Session 4 - Calculating the gas constant, R
Mg+2HCl -> MgCl2+H2
Ideal Gas law: PV=nRT
Table 1: Showing the results obtained during the experiment
Table 2: Showing the lab conditions
Table 3: Showing useful information needed for the calculations
- Calculations Explanation
We had to convert all our data so that it came out with the corresponding SI unit. We did this because in order to calculate R (gas constant), we needed to use the Ideal Gas law, in which pressure is measured in atm, volume in L, temperature in K, the gas constant in atm*L/K mol and the number particles in moles.
First of all, we measured the pressure in atm as it is the SI unit for pressure. We knew that the pressure of the room was 767.0 mmHg. We also knew that 1 atm= 760 mmHg. So we transformed it by dividing 767.0/ 760 multiplied by 1. The result was 1.009210526. When we divide, we must maintain the smallest number of significant figures, in this case 4. So, the final result was 1.009 atm.
Secondly, we measured the volume in L as it is the SI unit for pressure. We had it in mL, therefore we’ve got to convert it into L by dividing it by 1000, as 1 L is equal to 1000 mL.
So, as we had 11.1 mL, if we divide it by 1000, it comes out as 0.0111 L. This is because when we are dividing, we must maintain the smallest number of significant figures which in this case is 3.
Then, we measured the water temperature, which SI unit is K (kelvins). The thermometer gave us the temperature in celsius (ºC) so we had to convert it by adding 273: 273+22.2=295.2K. (When adding we must maintain the smallest number of decimal places, in this case 1)
Furthermore, we measured the number of moles of magnesium with the equation: moles= mass(g)/molecular mass(g/mol). We know that we have 0.0100 g of the substance and its molecular mass is of 24.31 g/mol. With this information, we can replace the values we know to find out the number of moles of magnesium like this: 0.0100/24.31= 0.0004113533525 moles. As we know that when we are dividing data from the lab, the result comes out with the less number of significant figures, which in this case is 3, therefore our result will be: 0.000411 moles of magnesium.
Moreover, as we know from studying stoichiometry last year, Mr Canning has given us the reaction equation, and both H2 and Mg have the same coefficient, so we know that they both have the same amount of moles, so therefore there will be 0.000411 moles.
Finally, we replace all of the results we’ve got from the calculations in the Ideal Gas Equation, now that we’ve got all of them with the right measurements (SI units), so that we can calculate our gas constant and compare it to the one it would actually be and calculate the percentage error to deduce some conclusions.
PV=nRT // 1.009·0.0111=0.000411·R·295.2 // 0.0112=0.121·R // R=0.0112/0.121 // R= 0.0923 atm l /K mol. Throughout all the operations we considered the number of significant figures, so finally, as we know that we dividing or multiplying we must maintain the least number of significant figures, which in this case is 3, so it will finally come out as:
R=0.0923 atml/Kmol
- Conclusion
Considering the Literature value of R is 0.082 the one we obtained , 0.0923 , is really close to it, although it is slightly bigger than the Literature one and this could have been originated by some mistakes we will mention in the Evaluation.
Now, we will calculate the percentage error to see the accuracy of our results:
% error = Experimental Value of R- Literature Value of R
_______________________________________ *100
Literature Value of R
% error = 0.0929- 0.082 % error= 0.0109
____________ *100// _______ *100// % error= 0.1329268292682927*100//
0.082 0.082
% error= 13.29268292682927 This will eventually come out as 13%. The percentage error we obtained is low, so this means we didn’t make lots of mistakes when doing the experiment. Although, Mr. Canning told us the percentage error must be under 10 to consider the experiment totally precise.Even though the results we obtained weren’t perfect, they were clear and precise enough for us to see what happens during the experiment.
Image showing the reaction between Magnesium and Hydrochloric acid.
Image showing pieces of Magnesium used during the experiment.- Evaluation:
We used an accurate method to collect the data for this experiment. Although, there could have been several errors that could have spoiled the experiment. Magnesium was exposed to air so it could have started to react a little bit and could have vary the results. Also, when we weighed it probably it wasn’t pure Magnesium but maybe Magnesium Oxide due to the air. This could have affected the final value of R and made it more inaccurate.This is a random error. We took turns to fill the beaker: The first time it was Ainhoa who filled the beaker and the second time I filled it. This could have maybe originated a mistake because not all humans have the same view, so this is a random error. Maybe, Ainhoa filled it a bit more than I did or vice versa. This could be improved next time by establishing an exact quantity of water to fill the beaker with and making sure the beaker is filled by the same person always. While doing the experiment we assumed that the pressure of the room was equal to the pressure of the tube and this was probably incorrect. This can have caused the value of R we obtained to be incorrect and can be considered a random error. This can be improved by using a small pressure sensor and putting it inside the tube to control the pressure.Probably the temperature of the gas wasn’t the same as the temperature of the water.This is also considered a random error and could be improved by putting a thermometer inside the test tube to control the temperature. An error that could have caused variations in our results was the incorrect calibration of the balance, which is a systematic error. We had to weigh the magnesium several times because we obtained different weights each time. This could be improved by making sure the balance is well calibrated and by weighing several times the substance used to make sure the weight the balance shows is correct. Other very common mistake in experiments like this is the incorrect reading of the thermometer or the meniscus. This is called a Systematic Parralax Error. This could be improved by placing your eye at the level of the appropriate measurement marking when measuring the level of a liquid in a graduated cylinder. Read the lower part of the curved surface of the liquid (the meniscus) to obtain an accurate measurement and avoid parallax errors. It’s also really important to deep the piece of Magnesium in a bit amount of acid for a short period of time to clean and purify it. We didn’t take into consideration that maybe the pieces of Magnesium weren’t the same size and so this could have made our results imprecise, so next time we have to make sure all the pieces of magnesium have the same size. Maybe, we didn’t close well the top of the test tube so a bit of gas escaped while the reaction occurred, next time we should make sure it’s well closed. Another mistake that could have altered our results is that maybe we didn’t pour the distilled water as slowly as we should have done and this could have caused the mix and spread of Hydrochloric Acid. A A thing that is crucial for the results of an experiment to be reliable is to use new equipment or clean it and dry to avoid substances to mix and vary results. Also, we could have done more tests to get more precise and reliable results as this reduces random errors, but we didn’t have time to do it.
As we can see above, there are lots of things that can be improved for the next time we repeat this experiment and make it more precise. 
