Chemistry!
Avinash Bharwaney
Hess’ Law Lab Aim: To determine the enthalpy change for the decomposition of sodium hydrogen carbonate into sodium carbonate. Introduction In this experiment, Hess‘ Law will be used to determine the enthalpy change for the decomposition of sodium hydrogen carbonate into sodium carbonate. This will be done by conducting two experiments (shown below). Experiment 1: Na2CO3 + 2HCl → 2NaCl + CO2 + H2O Experiment 2: NaHCO3 + HCl → NaCl + CO2 + H2O From the information gathered from these experiments, the enthalpy change of each of the experiments above can be determined. By manipulating these two equations (shown above) to form the target equation (shown below) of the decomposition of sodium hydrogen carbonate, this thus allows for the determination of the enthalpy change as specified in the aim. Target Equation: 2NaHCO3(s) → CO2(g) + H2O(g) + Na2CO3(s) Before determining the experimental value, the literature value of the decomposition of sodium hydrogen carbonate has to be calculated. Calculation: Equation required: ∆H (products) - ∆H (reactants) = ∆H (reaction) ΔH(products) ΔH(CO2) = -393.5 kJ/mol ΔH(H2O) = -285.8 kJ/mol ΔH(Na2CO3) = -1131.0 kJ/mol
∆H (reactants) ΔH(Na2HCO3) = -950.8 kJ/mol = 2(-950.8 kJ/mol)
= -1901.6 kJ/mol
a) [ΔH(CO2) + ΔH(H2O) + ΔH(Na2CO3)] - [ΔH(Na2HCO3)] b) (-393.5 + -285.8 + -1131.0) kJ/mol - 2(-950.8 kJ/mol) c) -1810.3 kJ/mol - (-1901.6 kJ/mol) d) +91.3 kJ/mol (Lit.Value) Literature Value of the Enthalpy Change (∆H) = +91.3 kJ/mol
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Chemistry!
Avinash Bharwaney
Uncertainties of the Apparatus Table 1: Uncertainties of the Apparatus Apparatus
Uncertainty
Electronic Balance
± 0.005g
Measuring Cylinder (50ml)
± 1ml
Thermometer
± 0.1ºC
Note that not all apparatus used in the experiment is stated in the table above. The purpose of providing the information above is solely to indicate where the uncertainties for the measurements and calculations (shown in the Data Collection and Data Processing stages) is derived from. Data Collection Note that trials 1-3 refer to the trials conducted for Experiment 1 and trials A-C refer to the trials conducted for Experiment 2. i. Experiment 1: Na2CO3 + 2HCl → 2NaCl + CO2 + H2O Background: Trials 1-3 consist of 2.00 grams ± 0.005 grams of sodium carbonate (Na2CO3), as well as 50 ml ± 1 ml of of 2M HCl. Note that the 50 ml of acid is assumed to be equal 50 grams of acid (this is assumed because the density and specific heat capacity of HCl is similar to water and 1ml of water is equal to 1g). The duration of each trial has been kept constant and so limited to 1 minute. Table 2: Table of Temperature Values (Initial and Final) of Trials 1-3 Trial
Temperature (ºC) Uncertainty: ± 0.1 Initial Temperature
Final Temperature
Uncertainty: ± 0.2 Change in Temperature ∆T
1
23.0
24.9
(+)1.9
2
23.0
25.1
(+)2.1
3
23.1
25.2
(+)2.2
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Chemistry!
Avinash Bharwaney
Table 3: Qualitative Observations of Trials 1-3 Qualitative Observations Immediate hissing sound when the reactants came in contact with each other. Bubbles also started to form, indicating a chemical reaction was taking place and that a gas was being formed as a byproduct. Furthermore, the temperature of the styrofoam cup (in which the reaction was taking place in) increased as we felt the cup getting hotter. Indication of an exothermic reaction taking place.
ii. Experiment 2: NaHCO3 + HCl → NaCl + CO2 + H2O Background: Trials A-C consist of 2.00 grams ± 0.005 grams of sodium hydrogen carbonate (NaHCO3), as well as 50 ml ± 1ml of of 2M HCl. Note that the 50 ml of acid is assumed to be equal 50 grams of acid (this is assumed because the density and specific heat capacity of HCl is similar to water). The duration of each trial has been kept constant and so limited to 1 minute. Table 4: Table of Temperature Values (Initial and Final) of Trials A-C Trial
Temperature (ºC) Uncertainty: ± 0.1 Initial Temperature
Uncertainty: ± 0.2
Final Temperature
Change in Temperature ∆T
A
23.1
20.5
(-)2.6
B
23.0
20.5
(-)2.5
C
22.3
20.9
(-)1.4
Table 5: Qualitative Observations of Trials A-C Qualitative Observations Immediate hissing sound when the reactants came in contact with each other. Bubbles also started to form, indicating a chemical reaction was taking place and that a gas was being formed as a byproduct. Furthermore, the temperature of the styrofoam cup (in which the reaction was taking place in) increased as we felt the cup getting cooler. Indication of an endothermic reaction taking place.
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Chemistry!
Avinash Bharwaney
Data Processing i. Experiment 1: Na2CO3 + 2HCl → 2NaCl + CO2 + H2O a) Calculate moles of 2.00g of Sodium Carbonate (Na2CO3) Molar Mass of Sodium Carbonate: 2(22.99 g/mol) + 12.011 g/mol + 3(15.999 g/mol) = 105.988 g/mol Moles of Sodium Carbonate: 2.00g ÷ 105.988 g/mol = 0.0189 mol of Na2CO3 Uncertainty: i. Absolute Uncertainty = 2.00g ± 0.005g ii. Percentage Uncertainty = 0.005/2 = 0.0025 x 100 = ± 0.25% iii. Total Uncertainty = 0.0189 mol ± 0.25% = 0.0189 mol ± 0.0000472 mol b) Calculate the percentage uncertainty of the 2M HCl Uncertainty: i. Absolute Uncertainty = 50ml HCl ± 1ml ii. Percentage Uncertainty = 1/50 = 0.02 x 100 = ± 2% iii. Conversion from milliliters to grams = 50ml ± 2% → 50g ± 2% c) Calculate the average temperature change (∆T) [Table 4] Average Temperature Change (∆T): (1.9ºC) + (2.1ºC) + (2.2ºC) = 6.2ºC 6.2ºC ÷ 3 = 2.066666667ºC = +2.1ºC ± 0.2ºC Percentage Uncertainty: i. Absolute Uncertainty = +2.1ºC ± 0.2ºC ii. Percentage Uncertainty = 0.2/2.1 = 0.095238 x 100 = 9% iii. Final Percentage Uncertainty = +2.1 ± 9% d) Calculate the energy (q) of Experiment 1 using q = mc∆T Key: q = Energy (J) m = 50 grams of HCl ± 2% c = 4.19 J/g*C (assumption that HCl has the same density as water and therefore the same Specific Heat Capacity). There is no uncertainty for this value. ∆T = +2.1ºC ± 9%
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Chemistry!
Avinash Bharwaney
q = mc∆T Calculation q = (50)(4.19)(2.1) = 439.95 J Percentage Uncertainty: 2% + 9% = 11% Percentage Uncertainty = 439.95 J ± 11% Total Uncertainty: i. Percentage Uncertainty = 439.95 J ± 11% ii. 11% of 439.95 J = 48.3945 J iii. Total Uncertainty = 439.95 J ± 48.3945 J iv. Total Uncertainty (in kJ) = 0.43995 kJ ± 0.0483945 kJ = 0.44 kJ ± 0.048 kJ e) Calculate the enthalpy change (∆H) of Experiment 1 using ∆H = -q/mol Finding -q: q = +0.43995 kJ ± 11% x -1 = -0.43995 kJ ± 11% Enthalpy (kJ/mol): -0.43995 kJ/0.0189 mol = -23.2778 kJ/mol Uncertainty: i. Percentage Uncertainty = (± 11%) + (± 0.25%) = ± 11.25% ii. 11.25% of -23.2778 kJ/mol = 2.61875 kJ/mol iii. Total Uncertainty = -23.3 kJ/mol ± 2.62 kJ/mol
Na2CO3 + 2HCl → 2NaCl + CO2 + H2O ∆H = -23.3 kJ/mol ± 2.62 kJ/mol
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Chemistry!
Avinash Bharwaney
ii. Experiment 2: NaHCO3 + HCl → NaCl + CO2 + H2O a) Calculate moles of 2.00g of Sodium Carbonate (NaHCO3) Molar Mass of Sodium Hydrogen Carbonate: 22.990 g/mol + 1.007g/mol + 12.011 g/mol + 3(15.999 g/mol) = 84.005 g/mol Moles of Sodium Hydrogen Carbonate: 2.00g ÷ 84.005 g/mol = 0.0238 mol of NaHCO3 Uncertainty: i. Absolute Uncertainty = 2.00g ± 0.005g ii. Percentage Uncertainty = 0.005/2 = 0.0025 x 100 = ± 0.25% iii. Total Uncertainty = 0.0238 mol ± 0.25% = 0.0238 mol ± 0.0000595 mol b) Calculate the percentage uncertainty of the 2M HCl Uncertainty: i. Absolute Uncertainty = 50ml HCl ± 1ml ii. Percentage Uncertainty = 1.0/50 = 0.02 x 100 = ± 2% iii. Conversion from milliliters to grams = 50ml ± 2% → 50g ± 2% c) Calculate the average temperature change (∆T) [Table 2] Average Temperature Change (∆T): (-1.4ºC) + (-2.5ºC) + (-2.6ºC) = -6.5ºC -6.5ºC ÷ 3 = -2.1666’ºC = -2.2ºC Percentage Uncertainty: i. Absolute Uncertainty = -2.2ºC ± 0.2ºC ii. Percentage Uncertainty = 0.2/0.2/2.2 = 0.090909 x 100 = 9% iii. Percentage Uncertainty = -2.2 ± 9% d) Calculate the energy (q) of Experiment 1 using q = mc∆T Key: q = Energy (J) m = 50 grams of HCl ± 2% c = 4.19 J/g*C (assumption that HCl has the same density as water and therefore the same Specific Heat Capacity). There is no uncertainty for this value. ∆T = -2.2 ± 9% q = mc∆T Calculation q = (50)(4.19)(-2.2) = -460.9 J
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Chemistry!
Avinash Bharwaney
Percentage Uncertainty: 2% + 9% = 11% Percentage Uncertainty = -460.9 J ± 11% Total Uncertainty: i. Percentage Uncertainty = -460.9 J ± 11% ii. 11% of -460.9 J = 50.699 J iii. Total Uncertainty = -460.9 J J ± 50.699 J iv. Total Uncertainty (in kJ) = -0.4609 kJ ± 0.050699 kJ = -0.46 kJ ± 0.051 kJ e) Calculate the enthalpy change (∆H) of Experiment 1 using ∆H = -q/mol Finding -q: q = -0.4609 kJ ± 11% x -1 = +0.4609 kJ ± 11% Enthalpy (kJ/mol): +0.4609 kJ/0.0238 mol = +19.3655 kJ/mol Uncertainty: i. Percentage Uncertainty = (± 11%) + (± 0.25%) = ± 11.25% ii. 11.25% of +19.3655 kJ/mol = 2.17862 kJ/mol iii. Total Uncertainty = +19.4 kJ/mol ± 2.18 kJ/mol
NaHCO3 + HCl → NaCl + CO2 + H2O ∆H = +19.4 kJ/mol ± 2.18 kJ/mol
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Chemistry!
Avinash Bharwaney
iii. Hess’ Law Calculation Equations: 1. Na2CO3 + 2HCl → 2NaCl + CO2 + H2O ∆H = -23.3 kJ/mol ± 2.62 kJ/mol 2. NaHCO3 + HCl → NaCl + CO2 + H2O ∆H = 19.4 kJ/mol ± 2.18 kJ/mol Methodology: i. Multiply the second equation by 2 = +19.4 kJ/mol x 2 = +38.8 kJ/mol. This is because the target equation has 2NaHCO3. Calculation: = 2(NaHCO3 + HCl → NaCl + CO2 + H2O) = 2NaHCO3 + 2HCl → 2NaCl + 2CO2 + 2H2O Uncertainty: = (± 2.18) x 2 = ± 4.36 kJ/mol ii. Reverse the first equation. When you reverse the equation, note that the ∆H is multiplied by -1. Calculation: = Na2CO3 + 2HCl → 2NaCl + CO2 + H2O ∆H = -23.3 kJ/mol x -1 = 2NaCl + CO2 + H2O → Na2CO3 + 2HCl ∆H = +23.3 kJ/mol iii. Cancel out these two equations to form the target equation. Calculate the enthalpy values in the process.
2NaCl + CO2 + H2O → Na2CO3 + 2HCl ∆H = +23.3 kJ/mol 2NaHCO3 + 2HCl → 2NaCl + 2CO2 + 2H2O ∆H = +38.8 kJ/mol 2NaCl + CO2 + H2O → Na2CO3 + 2HCl ∆H = +23.3 kJ/mol 2NaHCO3 + 2HCl → 2NaCl + 2CO2 + 2H2O ∆H = +38.8 kJ/mol = 2NaHCO3 → Na2CO3 + CO2 + H2O = (+23.3 kJ/mol) + (+38.8 kJ/mol) = +62.1 kJ/mol Since we’re dealing with addiction, we simply add the absolute uncertainties. (± 4.36) + (± 2.62) kJ/mol = ± 6.98 kJ/mol Target Equation: 2NaHCO3 → Na2CO3 + CO2 + H2O ∆H = +62.1 kJ/mol ± 6.98 kJ/mol 8
Chemistry!
Avinash Bharwaney
Final Answer (∆H): ∆H = +62.1 kJ/mol ± 7 kJ/mol iv. Percentage Discrepancy (% difference) The literature value calculated was +91.3 kJ/mol however after processing the data from our experiment, we received an experimental enthalpy value of +62.1 kJ/mol, a number considerably smaller in relation to the original literature value. This could be because of the heat lost due to the poor insulation of the styrofoam cup. Lit. Value = +91.3 kJ/mol Experimental Value = +62.1 kJ/mol Calculation: (Experimental Value - Lit. Value)/Lit. Value x 100 = % discrepancy = (+62.1 kJ/mol) - (+91.3 kJ/mol) = -29.2 kJ/mol = -29.2 kJ/mol/91.3 kJ/mol = -0.3198 = -0.3198 x 100 = -31.98% = -32.0%
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Chemistry!
Avinash Bharwaney
Conclusion and Evaluation Restating the Process: In this investigation, two reactions (Experiment 1 and Experiment 2 respectively) were carried out to determine the enthalpy change (∆H) of the decomposition of sodium hydrogen carbonate. This was done by firstly calculating the enthalpy change (∆H) of each reaction and then using Hess’ Law to manipulate the data to form the target equation: 2NaHCO3 → Na2CO3 + CO2 + H2O. The enthalpy change (∆H) of each reaction, measured in kJ/mol, was calculated using the heat energy change (kJ) divided by the moles of the 2.00g ± 0.005g of reactant (Na2CO3 for Experiment 1 and NaHCO3 for Experiment 2). Each reaction resulted in a change in temperature (∆T), which was required to determine ‘q’ (q = mc∆T), measured in kJ. This was the only primary data collected and is shown on Table 2 for Experiment 1 and Table 4 for Experiment 2.
Conclusion According to the data collected and processed, the final experimental enthalpy change value (∆H) for the decomposition of sodium hydrogen carbonate into sodium carbonate is 62.1 kJ/mol ± 7 kJ/mol. On the other hand, the literature value of the reaction, as calculated using the literature ∆H values for each of the reactants and products, is 91.3 kJ/mol. There is a clear difference between the two values, suggesting that the method used in the experiment to collect the primary data, the heat energy change data, may have proved to be futile. Calorimetry was the method used to collect the data required for the calculation of ‘q’ (q = mc∆T): the temperature change (∆T) of the reactions. To calculate the temperature change of the reaction (of either experiment), a styrofoam cup was used as the calorimeter. The main purpose of a calorimeter is to maintain the the heat energy within a system and keep the system closed, since heat energy can easily disperse into the surrounding environment if not insulated properly. Using a styrofoam cup as the calorimeter posed a threat to the reliability of the results as it is not the perfect insulator and therefore cannot maintain all the heat energy. If the heat energy cannot be maintained, the experimental values will not be reliable because not all the energy will have been accounted for. Through our qualitative observations, the change in temperature could be felt from the outside of the cup, indicating heat escaping through the cup. Due to this insulation problem with the styrofoam cup, a large amount of heat was lost in the reaction, which resulted in unreliable data results and inevitably, a large percentage discrepancy of -32.0% 10
Chemistry!
Avinash Bharwaney
between the literature value and the experimental value. An improvement to assure reliable results would be to make use of a bomb calorimeter when calculating the heat energy change in a reaction. Unlike styrofoam cup calorimeters, bomb calorimeters are equipped with better insulation, allowing for more reliable and accurate results. Furthermore, the final experimental enthalpy change value had an uncertainty of ± 7 kJ/mol giving us a wide range of 14 possible values, from 55.1 kJ/mol to 69.1 kJ/mol. The uncertainty is extremely significant as it highlights how the final answer is not precise. The difference between the literature value and the highest possible experimental enthalpy change value is 22.2 kJ/mol whereas the difference between the literature value and the lowest possible experimental enthalpy change value is 36.2 kJ/mol, which is 14 kJ/mol more than the former. Calculation: 1) 91.3 kJ/mol - 69.1 kJ/mol = 22.2 kJ/mol 2) 91.3 kJ/mol - 55.1 kJ/mol = 36.2 kJ/mol 3) 36.2 kJ/mol - 22.2 kJ/mol = 14 kJ/mol
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Chemistry!
Avinash Bharwaney
Evaluation Systematic Errors Table 6: Evaluating the Systematic Errors Systematic Errors Error
Comment
Improvement
Insufficient Heat Insulation
The problem with the styrofoam cup calorimeter meant that there were issues with insulating the heat and preventing the heat from escaping, resulting in the large percentage discrepancy between the literature values and the experimental values.
As mentioned above in the conclusion, to improve the reliability of the results and prevent the heat from escaping, a bomb calorimeter could be used. Although it may not be perfect and still have some limitations of its own, it has better insulation in relation to the styrofoam cup calorimeter and so can provide more reliable results.
Faulty Measuring Instruments
Another systematic error present in the experiment was that the electronic balance was faulty in its reading, providing constantly changing values. Even after any remaining residue/particles from previous experiments were wiped off the balance, the scale still continued read For instance, when the balance was calibrated (reset), it changed between 0.02g and 0.00g. When recording the mass, we did not take into account this uncertainty of 0.02g and assumed that the
Improvements for this error would be to either: 1) Test and calibrate measuring instruments before recording data to check whether that they work properly and can provide accurate results. If the instrument is faulty, inform the teacher and use another electronic balance. 2) Make use of the faulty electronic balance, but remember to account for the additional uncertainty.
Assumptions
One of the assumptions made in this experiment was that the Specific Heat Capacity of the Hydrochloric Acid (HCl) used was the same as water. Although dilute HCl does have a very similar SHC to water, the HCl used in the experiment was 2M and so of a higher concentration. This was however still a very minor error.
To improve the accuracy of the results, dilute HCl could have been used instead of 2M HCl, in order for the SHC value used to remain reliable.
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Chemistry!
Avinash Bharwaney
Systematic Errors Error Particles of reactant left in the weighing boat
Comment Another minor systematic error included the fact that there were particles of reactant left in the weighing boat after pouring the reactant into the calorimeter. This meant that the mass in the calorimeter was not what was recorded and in fact, slightly less, affecting the reliability of the results.
Improvement In order to make sure that the majority of the particles react in the experiment, a brush or tissue can be used to scrape the remaining particles from the weighing boat into the calorimeter. This however does create a number of problems, the first being that the reaction would have already started and so adding additional reactant into the calorimeter during the reaction may affect the fairness of the experiment. Another problem that may arise would be that the particles may get attached to the tissue.
Random Errors Table 7: Evaluating the Random Errors Random Errors Error Reading Measuring Instruments
Comment
Improvement
The measuring instruments used in this experiment include the electronic balance, the measuring cylinder and the thermometer. With the exception of the electronic balance, all the measuring instruments required us to rely on our own personal judgement and perception to manually read the scale (thermometer) and judge where the bottom of the meniscus was (measuring cylinder). This led to uncertainty and human error as it was difficult to pinpoint the exact volume of a solution. Also, Parallax error may have occurred as there were different people reading the scale/meniscus from different angles.
This random error is one that will occur in any experiment, however the magnitude of the error can be subdued if the person taking the reading stays constant ie. the same person does a specific task. This is to minimize potential misreadings and reduce Parallax error. Increasing the number of trials done for each experiment also would reduce the misreadings as averaging over a large number of values would counter any misreadings made.
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