The Coca-Cola Company considers the recipe for making Coke a trade secret and is patented. Mark Pendergrast generated Formula X, which estimates the recipe for making Coke. Formula X estimates that Coke contains 30 lbs of sugar in 2.5 gallons of water. The objective of the experiment is to test whether Formula X is consistent with the concentration of generic Coke. The experiment involves estimating the molarity of generic Coke, creating a solution with concentrations equal to that of generic Coke and a Formula X solution.
Data Analysis and Calculations
Molecular Formula of Sucrose, Sucrose
Molecular Formula of Sucrose = 12 C + 22H + 110
= (12*12.0107) + (22*1.0078) + (11*15.999) = 342.2890
The atomic mass of sucrose,
is 342.2890 g/mol
Figure 1
Information Box Output
Grams of sucrose in 1 Liter =
Grams of sucrose in 1 Liter = *0.638613 * 342.2890 = 218.59021 g
Grams of Sucrose in 93.954mL = Molarity * Volume in L * Molecular formula mass of Sucrose
Grams of Sucrose in 93.954mL = *0.638613 * 342.2890 = 20.53796414 g
Molarity estimates the concentration of a solution by giving the moles of solute present in 1 liter of the solution. The molarity of generic Coke is 0.638613 moles per liter, implying that 1 liter contains 218.59021 grams of sucrose. Using the molarity, we can estimate the number of moles in any volume of the generic. The recorded volume of generic Coke is 93.954 mL and contains 20.53796414 g.
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Making solution with equal concentration as Generic Coke
A solution of known concentration can be prepared by dissolving a solute of known volume. To establish accuracy, prepare three solutions of different volumes 100 mL, 250 mL, and 500 mL. For the different volumes, the procedure begins with selecting the mass in grams of sucrose.
Procedure
The first step is to measure the appropriate mass of a solute
The mass of sucrose in 1000 mL is 218.59021 g.
To create a 100ml solution, estimate the mass of sucrose in 100mL.
Grams of Sucrose in 100 mL = Molarity * Volume in L * Molecular formula mass of sucrose
(Soult, 2019).
Grams of Sucrose in 100 mL = *0.638613 * 342.2890 = 21.85902052 g
Accurately measure 21.8590g and place it in a 250mL conical flask.
Add distilled water until the solute is fully dissolved.
Transfer the solution to a 100 mL conical flask and fill distilled water to the 100 mL mark.
Repeat the procedure three more times to establish accuracy.
In procedure 2, create a 250 mL solution
Grams of Sucrose in 250 mL = Molarity * Volume in L * Molecular formula mass of sucrose (Soult, 2019).
Grams of Sucrose in 250 mL = *0.638613 * 342.2890 = 54.64755129g
In procedure 3, create a 500mL solution.
Grams of Sucrose in 500 mL = Molarity * Volume in L * Molecular formula mass of sucrose (Soult, 2019).
Grams of Sucrose in 500 mL = *0.638613 * 342.2890 = 109.2951026 g
In all the procedures, record the details in the information box.
Results
Results for Procedure 1
Figure 2
Information Box Output
Results for Procedure 2
Figure 3
Information Box Output
Results for Procedure 3
Figure 4
Information Box Output
In each of the experiment trials, the molarity is equal to 0.638635. The established molarity is approximately equal to the molarity of generic Coke 0.638613. The results confirm the accuracy of the procedure used in creating a solution similar to the concentration of generic Coke.
Making Solution with equal concentration as Formula X
Data analysis and Calculations to find the concentration of formula X solution.
1 lb = 0.453592 kg = 453.592 g
30lb =30 * 453.592 g = 13607.76 g
1 gallon = 3.78541L
25 gallons = 2.5 * 3.78541 L = 9.463525 L
Concentration of Formula X solution in g/L = 13607.76 g/ 9.463525 L = 1437.917 g/L
Concentration of Formula X solution in g/mL = 13607.76 g/ 9463.525 L = 1.437917 g/L
Molarity = (Soult, 2019)
Moles of solute =
The solute is sucrose
Molecular Formula of Sucrose , Sucrose
Molecular Formula of Sucrose = 12 C + 22H + 110
= (12*12.0107) + (22*1.0078) + (11*15.999) = 342.2890
The atomic mass of sucrose, is 342.2890 g/mol
Moles of sucrose in 1 liter = 1437.917 g/ 342.2890 g/mol = 4.200884728 moles
Molarity of formula X=
Molarity of formula X= 4.200884728 moles/ 1 L = 4.20088 moles/Liter
Making solution with equal concentration as Formula X
The concentration of Formula X is 1437.917 g/L. We prepare as a solution using Formula X by dissolving known grams of sucrose in the known volume. To establish accuracy, prepare three solutions of different volumes 100 mL, 250 mL, and 500 mL. For the different volumes, the procedure begins with establishing the mass in grams of sucrose.
Procedure
The first step is to mesure the appropriate mass of a solute
The mass of sucrose in 1000 mL is 1437.917 g.
To create a 100ml solution, estimate the mass of sucrose in 100mL.
Grams of Sucrose in 100 mL = mass in g/L * Volume in L
Grams of Sucrose in 100 mL = 1437.917 g/L* 0.1L = 143.7917 grams
Accurately measure 143.7917 g and place it in a 250mL conical flask.
Add distilled water until the solute is fully dissolved.
Transfer the solution to a 100 mL conical flask and fill distilled water to the 100 mL mark.
Repeat the procedure three more times to establish accuracy.
In procedure 2, create a 50 mL solution
Grams of Sucrose in 50 mL = mass in g/L * Volume in L
Grams of Sucrose in 50 mL = 1437.917 g/L* 0.05L = 71.89583163 grams
In procedure 3, create a 25 mL solution.
Grams of Sucrose in 25 mL = mass in g/L * Volume in L
Grams of Sucrose in 25 mL = 1437.917 g/L* 0.025L = 35.94791581 grams
In all the procedures, record the details in the information box.
Results
In all the experiments, the solute is too much to dissolve in the respective milliliters of distilled water. The virtual lab cannot make a solution similar to Formula X because the volume of the solute is too high such that adding distilled water surpass the estimated volume.
The atomic mass of sucrose, is 342.2890 g/mol
Moles of sucrose in 1 liter = 1437.917 g/ 342.2890 g/mol = 4.200884728 moles
Molarity of formula X=
Molarity of formula X= 4.200884728 moles/ 1 L = 4.20088 moles/Liter
Conclusion
The concentration of generic Coke is 218.59021 g/L as compared to 1437.917 g/L of Formula X solution. Similarly, the molarity of generic Coke is 0.6386 moles/liter relative to 4.20088 moles/liter. The concentration of sugar in formula X solution is significantly above the concentration of generic Coke. The formula advanced by Mark Pendergrast estimating that has 30 lbs of sugar in 2.5 gallons of water is wrong.
References
ChemCollective. (2021). Cola and sucrose concentration problem . https://chemcollective.org/activities/vlab/66
Soult, A. (2019, June 10). 8.1: Concentrations of solutions . Chemistry LibreTexts. https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Book%3A_Chemistry_for_Allied_Health_(Soult)/08%3A_Properties_of_Solutions/8.01%3A_Concentrations_of_Solutions#
