshoot the end-point of the titration.	This could result in less concordant readings and yield mean titre values that are less precise for certain temperatures.	Increasing the number of trials could reduce random errors and improve precision. Additionally, using a pH probe to better indicate the equivalence point would produce more accurate HCl "Added" volumes.
Choice of titration indicator.	The selected indicator may not best represent the unknown equivalence point and final pH for this titration.	A pH probe could be used to identify the final pH of titration, ensuring the indicator selected best represents the E.P. of titration, resulting in more accurate HCl "Added" volumes.
Time taken to reheat samples using a water bath.	Different trials may have received different amounts of time for reheating, potentially impacting the accuracy of the results.	Ensuring all trials are performed within the same time frame would control the reheating process more accurately, reducing variations in HCl "Added" volumes caused by inconsistent heating.