Final answer:
The cost per mole of acid-neutralizing compound in the antacid tablet is calculated by first finding the moles of HCl neutralized by one tablet, then multiplying by the total number of tablets to find the total moles neutralized per bottle. Dividing the total cost of the bottle by the total moles gives the cost per mole. Further calculation to find cost per gram of the active ingredient is not possible without knowing the molar mass.
Step-by-step explanation:
To calculate the cost per acid-neutralizing compound in the tablet, we need to establish how much of the active ingredient neutralized the hydrochloric acid (HCl). First, we determine the moles of HCl reacted: (26.00 mL or 0.02600 L) × (0.650 M) = 0.0169 mol HCl. Next, we calculate the moles of sodium hydroxide (NaOH) used in back titration: (11.44 mL or 0.01144 L) × (1.05 M) = 0.012012 mol NaOH. Since the reaction is 1:1 according to the equation HCl + NaOH → NaCl + H2O, the moles of NaOH used is equal to the moles of HCl reacted. The unreacted moles of HCl would be the initial moles minus those reacted with NaOH: 0.0169 mol HCl - 0.012012 mol NaOH = 0.004888 mol HCl neutralized by the antacid.
Next step is to calculate the total moles of acid neutralized by the entire bottle of tablets. If one tablet neutralizes 0.004888 mol of HCl and there are 200 tablets in a bottle, then total moles neutralized is 0.004888 mol/tablet × 200 tablets = 0.9776 mol. With the total bottle cost at $5.99, the cost per mole of acid-neutralizing compound is $5.99/0.9776 mol = $6.13/mol.
Finally, we calculate the cost per gram of the active compound by finding the molar mass of the antacid (which would vary based on the active ingredient, but is not provided) and adjusting the previous cost per mole accordingly. Since we only have an average tablet weight, we cannot complete this last step without additional information on the composition of the tablet.