The raw data for the two trials for both the compounds has been tabled with the average worked out for each species.
The average was worked out as:
= the mass of trials (1 + 2)/2
When using a balance that weighs ± 0.010g the uncertainty shown in the table of trial 1 for K2CO3 weighs 2.729g will equal to
(0.010/2.729) X 100 = 0.4%
Hence for trial 2 =
(0.010/2.613) X 100 = 0.4%
Therefore the overall uncertainty for the mass of K2CO3 is summing up all the individual uncertainties for both the trials.
Hence 0.4 + 0.4
= 0.8%
For KHCO3:
Trial 1:
(0.010/3.455) X 100 = 0.3%
Trial 2:
(0.010/3.665) X 100 = 0.3%
Therefore the overall uncertainty equals
0.3 + 0.3 = 0.6%
The moles of each species are required to be calculated. The calculation is,
Moles = mass/Mr
Therefore the Mr of K2CO3 = (2 X K) + (1 X C) + (3 X 0)
Mr = (2 X 39.10) + 12.01 + (3 X 16)
= 138.01
Therefore as the mass is 2.671, then
Moles = 2.67/ 138.21
= 0.0193 M
For KHCO3
Mr = 39.10 + 12.01 + (3 X 16) + 1.01
= 100.11 ± 4 %
Moles = 3.555/ 100.11
= 0.0354 ± 3 %
The enthalpy change is required to be calculated. Therefore the enthalpy change can be calculated by the following equation:
Energy change = X X
Since the solution has the same density as water (1g/cm3) and the same heat capacity as water (4.18 Jg -1 0C-1)
Therefore the energy change for for K2CO3
= (30/1000) X 4.18 X -2.25
= (-0.282/1000) KJ ± 2.6 % / ± 4 % 0.0193 moles
Due to using 30cm3 the uncertainty of the measuring cylinder is ± 0.5 cm3. That is 30 cm3.
Hence the uncertainty in measuring 30.000 cm3 will equal
(0.5/30) X 100 = 1.7 %
The uncertainty for measuring the temperature of K2CO3 has already been calculated above, that is (0.9 %).
Therefore the total uncertainty can be calculated by summing up all the uncertainties that has been calculated.
That is 1.7 + 0.9 = 2.6 %
Therefore -0.282/0.0193 = - 14.619 KJ mol -1 ± 6.6 %
2.6 + 4.0 = ± 6.6 %
The energy change for KHCO3
= (30/1000) X 4.18 X (+ 7.6)
= 0.953 KJ ± 2.9 % / 0.0354 moles ± 3 %
Therefore 0.953/ 0.0354 = 26.875 KJ mol -1 ± 5.9 %
The uncertainty is calculated by summing up ± 1.7 % (as shown above) and of ± 1.2 % as the uncertainty for measuring temperature.
Therefore 1.7 + 1.2 = 2.9 %
Therefore the total uncertainty of the enthalpy change is 2.9 + 3.0 = ± 5.9 %
By using Hess’s law the enthalpy change for the thermal decomposition of potassium hydrogen carbonate into potassium carbonate can be found.
Therefore according to Hess’s Law:
H1= 2 X H2 - H3
Therefore :
H1 = (2 X 26.875) – (- 14.619)
= 68.369 KJ / mol ± 12.5 %
The total uncertainty that is shown above is from the total of the enthalpy changes of K2CO3 and KHCO3.
6.6 + 5.9 = ± 12.5 %
Conclusion and Evaluation:
As shown above, of the calculation of the enthalpy change for the thermal decomposition of potassium hydrogen carbonate into potassium carbonate is calculated as + 68.396 KJ / mol ± 12 %. (± 8.207 KJ/mol).
I.e. 12/100 X 68.396 = ± 8.207 KJ mol -1. Therefore, 68.396 – 8.207 = 60.188 KJ/ mol.
However the Literature value given is + 92 KJ/mol. This shows that the value obtained from the experiment is below the literature values. That is 23.604 JK/ mole of a difference.
The enthalpy change was of a decomposition reaction. This means that a chemical reaction, where the molecules of a compound (in this case KHCO3 ) breakdown to form simpler molecules of two or more new substances. I.e K2CO3, CO2 and H2O. By the enthalpy change of not just the literature value but also the experimental value. It can be seen that the change was positive. I.E. the decomposition reaction was endothermic. This is where the reactants have less enthalpy than the products. This is an increase in energy taken from the surrounding, and the products are less energetically stable than the reactants. This is because in endothermic reactions heat is absorbed from the surroundings, as the bonds in the reactants are stronger than that of the bonds in the products. So it requires energy due to the fact that the reactant will not spontaneously decompose by itself. So in this reaction, the heat transferred from the water to the reaction can be calculated by measuring the lowered temperature of the known mass.
The enthalpy for a reaction depends on the difference between the enthalpy of the products and the enthalpy of the reactants. It is independent on the route of which the reaction might occur on. Therefore the enthalpy change for a reaction is the sum of the individual enthalpy changes for each step. Therefore Hess’s is a very beneficial method for determining the enthalpy change for the decomposition, due to the reaction being difficult to measure directly. Hess’s law is illustrated with an aid of a cycle. (as shown above for this reaction).
As mentioned before the experimental value obtained is well below the accepted literature value this also could be due to several reasons.
- The end point being subjective. i.e. the method was unclear as to when the temperature should be checked. This could have been the potential heat loss during the stirring or when the potential heat loss after the reaction had completed, i.e. the reaction had stopped effervescence. The method could be improved by creating test trials. In which, multiple readings could be recorded, where the optimum i.e. the highest temperature change recorded. The time that it took for the highest could be used as a controlled variable, where the reaction would take place for only that period of time. So the results obtained more precisely.
- The stirring technique was not uniform. This is a random error, which created problems as it could have caused the reaction to incomplete at incorrect time. So the method could be improved by defining the time of stirring and the stirring technique.
- The conditions of temperature and pressure might be slightly different to than of the standard enthalpy conditions would need to be. Which is 298 K and 1 atm. However this error will be minor. By controlling the laboratory environment can control the standard enthalpy conditions. This can be by using a water bath for the temperature at 298 K.
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In calculation the density of the solution was assumed to be 1g cm -3 and specific heat capacity was taken as 4.18 Jg -1 0C-1. This is only for pure water and the values would differ here, introducing an error in calculation.
- During the experiment the calorimeter was washed, but not sure all of the previous solution was removed. Therefore, use different calorimeters of polystyrene.
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The concentration of HCl was supplied yet the error of the concentration was unknown, therefore if the concentration was much lower than 1 mol dm-3 this would have resulted in a lower enthalpy value.
