Streptomycin, an antibiotic, is produced on a large scale in the United States. The purified solution contains 50 wt% streptomycin water. Preparation of 500 mL intravenous (IV) drip solution bag requires addition of diluent and preservative. The diluent solution is 2 wt% NaCl in water. The preservative solution is 10 wt% diluent and 5 wt% NaCl in water. The final product, ready for packaging,contains 10 wt% streptomycin and 3% preservative.
(a) Sketch the IV drip bag preparation process, clearly identifying all variables of interest with an appropriate symbol and associated units.
(b) Develop an equation to determine the ratio of streptomycin solution to total solution.
(c) Develop an equation to determine the ratio of preservative solution to total solution.
(d) Develop an equation to determine the ratio of diluent solution to total solution.
(e) What is the NaCl content (wt%) in the final product?
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(a) In the IV drip bag preparation process, several variables are involved, and we need to identify them with appropriate symbols and units. Let's represent them as follows:
- Mass of streptomycin solution: Mstrep (grams)
- Mass of diluent solution: Mdiluent (grams)
- Mass of preservative solution: Mpreservative (grams)
- Total mass of final solution: Mtotal_solution (grams)
- Mass fraction of streptomycin in the purified solution: wstrep_purified (%wt)
- Volume of IV drip bag: Vdrip_bag (milliliters)
- Mass fraction of diluent in the diluent solution: wdiluent (%wt)
- Mass fraction of NaCl in the diluent solution: wNaCl_diluent (%wt)
- Mass fraction of diluent in the preservative solution: wdiluent_preservative (%wt)
- Mass fraction of NaCl in the preservative solution: wNaCl_preservative (%wt)
- Mass fraction of streptomycin in the final product: wstrep_final (%wt)
- Mass fraction of preservative in the final product: wpreservative_final (%wt)
- Mass fraction of NaCl in the final product: wNaCl_final (%wt)
(b) To determine the ratio of streptomycin solution to total solution, we can use the mass balance equation. The mass of streptomycin in the final product should be equal to the mass of streptomycin in the original purified solution. Therefore, we have:
Mstrep_final = wstrep_final * Mtotal_solution
Mstrep_purified = wstrep_purified * Mstrep
The ratio of streptomycin to total solution is then:
Ratio_strep = Mstrep_final / Mtotal_solution
(c) Similarly, to determine the ratio of preservative solution to total solution, we can use another mass balance equation. The mass of preservative in the final product should be equal to the mass of preservative in the diluent and preservative solutions. Therefore, we have:
Mpreservative_final = wpreservative_final * Mtotal_solution
Mpreservative_diluent = wdiluent_preservative * Mpreservative
Mpreservative = Mpreservative_diluent * wNaCl_preservative
The ratio of preservative to total solution is then:
Ratio_preservative = Mpreservative_final / Mtotal_solution
(d) To determine the ratio of diluent solution to total solution, we can again use a mass balance equation. The mass of diluent in the final product should be equal to the mass of diluent in the diluent and preservative solutions. Therefore, we have:
Mdiluent_final = (1 - Ratio_preservative - Ratio_strep) * Mtotal_solution
Mdiluent = Mdiluent_final - Mpreservative_diluent
The ratio of diluent to total solution is then:
Ratio_diluent = Mdiluent_final / Mtotal_solution
(e) To determine the NaCl content (wt%) in the final product, we can use another mass balance equation. The mass fraction of NaCl in the final product is equal to the mass fraction of NaCl in both the diluent and preservative solutions. Therefore, we have:
wNaCl_final = (Ratio_diluent * wNaCl_diluent + Ratio_preservative * wNaCl_preservative)
Now, you can plug in the known values for the various mass fractions and solve for wNaCl_final to find the NaCl content (wt%) in the final product.