Calculations and Conversions

1. Calculations and Conversions LAT Chapter 14

2. LAT Presentations Study Tips • If viewing this in PowerPoint, use the icon to run the show. • Mac users go to “Slide Show > View Show” in menu bar • Click on the Audio icon: when it appears on the left of the slide to hear the narration. • From “File > Print” in the menu bar, choose “notes pages”, “slides 3 per page” or “outline view” for taking notes as you listen and watch the presentation. • Start your own notebook with a 3 ring binder, for later study!

3. Calculations & Conversions • Experimental methodology requires calculation. • water consumption, record and convert temperatures, determine the floor area of a cage, detergent solution • Pharmacology: the science of drugs, their composition, use, and administration • The amount of a drug administered to a patient, based on the species and body weight (usually noted in milligrams of drug per kilogram body weight or mg/kg) = dosage. • The dosage is also influenced by an animal’s age, health, and state of excitement.

4. Conversions • To determine dosages, it is often necessary to convert weights and volumes from one measuring system to the other (English to metric). • For example, a technician might be required to convert kilograms to pounds, centimeters to inches, or ounces to milliliters. • You can use tables or a conversion factor by which you either multiply or divide. • Generally we use ratios to convert metric to English systems or to change units of measurement within a system.

5. Dose Calculations 1 2.5% = 2.5 parts/100 parts, or in milligrams, 2.5 mg/100 mg 25 mg = 1000 mg1 ml ? Ml 25 mg x ? ml = 1000 mg x 1 ml 25 mg x ? ml = 1000 mg x 1 ml25 mg 25 mg ? ml = 1000 ml 25 ? ml = 40 ml 40 ml of dilutant must be added to prepare a 2.5% solution from 1000 mg of anesthetic.

6. Dose Calculations 1(part 2) 1000 mg = 300 mg40 ml ? ml 1000 mg x ? ml = 300 mg x 40 ml 1000 mg x ? ml = 300 mg x 40 ml1000 mg 1000 mg ? ml = 300 x 40 ml 1000 ? ml = 12 ml 12 ml of a 2.5% anesthetic solution contains 300 mg of anesthetic.

7. Dose Calculations 2 4/100 = 4% = 40 mg/ml 40 mg = 1000 mg1 ml ? Ml 40 mg x ? ml = 1000 mg x 1 ml 40 mg x ? ml = 1000 mg x 1 ml40 mg 40 mg ? ml = 1000 ml 40 ? ml = 25 ml 25 ml of dilutant must be added to prepare a 4% solution from 1000 mg of anesthetic.

8. Dose Calculations 2 (part 2) 18kg x 2.2 lb = 39.6 lb kg 1 ml = ? Ml 5 lb 39.6 lb ? ml x 5 lb = 1 ml x 39.6 lb ? ml x 5 lb = 1 ml x 39.6 lb 5 lb 5 lb ? ml = 39.6 ml 5 ? ml = 7.92 ml

9. Conversion of % Solutions • Solutions are homogeneous mixtures of two or more constituents. • A solution can take the form of a gas, a liquid, or a solid. • Gaseous solutions are made by dissolving one gas in another. • Since all gases mix in all proportions, any mixture of two or more gases is homogeneous and is a solution. • In solid solutions one component is randomly dispersed on an atomic or molecular scale throughout another component. • Liquid solutions are made by dissolving a gas, liquid, or solid in a liquid. • If the liquid is water, the solution is called an aqueous solution.

10. Solution Components • In making up a solution, at least one constituent must be a solute and one a solvent. • Substance present in larger amount = solvent. • Substance present in the smaller amount = solute. • % of solute may = % by weight or % by volume. • % by weight = total solution mass of solute. • % weight in volume (w/v) expresses the no. of grams of solute in 100 milliliters (ml) of solvent. • % weight in weight (w/w) expresses the no. of grams of solute in 100 grams of solvent.

11. Solution Components pt.2 • 5 g of dextrose dissolved in sufficient water to bring the final volume to 100 ml is a 5 % dextrose solution by weight in volume (w/v). • Set up in ratio fashion to translate them into a more useful expression of mg/g or mg/ml.5 g = ? g100 ml 1 ml100 ml x ? g = 1 ml x 5 g? = 0.05 g/mlor, since there are 1000 mg/g? = 50 mg/ml A simple way to translate % into mg/ml or mg/g is to move the decimal point one place to the right. For example:5.0 % = 50 mg/ml2.2 % = 22 mg/ml20.0 % = 200 mg/ml

12. Percent by Volume • % by volume is the percent of the final solution volume represented by the volume of the solute taken to make the solution (v/v). • For example, a 12 % alcohol solution by volume would be a solution made from 12 ml of alcohol and enough solvent to bring the total volume up to 100 ml.

13. Molar Solutions • Molecular weight = sum of atomic weights of atoms in a molecule. • A 1-molar solution contains the molecular weight (MW) in grams of that compound per liter of solution. • To make an aqueous solution of cobalt chloride (CoCl2) it would be necessary to calculate the MW of CoCl2 from the Periodic Table: Atomic mass of Co = 58.85 x 1 = 58.85Atomic mass of Cl = 35.5 x 2 = 71.00Molecular Weight in g of CoCl2 = 129.85 • 1 M solution of CoCl2, 129.85 g of CoCl2 are weighed & dissolved in water to a total volume of 1000 ml, or 1 L. • If 2 moles are needed, 129.85 x 2, which equals 259.7 g/L. This weight of cobalt chloride is added to a 1-liter volumetric flask, & the flask is filled to the one liter mark with water, giving a final volume of 1 liter of a 2M solution of CoCl2.

14. Molality • No. of moles of solute per 1000 grams of solvent. • Therefore, a 1-molar aqueous solution of sucrose, C12H22Oll, contains 342.2 g of sucrose in 1000 g of water. • This is calculated by multiplying the atomic mass of each substance by its respective number of moles. • C12H22O11Atomic Mass of C = 12.0 x 12 = 144.0Atomic Mass of H = 1.01 x 22 = 22.2Atomic Mass of O = 16.0 x 11 = 176.0Molecular weight of sucrose in g = 342.2

15. Statistics, Calculations and Conversions Additional Material and Review

16. Statistics, Calculations and Conversions Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of numerical data. The collection of the raw data is the most important step in the use of statistics to make valid conclusions about the topic being studied. Statistics are usually used to determine if any differences exist between treated groups and control groups of animals.

17. Statistics, Calculations and Conversions • Terminology Validity - conclusions are correctly drawn from the data Random, Random Selection, Random Number Tables - members in a given set have an equal probability of an event occurring Populations - sets of animals or objects that have some common characteristic Samples - subsets of the population Parameters - measurable characteristics Bias - tendency to deviate from the truth

18. Statistics, Calculations and Conversions Conversions - change weights or volumes from one measuring system to another using a conversion factor 1 inch = 2.54 cm 1 kilogram = 2.2 pounds 1 gallon = 3.87 liters 1 mile = 1.6 kilometer

19. 1/2 gram = 500 mg 1 ml of H2O = 1 gram 5% = 5 parts/100 parts or 5 mg/100 mg or 50 mg/1000 mg = 50mg/ml 50 mg = 500 mg 50 mg(? ml) = 500 mg (1ml) 1 ml ? ml 50 mg (?ml) = 500 mg (1 ml) ? ml = 500 mg ? ml = 10 50 mg 50 mg 50 mg Statistics, Calculations and Conversions Dose calculations: Reconstitute 1/2 gram antibiotic powder to give a 5% solution and give a 25 mg dose to the animal

20. Statistics, Calculations and Conversions Dose calculations: Reconstitute 1/2 gram antibiotic powder to give a 5% solution and give a 25 mg dose to the animal 500 mg = 25 mg 10 ml ? ml 500 mg (? ml) = 25 mg (10 ml) ? ml = 25 mg (10 ml) 500 ? ml = 0.5

21. Liquid solutions are made by dissolving gas, liquid, or solid into a liquid; if water is used, this is referred to as an aqueous solution. Statistics, Calculations and Conversions Solutions are homogenous mixtures of 2 or more constituents and can be gas, liquid, or solid.

22. Statistics, Calculations and Conversions Solutions = solute and solvent Percent by weight = total mass contributed by solute Percent weight in volume (w/v) = grams of solute/100 mls solvent Percent weight in weight (w/w) = grams of solute/100 grams solvent Percent by volume (v/v) = percent of final solution volume made up by the solute volume

23. Molecular weights are listed in the Periodic Table in the upper right CCl4 1 Carbon + 4 Chloride = 12g X 1 mole + 35.5 X 4 = 12 + 142 = 154 grams Statistics, Calculations and Conversions Mole = quantity of atoms = 6.022 X 1023 = Avagadro’s number A one molar solution = 1 M = molecular wt in grams/liter solution

24. Statistics, Calculations and Conversions Normality = N = the number of equivalents of solute/liter of solution The number of equivalents = actual weight of the substance/equivalent weight Equivalent weight = Atomic weight/valence

25. Statistics, Calculations and Conversions Valence (Net positive valence) = (Valence of + element) X (its subscript) NaCl K2CO3 CaSO4 AlCl3 Fe2(SO4) 3 1 X 1 = 1 1 X 2 = 2 2 X 1 = 2 3 X 1 = 3 3 X 2 = 6 Equivalent wt = Molecular weight/Net positive valence 58.5/1 138/2 136/2 133.5/3 400/6

26. Statistics, Calculations and Conversions 58.5/1 138/2 136/2 133.5/3 400/6 58.5 69 68 44.5 66.6 The number of equivalents = actual weight of the substance/equivalent weight. Normality = N = the number of equivalents of solute/liter of solution. Normality = molarity X net positive valence. Therefore, normality will always be equal to or greater than molarity.

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