IB Chemistry IA 2

Determining the equilibrium constant from pH values of changing concentrations of ethanoic acid

Design

Research question: How will altering the concentrations of ethanoic acid affect the pH value, and, in-turn, the equilibrium constant?

Background information:
When weak acids react, the reaction typically does not go to completion. Rather, the system goes to an intermediate state in which the rates of the forward and reverse reactions are equal. Such a system is said to be in chemical equilibrium. When equilibrium is reached, the reactants and the products have concentrations which do not change with time. When in equilibrium at a particular temperature, a reaction mixture obeys the Law of Chemical Equilibrium, which imposes a condition on the concentrations of reactants and products. This condition is expressed in the equilibrium constant Kc for the reaction.
In this experiment, I will study the equilibrium properties of the reaction between ethanoic acid, otherwise known as acetic acid (CH3COOH) and water (H2O):

CH3COOH(aq) + H2O(l)  CH3COO-(aq) + H3O+(aq)

When solutions containing ethanoic acid and water are mixed, they react to some extent, forming CH3COO- and H3O+. As a result of the reaction, the equilibrium amounts of CH3COOH and H2O will be less; for every mole of CH3COO- formed, one mole of CH3COOH and one mole of H2O will react. The equilibrium constant expression Kc for Reaction 1 is:

Kc = [CH3COOH] / [H3O+][CH3COO-]

The value of Kc is relatively constant at a given temperature. This means that mixtures containing CH3COOH and H2O will come to equilibrium with the same value of Kc, no matter what initial amounts of CH3COOH and H2O were used.
The purpose of this experiment will be to find Kc for this reaction for several concentrations that have been made up in different ways, and to show that Kc indeed has the same value in each concentration.

The solutions will be prepared by mixing solutions containing known concentrations of distilled water, H2O, and ethanoic acid, CH3COOH. I will measure pH, from which the hydronium ion concentration can be calculated. Knowing the initial composition of a mixture and the equilibrium concentration of CH3COO-, we can calculate the equilibrium concentrations of the rest of the pertinent species and then determine Kc.

Hypothesis: It is hypothesised that due to the constant nature of Kc values, each Kc for all concentrations will be equal.

Independent variable:
1. Concentrations of ethanoic acid and water solution.
In order to determine the equilibrium constant for differing concentration ratios of ethanoic acid to water, relatively, tests will be conducted under a variety of concentration ratios using 1M ethanoic acid:
20mL:80mL = 0.2M
40mL:60mL = 0.4M
60mL:40mL = 0.6M
80mL:20mL = 0.8M
100mL:0mL = 1M

Dependent variable:
2. pH value and by proxy the equilibrium constant, Kc.
These will be measured using a pH meter.

Controlled variables:
3. Volume of ethanoic acid and water solution.
The volume of each solution used for each trial will be 100ml.
4. Volume of beaker
I will use the same 200ml beakers throughout the experiment.
5. Volume of solution
Throughout the experiment, the ethanoic acid and water solution will be maintained at a constant 100mL. This is to minimise error.

Uncontrolled variables:

6. Air pressure
Throughout the experiment, the air pressure in the laboratory will be maintained at 1.20 hPa.
7. Air temperature
Throughout the experiment, the air temperature in the laboratory was constant at 25ºC.
8. Quality and accuracy of pH readers
The same pH reader will be used throughout the experiment will be used to minimize the effect of this uncontrolled variable.

Name
Size/concentration
Amount/quality
Uncertainty
Ethanoic acid
1M
1.5L
-
Distilled water
-
1L
-
Styrofoam cup
500mL
1
-
Beaker
250mL
5
±5mL
Measuring cylinder
100mL
1
±2.5mL
Test tube rack
-
1
-
Buffer solution
-
500mL
-
pH reader
-
1
±0.05pH
Materials:
Method:
1. Prepare a 0.2M of ethanoic acid solution
2. Using a measuring cylinder, measure 20mL of 1M ethanoic acid and pour into a Styrofoam cup
3. Using the same measuring cylinder, measure 80mL of distilled water and pour into the same Styrofoam cup
4. Pour 20mL of buffer solution into a different beaker, activate pH meter and suspend it in the buffer solution until the pH stabilises
5. After it is stabilised, rinse the pH meter using tap water, dry using paper towel and suspend inside Styrofoam cup containing ethanoic acid concentration
6. Observe when pH stabilises and record the pH reading
7. Rinse pH meter, dry and place in a new beaker of 20mL buffer solution
8. Repeat the trial four more times with the same concentration
9. Repeat steps 1-8 for 0.4M, 0.6M, 0.8M and 1M ethanoic acid solution using the concentration of ethanoic acid: water mL ratios of 40:60, 60:40, 80:20, 100:0 respectively.

Risk assessment

Chemical risks and handling:

Whilst concentrated ethanoic acid and even moderately-concentrated ethanoic acid is corrosive and irritable, dilute ethanoic acid (less than 1.7M), is a low-hazard chemical. However, it has a hazardous nature – it is flammable, and may cause redness and irritation of the skin. Ethanoic acid may cause pain if comes into contact with eyes. Do not inhale nor ingest.

Throughout the experiment, aprons and goggles must be worn at all times.

Procedural risks and disposal:

Throughout the experiment, glassware such as beakers and measuring cylinders will be used extensively. It is important that all glassware is handled with care as not to break, chip or smash the equipment.

Throughout the experiment, there is possibility for spilling of liquids in use to occur. Ethanoic acid or water may be spilled, and it is important to clean it up, using paper towel immediately.

Data and data processing

Raw data:

Concentration of CH3COOH (M)

pH value (±0.05pH)

Test 1

Test 2

Test 3

Test 4

Test 5

0.2

2.73

2.71

2.72

2.76

2.73

0.4

2.55

2.57

2.56

2.60

2.57

0.6

2.50

2.49

2.50

2.51

2.50

0.8

2.43

2.43

2.40

2.43

2.46

1

2.39

2.38

2.39

2.40

2.39

Qualitative observations:
The pH reader, during the last two concentration trials, deviated by ±0.2pH when submerged in the buffer solution.
However, despite the aberration, the results of the trials in the 80:20 concentration ratio and the 100:0 concentration ratio were in linear congruence compared with the first three concentration results.
There was some fluctuation (±0.73 pH)

Processed data
Table 1:
Average pH readings calculated from five trials

|Concentration of CH3OOH (M)

Average pH
0.2
2.73
0.4
2.57
0.6
2.50
0.8
2.43
1
2.39

Processed data
Graph 1
Average pH values in relation to molar concentration of ethanoic acid

Processed data
Calculation 1: Kc values from pH values of changing concentrations of ethanoic acid
The following Kc values for each concentration of ethanoic acid were calculated using the following method:
Trial 1 of 0.2M ethanoic acid average pH = 2.73
Using the formula: [H3O+] = 10-pH
[H3O+] = 10-2.73 = 0.001862M
Initial [CH3COOH] = 0.2M
Using Kc = [H3O+][CH3OO-] / [CH3COOH]
And knowing that [H3O+] : [CH3OO-] is in a 1:1 ratio
Therefore, Kc = (0.001862)2 / 0.2 = 1.7 x 10-5

Trial 1: 0.2M ethanoic acid
Trial 2: 0.4M ethanoic acid
Trial 3: 0.6M ethanoic acid
Trial 4: 0.8M ethanoic acid
Trial 5: 1M ethanoic acid
Kc = 1.7 x 10-5
Kc = 1.8 x 10-5
Kc = 1.7 x 10-5
Kc = 1.7 x 10-5
Kc = 1.7 x 10-5

Processed data
Graph 2
Experimental Kc values of varying concentrations of ethanoic acid

Processed data
Graph 3
Theoretical Kc values of changing concentrations of ethanoic acid

Source: Derry et al. 2011. “Chemistry for use with the IB Diploma Programme”, Pearson Heinemann. Port Melbourne, Australia.

Uncertainty
The uncertainty for this data set was calculated based on the range, as the uncertainty value based on range is bigger than the standard deviation, or instrumental uncertainty.

Instrumental uncertainty:
Uncertainty of pH meter: ±0.05pH. This value is based upon “the uncertainty of a pH meter is ± the smallest scale division.” (Brown.C, Ford.M, page 216). As such, since the smallest division is ±0.1pH, then the instrumental uncertainty is ±0.05p
Uncertainty of the measuring cylinder: ±2.5mL. This value is based upon “the uncertainty of a measuring cylinder is ± the smallest scale division.” (Brown.C, Ford.M, page 215). As such, since the smallest division is ±5mL, then the instrumental uncertainty is ±2.5mL.

Uncertainty based on range pH:

Conclusion
From the graph and table of Kc values, I deduce that my results are congruent with my hypothesis, in that despite varying concentrations, the equilibrium constants will be equal. Pearson’s correlation coefficient, r, shows that there is a strong, negative correlation between acid concentration and pH. Moreover, my results strongly support my hypothesis. Graph 1, exhibiting the average pH values, strongly contrast with Table 1, in-turn presenting the average Kc values. Discrepancy in results was expected and is encouraged, as it further proves that altering concentrations of ethanoic acid and water will change pH values, but ultimately not change the equilibrium constants.

My average experimental Kc value of ethanoic acid was (actual) 0.17 x 10-5, and is line with the theoretical Kc value of ethanoic acid of 1.74 x 10-5. And with a percentage error or 2.30%,
[(1.74 x 10-5 – 1.7 x 10-5 / 1.74 x 10-5) x 100]

My experiment proves a relatively accurate observation, recording and evaluation of results.

Error present in the experiment

Total random error:
Using the standard error of the mean:
Total random error= (average value +/- standard error of the mean)

Total systematic error:
Measuring cylinder = 2.5/100 x 100 = 2.5% pH meter = 0.05/ (2.52) x 100 = 2.0%
Total = 2.5% + 2.0% = 4.5%

Uneven cleaning of pH readers Unfortunately during the procedure of this experiment, there was no control as to how much of the pH readers were cleaned, and the degree of efficacy to which they were completed.
This could hinder the accuracy of the data, as residual buffer solution may affect the reading of the pH, resulting in a higher record than expected.
Suggested improvement 
When cleaning the pH readers, make sure that for each trial, they are cleaned with approximately the same amount of effort and time.

Fluctuation of pH readings
It has been noted that during the process of the fourth and fifth trials, the pH reader fluctuated by 0.2pH when submerged in the buffer solution.
However, when the pH reader was placed in the ethanoic acid and water solution, the readings were congruent with the average trend line of values.
These fluctuations has been taken into account by the propagated uncertainties of average voltages.
However, for the last two measurements, the instrumental uncertainties are higher than the propagated uncertainties.
This means that the instrumental uncertainties could have a greater impact on the accuracy of data than expected; however, its impact may not be as significant in comparison to other systematic errors. Repeating the experiment several times can reduce the effect of this error.

Evaluation
The results of the experiment showed that the equilibrium constant remained equal, whilst pH values altered, which is what I hypothesised. Whilst my experimental graph in section 2 may show what appears to be an outlier for the second concentration, the supposed anomaly can be attributed to the very small scale of the y-axis. The error bars should further explain this.

Major weaknesses:
Weakness 1:
I only investigated the changing concentrations of ethanoic acid, which is a relatively weak acid.
Whilst the weaknesses of my experiment were not significant as to effect my data, it would be interesting to investigate the Kc value of altering the concentration of an acid of a lower pH, to see whether my hypothesis
Through comparing my experimental values and theoretical values, I conclude that I was highly precise and highly accurate. Given the very small 2.30% difference between my experimental values and my theoretical values, the experiment’s reproducibility is highly attainable. The extremely small error value of ±0.05pH further supports my experiment’s reproducibility.

Further Suggestion for Improvements

Limitation 1 – More accurate equipment (pH meter and measuring cylinder)
Improvement: One aspect in which my experiment could be improved is through performing my experiment with more accurate equipment to limit error. For example, the pH meter is only correct to 0.01 decimal places. It would exponentially improve the accuracy of the pH readings if the meter was correct to more significant figures.
Limitation 2 – Performing experiment on one day
Improvement: Another aspect in which my experiment could be improved is performing the experiment on one day. In doing this, I would improve accuracy as fluctuations in air temperature and pressure would be negligible.