To determine the molecular mass of an unknown alkali metal carbonate, X2CO3.

PROCEDURE:

1. The 50cm3 beaker was placed on the digital balance and the balance was calibrated to 0.  
2. Using the metal spoon, slowly and carefully, 1.5g of substance Z was weighed out into the 50cm3 beaker.
3. Distilled water was added to completely dissolve the solid mass of substance Z.
4. The solution was poured into the 250cm3 volumetric flask making sure no solid or solution was left behind in the 50cm3 beaker.
5. Enough distilled water was added to make a 250cm3 solution in the 250cm3 volumetric flask.
6. The 250cm3 of substance Z solution was kept aside.
7. Now, the 50cm3 burette was clamped onto the retort stand.
8. 0.1M HCl was poured from the stock solution container into the 100cm3 beaker.
9. Using the glass funnel, the burette was filled with 0.1M HCl up to the 0.00cm3 mark.
10. 25cm3 of substance Z solution was pipetted out into the Erlenmeyer flask.
11. The reaction site, was kept on top of the white tile and 3 drops of methyl orange indicator was added to the 25cm3 solution of substance Z solution.
12. The process of titration was started keeping in mind to keep swirling the flask at a constant rate.
13. Once orange color was obtained, the amount of 0.1M HCl used was recorded.
14. The experiment was repeated 2 more times with 1.5g of substance Z, 3 times with 2.0g of substance Z and finally, 3 times with 2.5g of substance Z.
15. All nine readings were recorded in the pre-made data tables.

Safety Precautions:

1. Throughout the experiment, a lab coat was worn so that any spills do not cause damage to clothes or body.
2. Covered shoes and Safety goggles were worn to avoid damage from spillage of HCl.
3. The work-table was wiped clean and dried before and after the experiment.

RAW DATA COLLECTION:

Volume of HCl required to neutralize each trial of each sample of substance Z solution was noted by reading the lower meniscus of the solution in the burette.

Table 1: Volume of HCl used to neutralize substance Z solutions in all trials.

DATA PROCESSING:

Average volume of HCl required to completely neutralize each of the basic substance Z solutions is determined by taking the arithmetic mean of the all the three trials for each solution containing 1.5g, 2.0g and 2.5g of substance Z.        

Sample calculation for finding the average volume of HCl required to completely neutralize 25.0cm3 solution containing 1.5g of substance Z:

 =  = 28.0cm3.  

Uncertainty for the value of average volume of HCl required for complete neutralization is ±0.10cm3 since averaging values do not lead to change in uncertainties.

This data is represented in the following table.

Table 2: Average volumes of substance Z solution and HCl used in all trials.

To determine the molar mass of X2CO3, we need to find the moles of X2CO3 that are present in 25.0cm3 of substance Z solution.

Part 1: Determining number of moles of X2CO3 in 1.5g of substance Z

Since 1.5g was used to make 250cm3, 25cm3 of solution is assumed to have 0.15g of X2CO3.

Number of moles (mol) = Concentration (mol/dm3) x volume (dm3).                                   Therefore, moles of HCl = Concentration of HCl (mol/dm3) × Volume of HCl (dm3)                                              = 0.1 ×                                                                                                              = 0.0028 moles

HCl reacts with substance Z according to the following balanced chemical equation:          

X2CO3 (aq.) + 2HCl → 2XCl (aq.) + CO2 (g) + H2O (l)

Therefore, it can be seen from the balanced equation of the reaction that every two moles of HCl require one mole of X2CO3 which means that 0.0028moles will require 0.0014moles of X2CO3.  

Since the reaction had reached completion, it can be assumed that the required 0.0014 moles of X2CO3 was present in the 25cm3 of the solution which was assumed to have 0.15g of X2CO3. Therefore, total mass of 0.0014 moles of X2CO3 is considered to be 0.15g.

 This formula can be rearranged to make molecular mass the subject → .

In this case,                                                                       =  = 107.14g/mol

Since, molecular mass of the Carbonate Ion (CO3-2) = 60.01g/mol; atomic mass of X is calculated by subtracting the mass of carbonate ion from the mass of X2CO3 and dividing the result by two;                                                                                                    = 23.56 g/mol.

Part 2: Determining number of moles in 2.0g of substance Z.

Since 2.0g was used to make 250cm3, 25cm3 of solution is assumed to have 0.20g of X2CO3.

Moles of HCl = 0.0037moles.

Therefore, 0.20g had 0.00185moles of X2CO3.

Therefore, molecular mass of X2CO3 =  = 108.1g/mol

Atomic mass of X =  = 24.045g/mol

Part 3: Determining number of moles 2.5g of substance Z.

Since 2.5g was used to make 250cm3, 25cm3 of solution is assumed to have 0.25g of X2CO3.

Moles of HCl = 0.00472moles.

Therefore, 0.25g had 0.00236moles of X2CO3.

Therefore, molecular mass of X2CO3 =  = 105.93g/mol

Atomic mass of X =  =22.945g/mol.

Summarizing the Results: The results of all the nine trials of titration of 0.1M HCl against the X2CO3 solutions are tabulated below:

Table 3: Atomic mass of X derived from the three trials of each sample.

The average atomic mass of X =  = 23.52g.mol-1.

Since the atomic mass of X (23.52g.mol-1) is closest to the atomic mass of Sodium   (22.99g/mol); it can be concluded that substance Z (X2CO3) is Sodium Carbonate (Na2CO3).

Therefore, the relative molecular mass of Na2CO3 = 107.05g/mol.        

Error Propagation:

Total error = Total random error + Total systematic error.  

To calculate the total random error, the percentage uncertainty of the lowest reading on each instrument shall be added together.

Percentage uncertainty =   

Table 3: Total Random Error Calculation.

Since X is determined to be Sodium, the literature value to be considered is the molecular mass of Na2CO3 which is 105.99g/mol (www.sigmaaldrich.com).

Therefore, percentage error in the derived value for the relative molecular mass of Sodium Carbonate                                                                                                       

CONCLUSION AND EVLUATION:

The results of our experiment have yielded very accurate results because the derived relative molecular mass of X2CO3, 107.05g/mol, is impressively close the literature value of 105.99g/mol. In fact, the total error percentage is smaller than the random error percentage; 1.00% < 1.15% which means that the literature value for the relative molecular mass of X2CO3 (105.99g/mol) lies within the range of derived values, 105.44g/mol to 108.66g/mol. Due to a respectably high accuracy and consistency in all our values, I can conclude with a large magnitude of confidence that the experiment was successful and indeed the compound Z, X2CO3 was Sodium Carbonate, Na2CO3.  

I feel that one of our major strengths in yielding such accurate results was our ability to recognize the end point of the acid-base titration with considerable accuracy. This made sure that the volume of 0.1M HCl required to neutralize the substance Z solution was not under or over stated.

Secondly, the high accuracy in the experimental data also owes to the fact that the compound Na2CO3 is stable in air which means that other than the inherent impurities, there is not much scope for contamination of the compound due to any significant reaction with air, like in the case of NaOH or other similar chemicals where storage under air tight conditions is a must.

Lastly, another factor that could be responsible for high accuracy is that while making the solutions of substance Z, not a single visible droplet of substance Z solution was left behind because the beaker had a non-stick coating on its inner walls and on top of that, all of us lab partners made sure that beaker was help in the up-side position for long enough for all solution to fall out into the volumetric flask.

Despite yielding quite accurate experimental results, there were limitations with the equipment and some systematic error was unavoidable. One such limitation was the inability of the digital balance to reach higher degrees of precision. Although the digital balance used was very precise with an uncertainty of only ±0.1g, the masses that were weighed out were very small and hence even a small absolute uncertainty translated into a large percentage uncertainty. In this case, the percentage uncertainty for the readings of the digital balance was 0.67% which is the largest percentage uncertainty in comparison to the other instruments such as the burette or the pipette. If these uncertainties could be avoided a result much closer to the literature would be possible to obtain.

Some other possible shortcomings to this experiment are also listed below:

1. The solid substance Z might not be pure Sodium Carbonate and some impurities present could have led to the overstatement of the value for the molecular mass of X2CO3. These impurities might have been introduced due to long storage periods and moisture from the air. Therefore, a more pure sample should preferably be used and it should be sifted to remove any clumps of moisture which might add unwanted mass to the sample.
2. The molarity of HCl was determined only from the label on the stock solution. However, over time, evaporation of water from the solution may lead to increase in molarity which in turn would lead to overstatement of the value for the molecular mass of X2CO3. This problem can be solved rather easily by simply making a standardized solution in the lab itself eliminating any dependence on the labels.
3. Parallax error in reading the burette might have led to overstatement or understatement of the value for the molecular mass of X2CO3. This can be avoided by using a mirror against the markings to obtain a more accurate readings and reading only the lower meniscus of the liquid in the burette.
4. Due to the continued usage of the white tile by various students for various experiments, it is unavoidable to have some stains on it. Our white tile had very minute yellowish stain on it which might have interfered with the orange color leading to some inaccuracies in reading the end-point of the reaction. Nonetheless, as much care as possible was taken but a very minor systematic error was unavoidable.

Overall, I would say that the experiment was satisfactory in the given conditions where both time and resource were limited. Alternate methods to obtain the molecular mass of unknown substance Z could be used in addition to this method after which, the results can be analyzed to give a much more accurate value for the molecular mass of X2CO3. However, in the time constraints of our lab classes, it was not possible to perform both experiments with the same level of accuracy and we chose not to perform two experiment because that would compromise with the accuracy of both.