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Analysis and evaluation exercise
When the experiment was carried out 0.126 grams of calcium metal produced 72.0 cm3 of gas. Calculate the percentage purity of the calcium sample. Carry out an error analysis and suggest any improvements. What additional problems might occur if a similar experiment were attempted with sodium metal?
Number of moles of H2 = 72.0/24000 = 0.00300
|
Ca(s) + 2H2O(l) ⇒ Ca(OH)2(aq) + H2(g) |
Ca º H2
\ number of moles of Ca = 0.00300
Ca = 40
\ mass of Ca = 0.00300 × 40 = 0.120 g
\ percentage purity of Ca = 0.120/0.126 × 100 = 95.2%
Error analysis
The error in the balance is ± 0.001 g, giving a percentage error of 0.001/.0126 × 100 = ± 0.8%. There should be no need to weigh by difference. The beads of calcium are large enough not to stick to the weighing boat, so should all be transferred.
The gas syringe markings are quite accurate, but most syringes have a degree of stickiness. This allows the plunger to be moved in and out by 2 or 3 cm3, with the correct reading probably being somewhere near the middle of this movement. Given this, it is unlikely that the syringe is accurate to more than ± 1 cm3. This gives a percentage error of 1/72 = ± 1.4%.
This gives a total measurable error of ± 2.2%.
Another error which occurs is the loss of some gas in the short time between adding the calcium and placing the bung in the test tube. This is a systematic error. It will always lead to a smaller volume of gas being measured, and therefore a lower purity for the calcium.
We have also assumed that the apparatus is at room temperature and pressure (we could, of course, always have measured the temperature and pressure!). However, it is unlikely that either is far out, so this should only introduce a very small error.
It is always possible that some gas may have leaked from the apparatus, also leading to a smaller value. This should be avoidable, though.
Improvements
Only one result is given. The first obvious improvement is to repeat the experiment to ensure consistent results.
The problem of the initial gas loss can be avoided through a change of apparatus and method. You can find out how in exercise 4.
A more accurate balance (± 0.0001 g) would reduce the weighing error, but is unlikely to be available in school. We could also reduce the weighing error with a larger mass, but this would require a larger gas syringe (not readily available) for the volume measurement. A more accurate method of volume measurement would reduce the 1.4% error.
Problems with sodium
Safety issues are more concerning here. The reaction is considerably more rapid than with calcium. This may cause a greater error if gas loss is more significant before the apparatus has the bung inserted. Because sodium is so reactive it is stored under oil (to prevent reaction with air and water). This oil will have to be removed before the metal is added to the water. It will be difficult to remove all the oil so this will lead to an additional weighing error.