Ian Jacobi

Group 6

Section 01

September 20, 2004

Stoichiometry: Determination of Percent Mass of NaHCO3 in Alka Seltzer Tablets

A majority of substances in the world are by far mysterious with regards to their ingredients. While their ingredients may be known on labels, it is much less likely to know how much of each ingredients exists in the substance. Just as this is as important for real-life, it is especially important for chemistry purposes in which a chemist desires to determine the molecular formula of a substance, so as to better understand chemical reactions. One of the most important ways to determine the contents of a substance is to subject it to a reaction in which one of the reactants and one of the products is known and measurable. This particular experiment thus illustrates this method by attempting to determine how much sodium bicarbonate, the active agent of Alka Seltzer tablets, is present in these tablets.

The process by which the amount of sodium bicarbonate by mass can be determined is through stoichiometry. As a base, sodium bicarbonate will react with any acid in an acid-base reaction to create a salt, water, and carbon dioxide gas. For example, as in the stomach, when reacting with hydrochloric acid to produce sodium chloride:

or in this experiment, when reacting with acetic acid to create sodium acetate:

Given the fact that sodium bicarbonate will thus fizz in an acid, the fizzing being representative of the carbon dioxide given off, one might wonder what chemical reaction causes Alka-seltzer to fizz in water, given that water is neutral, rather than acidic. The solution is found in the fact that Alka-seltzer also contains an amount of citric acid that, when entering solution along with the sodium bicarbonate, will cause fizzing through the following reaction to create sodium citrate:

Given that the following experiment is performed with differing concentrations of acetic acid and water, the previous two equations should be considered during the course of the experiment.

The experiment is actually quite a simple one. By measuring the mass differential between the starting mass of the reactants (being various mixtures of water and acetic acid and the alka-seltzer tablet) and the measurable mass of the non-gaseous products, one can calculate the mass of carbon dioxide given off, and subsequently use this to calculate the moles of this, and then the moles, and then subsequently the mass of sodium bicarbonate. Finally, the percent mass of the sodium bicarbonate in the Alka-Seltzer tablet can be calculated from a simple division of the mass of sodium bicarbonate by the mass of the tablet.

The process by which these values can be measured however, is slightly more complicated. First, in order to calculate the initial mass of the reactants, the mass ofa quantity of 35 milliliters of differing parts water and acetic acid must be measured inside a beaker. Given that this experiment was run eight separate times, the portions of water and acetic acid vary depending on the trial run, varying in 5 milliliter increments from 35 milliliters of water to 35 milliliters of acetic acid. In any case, after these quantities of the liquids are carefully measured and placed in a beaker, the beaker's mass as well as its that of its solution is measured. While this may seem inaccurate due to the added mass of the beaker in the experiment, in the end it cancels out as the mass differential ignores the mass of the beaker, which will not change. In any case, the mass of the Alka-seltzer may be measured next, so as to obtain the second quantity necessary to calculate the entire initial mass.

Following these initial observations, the Alka-seltzer tablet is dropped carefully into the solution to allow for the reaction to take place. While the reaction is primarily over by the time that the fizzing had stopped, a considerable amount of carbon dioxide can still be found in solution, and further more, the mass of the final products can not be properly measured until the carbon dioxide bubbles that remain inside the beaker are properly removed from the solution. By swirling the solution however, one may properly and carefully remove almost all excess carbon dioxide in solution as well as the bubbles along the walls. Subsequently, one may finally measure the mass of the products and then solve for the mass of carbon dioxide released due to the conservation of mass. From this final mass, the initial mass (that is, the sum of the initial beaker mass and the alka-seltzer tablet) can be subtracted so as to calculate the mass differential, being (almost) entirely carbon dioxide.

Lastly, all calculations as listed above (that is the conversion of carbon dioxide mass to molar quantity, followed by the use of stoichiometry to convert such to molar quantity of sodium bicarbonate in the initial alka-seltzer tablet, and finally a mass, for which a percentage of the initial tablet mass can be calculated.

Reaction #	1	2	3	4	5	6	7	8
Volume of Acetic Acid (mL)	0	5	10	15	20	25	30	35
Volume of Water (mL)	35	30	25	20	15	10	5	0
Mass of solution and beaker (g)	49.197	48.905	48.651	49.068	48.790	48.674	49.046	49.454
Mass of Tablet (g)	3.249	3.036	3.237	3.349	3.212	3.228	3.250	3.157
Final mass of solution (g)	51.518	51.160	50.989	51.472	51.032	50.892	51.322	51.760

Table 1. Observed Values

The observations of our particular team (table 1) included an average mass of solution and beaker of about 49g, with minimal and unpredictable changes, even as the contents of the solution changed. This clearly indicates that the density of water and acetic acid is very nearly equal. Indeed, this correlates with the liquid density of acetic acid of 1.05 x 103 kg/m3 , which is very close to that of water: 1.00 x 103 kg/m3. Furthermore, barring the exception of test 2, the mass of the Alka-seltzer tablet also was within a close range of 3.25g. Lastly, the final measurements of volume appear to be rather standardized as well with no visible trend, approximating 51g, and varying roughly based on the mass of the solution. This can be illustrated through the mass differentials of the total initial mass (that is, the sum of tablet and initial solution masses) and the final masses (table 2).

Reaction #	1	2	3	4	5	6	7	8
Total initial mass (g)	52.446	51.941	51.888	52.417	52.002	51.902	52.296	52.611
Final mass (g)	51.518	51.160	50.989	51.472	51.032	50.892	51.322	51.760
Mass differential (g)	0.928	0.781	0.899	0.945	0.970	1.010	0.974	0.851

Table 2. Mass Differentials

Assuming that these mass differentials are due to carbon dioxide that has left solution in the sodium bicarbonate (as all other products either result in aqueous solutions or liquid water), the group was thus able to convert these masses into moles of carbon dioxide by dividing by the molar mass of carbon dioxide (44.0 amu ), which, according to the stoichiometric coefficients of the equations above, would inevitably equal the molar quantities of sodium bicarbonate. By multiplying this value by the molar mass of sodium bicarbonate (84.0 amu ), the mass of sodium bicarbonate can be calculated, and then divided into the mass of the tablets (as mentioned before) to calculate the percent mass of sodium bicarbonate in the tablet (table 3).

Reaction #	1	2	3	4	5	6	7	8
Carbon dioxide mass (g)	0.928	0.781	0.899	0.945	0.970	1.010	0.974	0.851
Moles of Carbon Dioxide	0.0211	0.0178	0.0204	0.0215	0.0220	0.0230	0.0221	0.0193
Moles of Sodium Bicarbonate	0.0211	0.0178	0.0204	0.0215	0.0220	0.0230	0.0221	0.0193
Mass of Sodium Bicarbonate	1.77	1.49	1.72	1.8	1.85	1.93	1.86	1.62
Mass percentage of Sodium Bicarbonate (%)	54.5	49.1	53.0	53.9	57.7	59.7	57.2	51.5

Table 3. Calculating Mass Percentage of Sodium Bicarbonate

While the exact chemical reaction that takes place when entering the solutions cannot be known, given that both the acetic acid and citric acid solutions both release one mole of carbon dioxide for each mole of sodium bicarbonate, it can be assumed that, regardless of what happened during the reaction, the amounts of carbon dioxide produced will be approximately equal to that of the sodium bicarbonate reacted. In the reactions where there are lower amounts of vinegar (especially in reaction 1), the only acid present is the citric acid which acts as a limiting reactant. As the amount of vinegar increases however, a greater amount of acid is present to react with the sodium bicarbonate, and thus the amount reacted will be slightly higher. This subtle trend is visible in the moles of sodium bicarbonate reacted (graph 1).

Graph 1. Trend of Sodium Bicarbonate Reacting in Reaction

While the second and eighth reactions are rather off the gradual trendline from 0.0200 to 0.0250 moles reacted that is most visible between the 10 to 25 milliliter reactions, the trendline is rather clearly visible, illustrating that the limiting reactant is slowly becoming no longer limiting. Unfortunately, the errors present in reactions 2 and 8 present an incomplete trendline, ideally, as the limiting reactant changes from the acids needed to dissolve the sodium bicarbonate to the sodium bicarbonate itself, the amount of sodium bicarbonate reacted would ideally level off to a limited point (limited as mentioned before, by the sodium bicarbonate).

Furthermore, the amount of sodium bicarbonate that was anticipated to be reacted can be calculated approximately from the sum of the moles of acetic acid and citric acid present and utilising stoichiometry to calculate the limiting reactant, assuming that one mole of acid is necessary to react with one mole of sodium bicarbonate by the above reactions (table 4). The mass of citric acid and mass of sodium bicarbonate is assumed to be 1000mg and 1916mg respectively, assumed from the literature values present on the Alka-seltzer labels. The mass of acetic acid is calculated by multiplying the percentage of acetic acid in solution (4%) by the density listed above (1.05 g/mL) by the volumes listed above. The molar mass of citric acid assumed is 192.13 amu , and the molar mass of acetic acid is 60.05 amu .

Reaction #	1	2	3	4	5	6	7	8
Mass of Citric Acid (g)	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
Mass of Acetic Acid (g)	0.0	0.2	0.42	0.63	0.84	1.1	1.3	1.5
Moles of Acetic Acid	0.0	0.003	0.0070	0.010	0.014	0.017	0.021	0.024
Moles of Citric Acid	0.005205	0.005205	0.005205	0.005205	0.005205	0.005205	0.005205	0.005205
Moles of Acid able to react	0.0	0.009	0.012	0.016	0.019	0.023	0.026	0.030
Moles of Sodium Bicarbonate able to react	0.0228	0.0228	0.0228	0.0228	0.0228	0.0228	0.0228	0.0228
Moles of Sodium Bicarbonate anticipated to react	0.0	0.009	0.012	0.016	0.019	0.0228	0.0228	0.0228
Limiting Reactant	Acid	Acid	Acid	Acid	Acid	NaHCO3	NaHCO3	NaHCO3

Table 4. Anticipated reaction amounts

Clearly, as can be seen even by comparing values of the anticipated reactions to that of the actual reactions, there is a fairly large percentage error (table 5). In part, this percentage error can be attributed to experimental errors, such as not accounting for the amount of water that spattered out due to the bubbling of the carbon dioxide (which would cause the moles of sodium bicarbonate reacted to appear higher, due to a slightly greater mass loss than anticipated. Furthermore, as a significant bit of water spattered out of the beaker in reaction #2, the amount of reaction there is significantly higher than it should be.

Reaction #	1	2	3	4	5	6	7	8
Moles of Sodium Bicarbonate anticipated to react	0.0	0.009	0.012	0.016	0.019	0.0228	0.0228	0.0228
Moles of Sodium Bicarbonate reacted	0.0211	0.0178	0.0204	0.0215	0.0220	0.0230	0.0221	0.0193
Percent Error	Infinite	97.22	70.27	34.23	16.03	0.68	-2.91	-2.91

Table 5. Percent Error Calculations

The percentage error is rather surprising through experiment 4, perhaps due to the water not being distilled, instead being taken from the tap (which may or may not be more acidic, thus leading to further chemical reactions unaccounted for.

In any case, the above lab clearly shows at least some illustration of the use of stoichiometry in the calculation of percentage mass. Interestingly enough, however, it also proves quite clearly that a side-effect of stoichiometry and reactions with limited quantities of reactants, the limiting reactant, also proves to partially foil attempts to measure the percentage mass from one mere circumstance in which the amount of acid present in a solution is such that it actally limits the amount of sodium bicarbonate reacted, thus giving a false impression of the percentage mass. This makes it extremely important to be liberal in attempts to measure percent mass through reactions, though this carefulness leads to even more need to be careful in cases of titration experiments.

http://en.wikipedia.org/wiki/Sodium_bicarbonate

http://en.wikipedia.org/wiki/Sodium_bicarbonate

http://en.wikipedia.org/wiki/Acetic_acid

http://en.wikipedia.org/wiki/Carbon_dioxide

http://en.wikipedia.org/wiki/Sodium_bicarbonate

http://en.wikipedia.org/wiki/Citric_acid

http://en.wikipedia.org/wiki/Acetic_acid

2004-09-20T20:05:03