Collating, Interpreting and Analysing Results:
Known Values
Mass of Crucible: 8.024g ± 0.002g
Mass of Crucible and CuSO4 · xH2O: 10.058g ± 0.002g
Mass of Crucible and CuSO4 · xH2O after heating: 9.291g ± 0.002g
Calculation of Key Values
Mass of CuSO4 · xH2O:
m(CuSO4 · xH2O) = m(Crucible and CuSO4 · xH2O) – m(Crucible)
= 10.058 – 8.024
m(CuSO4 · xH2O) = 2.034g ± 0.004g
Mass of CuSO4:
Calculated by finding mass of water loss
m(CuSO4) = m(Crucible and CuSO4 · xH2O after heating) – m(Crucible)
= 9.291 – 8.024
m(CuSO4) = 1.267g ± 0.004g
∴ Mass of xH2O:
Calculated by subtracting the mass of copper (II) sulfate from total mass
m(xH2O) = m(CuSO4 · xH2O) - m(CuSO4)
= 2.034 – 1.267
m(xH2O) = 0.767g ± 0.008g
Solving to find “x” in (CuSO4 · xH2O) is now a simple matter of deducing the amount in moles of each compound, and finding the simplest integer ratio between CuSO4 and H2O. See:
CuSO4 xH2O
1.267g ± 0.004g 0.767g ± 0.008g
Using the formula: n = m/M, where n = moles, m = mass of sample, and
M = molar mass of compound
n(CuSO4) = 1.267g/[63.55 g.mol-1 + 32.06 g.mol-1 + 4(16.00) g.mol-1]
= 1.267/159.61 mol
n(CuSO4) ≈ 0.00794 mol ± 2.5x10-5 mol
n(H2O) = 0.767g/[2(1.01) g.mol-1 + 16.00 g.mol-1]
= 0.767/18.02 mol
n(H2O) ≈ 0.0426 mol ± 4.4x10-4 mol
The ratio can now be easily determined: CuSO4 : H2O
n(CuSO4)/ n(CuSO4) : n(H2O)/n(CuSO4)
(1.267/159.61)/( 1.267/159.61) mol : (0.767/18.02)/(1.267/159.61) mol
≈ 0.00794/0.00794 mol : ≈ 0.0426mol/0.00794mol
1 : ≈ 5.36
So both the exact and the approximate ratio has been determined. However, presumably due to experimental errors the ratio is, of course, not a perfect integer. This can be dealt with in two ways:
-
the ratio of 1 : ≈ 5.36 can be rounded to a ratio of 1 : 5 (which gives the formula of the hydrate as 5H2O) – but since 5.36 does not closely approximate 5.00, this is not an appropriate assumption.
- Alternately, a smaller rounding gives a ratio of 1 : 5.4 and this ratio can be easily multiplied to give an integer ratio as such:
5 x (1 : 5.4) = 5 : 27
which is simply a ratio, the derivation of which required fewer assumptions than the simpler ration of 1 : 5.
Hence the empirical formula has been determined as follows:
Ideally* Experimentally
CuSO4 : xH2O CuSO4 : xH2O
1 : 5 5 : 27
CuSO4 · 5H2O 5CuSO4 · 27H2O
*NOTE: this formula has been
included for the purpose of discussion
So according to experimentation, the degree of hydration in hydrated copper (II) sulfate is 5 : 27 (27H2O) – that is to say, for every five moles of copper (II) sulfate there are twenty-seven moles of water. This seems a rather elaborate hydrate compared to copper (II) sulfate pentahydrate, and the reasons for this shall be discussed later in the section for evaluation.
Conclusion:
Through empirical investigation, the degree of hydration in hydrated copper (II) sulfate was determined to a relative degree of accuracy. The value of “x” in the formula: yCuSO4 · xH2O was determined to be approximately 27 as an integer value, and “y” to be 5, giving:
5CuSO4 · 27H2O
Evaluation:
The ratio achieved through this experiment was, while approximately accurate to the accepted literature value of 1 : 5, not so precise that this ratio could be assumed to anything greater than 1 significant figure. This anomaly can be explained by acknowledging several errors within the experimental process. While the determined degree of hydration was not perfect, and indeed to find the current rather elaborate ratio a degree of rounding was still required, it was still reasonably accurate. Results of others who perform this experiment may vary for several reasons, which are much the same reasons for the imprecision of these results:
Sources of Error:
- Over heating of the hydrated copper (II) sulfate can result in burning the anhydrous compound of copper (II) sulfate remnant, thus contaminating it with oxygen and altering the mass present in the crucible. This could lead to varying degrees of inaccuracy.
- In contrast to burning the anhydrous compound, the heating could have failed to completely remove all the water – i.e. constant mass may not have been achieved.
-
There is a systematic calibration error associated with the electronic balance (± 0.002g as aforementioned), and in addition to this the zero of each balance can randomly vary, or minute changes in the environment may result in a change on the balance, so results may be affected in this way. Specifically, since each of the masses taken from the balance had an uncertainty of ± 0.002, every addition of uncertain values resulted in a sum of uncertainties, and every multiplication resulted in the sum of percentage uncertainties being carried through. These uncertainties have been included in calculations above without working.
It is likely that a culmination of these errors – with an emphasis on burning the sample – resulted in a degree of imprecision in these results. Regardless, the results were still quite conclusive.
Improvements:
Several aspects of this experiment could be developed to yield more accurate and precise results. The influence of random and systematic errors in this experiment was probably of less consequence than the overheating of the sample which, while minor, would have had an effect on the mass of the sample. The key improvement to this experiment would therefore be to decrease the intensity with which flame is applied to the crucible. This would be to reduce the possibility of overheating, and increase the period of time spent dehydrating the sample to ensure a slower, more thorough (i.e. ensuring that most of the sample is anhydrous) and less intense dehydration. This improvement would allow a more thorough development of the sample, and more frequent processing on the scales.
In addition to this, either repetition of the experiment to obtain a broader spread of results or a collation of class results may have yielded more accurate results, as the mean of the results would probably have given a ratio for hydrated copper (II) sulfate much closer the accepted literature value of 1 : 5, or CuSO4 · 5H2O.
Chris Bolton