The molar volume of hydrogen gas at STP is calculated using the combined gas law:
According to the combined gas law:
The molar volume of hydrogen gas at STP is
Theoretical value:
Molar volume of hydrogen gas
Percentage error
100%
4.02%
Trial 2
Raw Data Table
Reference Data Table
*All these reference data are from the supervisor.
Observation
This time, faster and more vigorous reaction occurred than first trial reaction. Many bubbles spurted up along the burette. The surface of the HCl solution falls rather quickly.
The tiny flow of liquid was still present in this trial.
No fragment fell from the Magnesium ribbon and no bubbles leak out of the burette. No obvious mistakes were made during the operation.
It took a less time for the reaction to go to the completion than the first trial.
Calculation
The number of moles of hydrogen gas produced is calculated through the reaction that it undergoes:
The molar volume of hydrogen gas at STP is calculated using the combined gas law:
According to the combined gas law:
The molar volume of hydrogen gas at STP is
Theoretical value:
Molar volume of hydrogen gas
Percentage error
100%
1.34%
Conclusion
Two results of molar volume of hydrogen have percentage errors of 2% and 3%, respectively. These percentage errors are from the calculation of mole of hydrogen gas. The mole of hydrogen gas equals the mole of magnesium. Although the mass of magnesium is measured by the electronic scale and has a very small systematic error of 0.001g, the percentage error is relatively large. It is because of the small measurement value of magnesium, which is about 0.040g. Thus, the mole of magnesium has percentage error of 2% and 3% respectively in two trials. Percentage errors of other values, like temperature and volume of hydrogen gas, are all below 0.3%. They are so small that have no effect on the final percentage error when added up with percentage error of mole. As a result, the percentage errors of moles of hydrogen gas are exactly the same as the final percentage errors.
Two calculated values of molar volume are
and
. They are both smaller than the acceptable value and have a percentage error of 4.02% and 1.34% respectively. At the beginning, I suppose these systematic errors are due to the dilation of hydrochloric acid. There was a tiny flow of liquid out of the burette and the sunken magnesium fragment produced bubbles. Both are evidences that hydrochloric acid solution in the burette mixed with water in the beaker and the concentration of solution in the burette fell. However, I denied the idea soon because no lump remained in the gauze after the reaction went to the completion. So I suppose the source of systematic errors is the measurement of hydrogen gas produced. In the first trial, I observed many tiny bubbles attached to the gauze during the reaction. Hydrogen is weakly soluble in the water and these hydrogen bubbles might be dissolved in HCl solution instead of coming to the surface. This caused the measured value of hydrogen gas produced and thus the result of calculation to be slightly smaller than the actual values.
The result from the second trial is relatively accurate. The theoretical value of 22.4
is within the range of
. This means that my method is acceptable and my measurement is relatively right.
In contrast to the second one, the first value of molar volume is less accurate. The theoretical value of even out of the range
. Since I used the same method as the second trial, method is not the source of systematic error. This indicates that some mistakes were made during the operation. The relatively large percentage error of 4.02% is mainly owing to the small fragment of magnesium fallen into the beaker. The actual mass of magnesium took part in the reaction is smaller than the measurement value of magnesium mass. However, the slightly larger, inaccurate measurement value is still used in the calculation. So the calculated mole of hydrogen gas produced is bigger than the actual value. In addition, hydrogen bubbles dissolved in the solution caused the measured volume of hydrogen gas to be slightly smaller than the actual volume. The molar volume is calculated by dividing the volume with the mole. Since the measurement of volume is smaller and the mole is bigger than the actual value, the result is relatively larger than the theoretical value.
Although the first result is less accurate, it has a higher precision than the second, more accurate one. The random uncertainty of the first is only
, while the second has a relatively high random uncertainty of
. The great difference between random uncertainties owes to difference in percentage errors of the mole of hydrogen gas produced. The percentage uncertainties of the mole of hydrogen are 2% and 3% respectively, which are exactly the same as percentage uncertainties of the final results. These relatively high percentage uncertainties account to the small mass of magnesium. Although the mass is measured by the electronic scale and has a quite small uncertainty of only
, the measured value of mass is also quite small, about 0.040g. It makes the percentage uncertainty relatively large. So the slight difference in the mass of magnesium causes the percentage uncertainties to be relatively large.
Evaluation
To reduce the systematic error to the least extent, the experiment should be improved in several aspects. The magnesium ribbon should not be torn into several small pieces to prevent the falling of magnesium fragment. It would make the calculated result more accurate. To reduce the amount of hydrogen gas dissolved in the solution, I would increase the rate of reaction by using HCl solution of a slightly higher concentration. Then, the time needed to complete the reaction would decrease a lot and the accuracy of the result would be higher as well. Also using the purer and untarnished magnesium ribbon would increase the accuracy.
To reduce the random error, the random error of the mole of hydrogen should be reduced mainly. The mole of hydrogen gas produce equals the mole of magnesium in the reaction. The percentage uncertainty of magnesium mass can be reduced by a larger mass of magnesium consumed. Thus, increasing both the mass of magnesium and concentration of hydrochloric acid would increase the precision of the result value.
by
youhyunlee (student)
