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Math for the Pharmacy Technician: Concepts and Calculations

Math for the Pharmacy Technician: Concepts and Calculations. Egler • Booth. Chapter 9: Special Preparations and Calculations. Special Preparations and Calculations. Learning Objectives. Determine the percentages of solutions, dilutions, and solids. Prepare solutions from a concentrate.

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Math for the Pharmacy Technician: Concepts and Calculations

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  1. Math for the Pharmacy Technician: Concepts and Calculations Egler • Booth Chapter 9: Special Preparations and Calculations

  2. Special Preparations and Calculations

  3. Learning Objectives • Determine the percentages of solutions, dilutions, and solids. • Prepare solutions from a concentrate. • Prepare a compound. • Measure insulin doses accurately. When you have successfully completed Chapter 9, you will have mastered skills to be able to:

  4. Introduction • You may be required to have additional knowledge related to dosage calculations • This special knowledge will require specialized calculations • Preparation of solutions • Alligations • Insulin

  5. Compounds • When two or more chemicals are mixed together to make a specific mixture or solution, it is known as a compound in the pharmacy industry. • It is occasionally necessary to prepare a solution “from scratch,” dilute a solution that is more concentrated than what is needed, or mix two solids together.

  6. Preparation of Solutions, Dilutions, and Solids • Solutions are liquid mixtures containing 2 or more chemicals. • Solvent – used to dissolve other chemicals. • Solutes – chemicals dissolved in the solvent. • Common solvent is water. • Universal solvent • Normal saline = 0.9% sodium chloride in every 100 mL of solution.

  7. Preparation of Solutions, Dilutions, and Solids (cont.) • Common examples of manufacturer solutions. • Injections • Eye drops • Cough syrups • You may have to prepare a solution “from scratch”.

  8. Final Volume/Final Strength • As a pharmacy technician you may have to find the final volume, initial volume, initial strength, or final strength of a mixture. To find the missing value you can use either the ratio proportion method or the fractional proportion method. • As you work through this chapter, both methods are used to solve for final volume/final strength.

  9. Final Volume/Final Strength (con’t) • Set up the equation for ratio proportion method as: Final volume : initial volume : : initial strength : final strength • Set up the equation for the fraction proportion method as:

  10. Percentage Concentrations • Common way to express concentrations is in percentages. • Percent means “per hundred.” • How much solute is found in every 100 mL of solution?

  11. Percentage Concentrations (con’t) • Solid solute • % = grams of the solute in 100 mL • 2% lidocaine = contains 2 g of lidocaine in every 100 mL of solution • Liquid solute • % = milliliters of the solute in 100 mL • 70% isopropyl alcohol has 70 mL of isopropyl alcohol in every 100 mL solution

  12. Percentage Concentrations (con’t) • Solid solute and solid solvent • % = grams of the solute in 100 g of the product • 2% hydrocortisone ointment means that 100 g of ointment will contain 2 g of hydrocortisone

  13. Preparing % Solutions and Solids • You must first measure the solute • Then add sufficient quantity of solvent to bring the total to desired volume

  14. 2% Lidocaine Solution Lidocaine 2 g Water *qsad 100 mL Review and PracticePreparing % Solutions and Solids (con’t) A “recipe” for preparing 100 mL of 2% lidocaine solution would look like this: *qsad = “sufficient quantity to adjust the dimensions to”

  15. 10% zinc oxide Zinc oxide 10 g Petroleum jelly 90 g Review and PracticePreparing % Solutions and Solids (con’t) Write the recipe for preparing 100 g of 10% zinc oxide powder and petroleum jelly.

  16. Preparing a Dilution from a Concentrate • You may need to prepare a solution from a concentrated solution that is already prepared. • Alligation method • Use of formula

  17. Preparing a Dilution from a Concentrate (con’t) To prepare a dilution from a concentrate, determine: Vn = the volume needed Cn = the concentration needed Ca = the concentration(s) available* * If water is being used, one of the these concentrations is zero. Then use the alligation method or formula to obtain your answer

  18. Alligation Method • Write out a tic-tac-toe grid and fill in the following values. • Find the total number of parts in the solution by adding the 2 values in the right column.

  19. Alligation Method (con’t)

  20. Alligation Method (con’t) • Find the volume of 1 part by dividing the total number of parts into the volume needed. • Multiply the volume of 1 part (answer from Step 3) by the number in the top right of the grid. The result is the amount of the more concentrated solution needed.

  21. Alligation Method (con’t) • Add a sufficient quantity of the less concentrated solution to bring the final volume up to the desired volume.

  22. Review and PracticeAlligation Method (con’t) How would you prepare 500 mL of 50% ethanol from 90% ethanol? Desired volume is 500 mL - you would dilute the 90% by adding water up to a final volume of 500 mL.

  23. Preparing a Dilution from a Concentrate – Formula Method* 1. Identify the following information: Cn = the concentration needed Ca= the concentration available Vn = volume needed 2. Solve for: Va = the volume available *The formula method can only be used when one of the solutions has a concentration of 0%, such as water.

  24. Preparing a Dilution from a Concentrate – Formula Method (cont.) • Plug the values into the following formula: • Cancel units • Solve for the equation for Vn

  25. 50% Ethanol 90% ethanol 278 mL Water qsad 500 mL Review and PracticePreparing a Dilution from a Concentrate – Formula Method How would you prepare 500 mL of 50% ethanol from 90% ethanol? Answer: 278 mL of 90% ethanol solution is needed to prepare 500 mL of a 50% solution

  26. Insulin • Insulin is a pancreatic hormone that stimulates glucose metabolism. • People who have low or no insulin production may have insulin-dependent diabetes. • They often need routine injections of insulin to keep their glucose (blood sugar) from rising to levels that could be life threatening. • Rotate injection sites. • Insulin is commonly supplied in a 10-mL vial.

  27. Insulin Syringes • Insulin administration is different from other types of injections. • The syringe measures the amount of insulin rather than a volume of solution. • Must use special insulin syringes marked in units.

  28. Insulin Syringes(con’t) • Standard U-100 syringes hold up to 100 units per 1mL solution. • Calibrated for every 2 units or some in each unit. • Smaller syringes hold up to • 50 units (0.5 mL of solution) • 30 units

  29. Insulin Syringes(con’t) • For more accurate measurements, use a 50-unit insulin syringe for insulin doses less than 50 units when available, and a U-30 insulin syringe for insulin doses less than 30 units of 100 units/mL of insulin if these syringes are available.

  30. Review and PracticeInsulin Syringes (con’t) Decide which syringe to use. Ordered: Humulin R 55 units Answer – 100-unit syringe and fill it to between the 54 and 56 units line

  31. Insulin Syringes(con’t) • U-500 insulin is used for patients with highly elevated blood sugars. • Insulin may be given by IV. • Use tuberculin or standard syringe when U-500 or doses over 100 units are ordered. • These doses will not fit in a 100-unit syringe.

  32. Insulin Syringes(con’t) When using U-500 or a dose of insulin over 100 units use a tuberculin or standard syringe.

  33. Review and PracticeInsulin Syringes(con’t) Determine amount of insulin to give. Ordered: Humulin R U-500 insulin 80 units Administer 0.16 mL in a tuberculin syringe

  34. Special Preparations and Calculations These calculations, like all other calculations, require attention to detail and 100 percent accuracy; completing them successfully will help you step into your new career as a pharmacy technician. THE END

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