It is also very important to note the conditions of room temperature and pressure, since these values for ambient temperature and pressure are assumed to be equivalent to the conditions of the gas released. Using an electronic device to measure these conditions yielded quite precise values.
Fig. 5
A Table to Show Ambient Conditions
Collating, Interpreting and Analysing Results:
Known Values
(I) Mass of Test tube, KMnO4(s), Cotton Wool Prior to Heating: 32.433 ± 0.002g
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Mass of Test tube, Solid Remnant, Cotton Wool After Heating: 32.325 ± 0.002g
Final Volume of Gas Present at ≈ STP: 89.0 cm3 ± 0.5 cm3 = 8.9 x 10-5 m3 ± 5 x 10-7 m3
Ambient Temperature: 294.5 K ± 0.25 K
Ambient Pressure: 101300 Pa ± 2 Pa
Calculation of Key Values
Mass of O2 released:
m(O2) = m(I) – m(II)
= 32.433 – 32.325
m(O2) = 0.108 ± 0.004g
The molar mass of O2 is also relevant for processing:
M(O) = 16.00 g.mol-1
M(O2) = 32.00 g.mol-1
Now that the specific mass of oxygen occupying the final volume of 89.0 cm3 has been found, by applying the gas equations a value for the empirical gas constant and molar volume for oxygen can be determined. Observing that all values composing the Ideal Gas Equation (p.V = n.R.T) have been established or can be directly deduced, with the exception of R, all that is necessary is to solve for the empirical gas constant.
Rearranging the Ideal Gas Equation;
p.V = n.R.T
p.V = (m/M).R.T
R =[p.V.M]/[m.T]
Now substitute in known values to solve for “R”
R =[(101300 N.m-1)(8.9x10-5 m3)(32.00 g.mol-1)]/[(0.108 g)(294.5 K)]
R = 9.07 J.K-1.mol-1
So an empirically determined gas constant has been found, though it deviates from the literature value by about 0.8 J.K-1.mol-1, and there are several associated errors present in the calculation alone. It is therefore useful to find the absolute error associated with the determined value for R. The percentage error of the experimental result is easily calculated by taking the sum of parts;
m(O2) = 0.108 ± 0.004g → ± 100/27 % or ± 3.70 %
M(O2) = 32.00 (assume effectively no error)
VF(O2) = 8.9 x 10-5 m3 ± 5 x 10-7 m3 → ± 50/89 % or ± 0.562 %
Temp. = 294.5 K ± 0.25 K → ± 50/589 % or ± 0.0849 %
Pressure = 101300 Pa ± 2 Pa → ± 2/1013 % or ± 0.00197 %
Total Percentage Error (sum of all % errors):
(100/27)+(50/89)+(50/589)+(2/1013) = 4.35 %
⏐error⏐ = 0.0435 x 9.07
= ± 0.395
NOTE: technically, a greater uncertainty is associated with the experimentally determined mass due to various random and systematic errors, but some of these will be discussed later
Now an absolute error has been found for the experimentally determined gas constant, so the value can be accurately expressed as:
R = 9.07 ± 0.395 J.K-1.mol-1 at 294.5 K and 101300 Pa
Using the data collected during this experiment, it is also possible to calculate the volume of one mole of oxygen gas (i.e. to empirically determine the molar volume of an ideal gas at ≈ STP). For this calculation, applying the Pressure Law, see that:
(P1V1)/T1 = (P2V2)/T2
[(101300 N.m-1)(8.9x10-5 m3)]/(294.5 K) = [(101325 N.m-1)(V2)]/(273 K)
V2 = [(101300 N.m-1)(8.9x10-5 m3)(273 K)]/[(294.5 K)(101325 N.m-1)]
V2 = 8.25 x 10-5 m3
The actual volume of the same quantity of gas would have this value, but to find the molar volume of oxygen, this volume must be divided by the number of moles present:
n(O2) = 0.108/32.00
n(O2) = 27/8000 ≈ 0.003375 mol
Now divide the volume by the number of moles present;
(8.25 x 10-5 m3)/(27/8000) = 0.0244 m3.mol-1
= 24.4 dm3.mol-1
The same relative/percentage errors are associated with this figure, since each value is multiplied or divided by the other in much the same fashion. Hence;
Total Percentage Error (sum of all % errors):
(100/27)+(50/89)+(50/589)+(2/1013) = 4.35 %
⏐error⏐ = 0.0435 x 24.4
= ± 1.06
Now an absolute error has been found for the experimentally determined molar volume of oxygen at STP, so the value can be accurately expressed as:
VM(STP) = 24.4 ± 1.06 dm3.mol-1 at 273 K and 101325 Pa
*NOTE: This value was determined independent of the established “R” value, and is based on extrapolated ambient temperature and pressure (at STP, in fact).
Comparison with Literature Values:
The literature value of the Gas Constant is 8.31 J.K-1.mol-1 at 273 K and 101325 Pa. The empirically determined value found by processing the results of this experiment was 9.07 ± 0.395 J.K-1.mol-1 at 294.5 K and 101300 Pa. Clearly the conditions under which the experiment were carried out differed from STP, so results are already tainted, but the percentage difference is of some interest:
⏐error⏐ = 9.07 – 8.31
= ± 0.760
relative = 0.760/8.31
= 0.0915
percentage = ± 9.15 % deviation
Hence, the empirically determined “R” is approximately 9.15% off the literature value. Interestingly, 4.35% of this error has already been accounted for by systematic error calculations, leaving less than a ±5% deviation. Under normal conditions, real gases are said to deviate in their behaviour from ideal gases by approximately 4%, so really less than 1% of the error is left unaccounted for by systematic and inherent errors. This 0.80% anomaly is easily accounted for by various gross and random errors that will be discussed later, but most obviously, the experiment was not carried out at STP, so values for both the gas constant and the molar volume at STP are obviously tainted.
The literature value of the molar volume of an ideal gas at STP is 22.4 dm3.mol-1. The empirically determined value was 24.4 dm3.mol-1 under conditions extrapolated to STP. Since conditions were closer to SLC, again the results may have been tainted – though extrapolation to STP by the Pressure Law more or less removes this effect. The percentage error is calculated thus:
⏐error⏐ = 24.4 – 22.4
= ± 2.0
relative = 2.0/22.4
= 0.0893
percentage = ± 8.93 % deviation
Hence the empirically determined molar volume is approximately 8.93% off the literature value. Again, 4.35% of the error is accounted for by systematic error and real gases deviate from ideal gases by about 4%. This leaves only 0.58% of the error to be accounted for by other various errors discussed later.
Conclusion:
Through experimental investigation, the gas constant (R) was found to be: 9.07 ± 0.395 J.K-1.mol-1 at 294.5 K and 101300 Pa. This value deviates only 9.15% from the literature value for the gas constant, and most of the deviation (≈8.35%) is accounted for by systematic or inherent error. The molar volume of oxygen (and of an ideal gas) extrapolated to STP was found to be: 24.4 dm3.mol-1 at STP. This value deviates only 8.93% from the literature value for the molar volume of an ideal gas at STP, and once again, most of the deviation (≈8.35%) is accounted for by systematic or inherent error. The empirically determined values do appear to approximate the literature values to the degrees of accuracy permitted by experimental procedure.
Evaluation:
The values for both the gas constant and the molar volume were, while reasonably accurate to the accepted literature values (as demonstrated above), not so precise as to avoid significant absolute errors.
Results of others who perform this experiment may vary for several reasons, which are much the same reasons for the imprecision of these results. The margin of percentage error is largely accounted for by systematic errors, indicating minimal experimental erratum, but several obvious errors may have had a significant impact on results. Most obviously, although both the ideal gas constant and molar volume are specifically contiguous with STP, the actual experiment was carried out at 21.5°C and 101300 Pa – closer to SLC. 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:
Gross/Random – cotton wool placed in test-tube below bung
- Some solid remnant may have escaped during heating, thus increasing the perceived mass of oxygen released
Gross/Random – apparatus allowed to cool substantially (≈10mins)
- Apparatus may not have been allowed to cool to room temperature, thus the oxygen may not have been in thermal equilibrium with surroundings, so temperature/pressure readings may have differed from the actual condition of the oxygen
Random – no method of controlling this factor
- Temperature and pressure neither constant nor SLC or STP; building heaters activated sporadically leading to variation of room temp. Also, body temperature of many students may have raised room temperature
Gross/Random – syringes set almost horizontal
- Gas syringe not entirely horizontal, so gravity may effect level of gas in syringe
Random – no method of controlling this factor
- Syringe may have jammed or experienced friction – thus increasing the pressure the incoming gas was under; may have been held/influenced by wire safety string coiled about plunger
Random – no method of controlling this factor; negligible
- Gas may have been lost through the system; through gaps in the bung, leaks in the syringe, space between plunger and syringe wall
Systematic
-
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 (random error), so results may be affected in this way. These uncertainties have been included in calculations above without working.
*NOTE: Since relatively small masses are involved, even a minute error of ± 0.002g becomes significant, as shown above.
Gross
-
There is also an error of ± 0.5 cm3 associated with the gas syringe due to parallax
It is likely that a culmination of these errors – with an emphasis on a failure to reach room temperature on cooling and a divergence from STP/SLC in the actual conditions of the experiment – resulted in a degree of imprecision in these results. Regardless, the results were still reasonably accurate considering the lapse of STP/SLC and were more than sufficient to solve for empirical values for the gas constant and molar volume.
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 felt along with a possible failure to reach a room temperature and a neglect of STP/SLC. The key improvements to this experiment would therefore include:
- Since STP would be rather difficult to simulate in a school lab, performing the experiment at SLC – with correct temperature and pressure (298 K; 101325 Pa) – is a more plausible alternative. Such a modification would allow the comparison of definite literature values with empirical results.
- Tilting the gas syringes more substantially to reduce effects of gravity on volume
- Removing safety wire holding plunger in syringe and replace with a less tense string to avoid having the syringe inhibited
- Lubricate plunger to avoid friction inhibiting plunger
- Heat the sample more gently and use less of the potassium permanganate in order that all the gaseous oxygen of the sample may be removed and the scale of the syringe is not exceeded
- Allow much more time (in the order of hours) for the apparatus to cool and for the oxygen to reach room temperature and pressure in order that calculations are valid
- Collation of multiple results, or repetition of experiment to ensure a normal distribution of results finds a reasonably accurate mean result and that random errors are gradually reduced in effect
- Use of a larger quantity of potassium permanganate and more accurate gas syringes to reduce the associated percentage errors
- Use of multiple sets of balances (ideally of greater precision) to reduce the associated systematic errors
If these improvements were implemented, the accuracy of the results (and the precision with which the empirical values and the literature values matched) would certainly increase.
Chris Bolton
