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MT 301 LABORATORY MATHEMATICS

© Virginia Randolph

August 1997

For this topic area, you will help teach yourself. It will be your responsibility to fulfill all the objectives listed on the following page. This packet of information and math problems should help you to fulfill the objectives. If the sections and problems are not sufficient, references are listed at the end of each section. You have the responsibility of deciding how much time and effort you need to spend on this topic. It is imperative that you learn these math manipulations as they are used daily in the laboratory.

Discussion sessions will be held for those students desiring assistance. It is important for your learning that you come to the discussions prepared by having worked the appropriate problems and have questions concerning problem areas for you.

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Enclosed in this web site are:

  1. Objectives for the subject
  2. Pretest to let you know what will be expected
  3. Information and problems covering:
  4. Periodic Table of the Elements (given as handout)
  5. Formulas for problems
  6. Mock Exam
  7. Answers to the problems
  8. e-mail Virginia Randolph

One exam will be given, date to be announced. It will cover all of the objectives listed.

You may use a calculator.

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OBJECTIVES

Following completion of the problem sets and any extra material the student requires, the student will

1. Prepare easily legible graphs using the appropriate linear or semilogarithmic graph paper.

2. Determine the amount of standard required to obtain a working graph for a test procedure.

3. Solve solution preparation problems.

a. Molar

b. Normal

c. Percent (weight/weight, weight/volume, volume/volume)

d. Saturated

4. Solve preparation of solutions from previously prepared solutions.

5. Discuss titration of solutions with standard solutions to determine normality and calculate the true normality.

6. Calculate concentration of stock solutions, given the molecular formula, specific gravity, and percent concentration (purity).

7. Solve problems involving dilutions.

8. Calculate amount of hydrated versus anhydrous reagent to be used in reagent preparation.

9. Convert values in mg/dL to mM/L and mM/L to Mg/dL and convert currently used nomenclature to SI units.

10. Use metric system correctly.

11. Convert values in metric system to other values.

12. Convert between metric system and Avoirdupois weight and Fahrenheit temperature systems.

a. kilogram - pound

b. degrees Centigrade - degrees Fahrenheit

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CHECKLIST:

Keep track of the material and problems you have covered.

_____ Metric system nomenclature

_____ Convert values in metric system to other metric values

_____ Convert between metric system and nonmetric

a. kilogram - pound

b. degrees Centigrade - degrees Fahrenheit

_____ How to make Percent solution

_____ How to make Molar solution

_____ How to make Normal solution

_____ Determining Percent concentration

_____ Determining Molar concentration

_____ Determining Normal concentration

_____ Preparation of solutions from previously prepared solutions

_____ Determine concentration based on titration of solutions

_____ Calculate concentration of stock solutions, given the molecular formula, specific gravity, and percent concentration (purity).

_____ How to make Saturated solution problems

_____ Calculate amount of hydrated versus anhydrous reagent to be used in reagent preparation

_____ Solve problems involving dilutions

_____ Determine the amount of standard required to obtain a working graph for a test procedure

_____ Convert values in mg/dL to mM/L and mM/L to Mg/dL and convert currently used nomenclature to SI units

_____ Legible graphs using the appropriate linear or semilogarithmic graph paper

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PRE-TEST

NAME _____________________________________

This is a pre-test. This will give you an idea of what you know and what you will be learning. If you don't know how to do a problem, go on to the next question. Please do not do any random wild guessing. But if you want to try to rationalize or figure out a problem, go ahead. You will NOT get a grade on this. This will just help you and me know where we should start.

1. If a sycamore tree grows an average of 45 cm per year how tall will it be when the tree is 25-years old? What other object (not a tree) will be about the same size?

2. A sahuaro cactus grows 6 cm per year. How old is a 38m cactus? What other object is about the same size as 6 cm?

3. The test required that you pipet 2 mL of serum into 8 mL reagent A. Then take 1 mL of that solution and add it to 4 mL of solution B. What is the final dilution of the serum?

4. Your patient weighs 150 pounds. How many kilograms does he weigh?

5. Normal body temperature is 98°F. What is this in degrees centigrade?

6. Convert the following.

1 gram = _______ mg

1 meter = _______ mm

1 gram = _______ Kg

1 liter = _______ mL

2 ng = _______ mg

52 mg = _______ g

100 µL = _______ mL

7. You weighed out 4.5 g of CaCl2 and diluted it to 250 mL with distilled water. What is the percent solution (W/V)?

8. Referring to the previous problem, what is the molarity?

9. Again referring to Question 7, what is the normality?

10. How much NaOH would you have to weigh out to make 150 mL of 10N?

11. How much BaCl2 will you need to weigh to be equivalent to 88 g of BaCl2·5H20?

12. How much dry reagent would you weigh to make 1 liter of 2 N NH4OH?

13. How would you make 500 mL of 0.2 N CaCl2 solution from a stock (concentrated) solution with a specific gravity of 1.32 and 75% assay?

14. Convert 40 mg/dL Ca++ to mM/L.

15. A glucose of 95 mg/dL is equivalent to how many mM/L?

16. A urea [(NH2)2CO] of 3.5 mM/L would be equivalent to how much in mg/dL?

17. You have a series of 10 tubes, each of which contain 4 mL. You add 1 mL of serum to the first tube, mix and take 1 mL of this mixture and add to the second tube, mix and take 1 mL of this mixture and add to the next. If you continue this process with each tube, what is the dilution of the serum in the last tube?

18. If a patient's 24-hour urine volume is 1125 mL and has a creatinine of 75 mg/dL, how much creatinine was excreted in 24 hours?

19. How would you make a 1:3 serial dilution such that 2 mL are left in each tube?

20. A 150 mg/dL glucose solution was diluted 1:2. Then 0.5 mL of it was added to 4.5 mL saline. 2 mL of this solution was diluted to 10 mL. What is the final concentration of glucose?

21. How will you make 200 mL of a 25 mg/dL BUN working standard from a 1 mg/mL solution?

22. If the solubility of sodium acetate is 119 g/100 mL how will you make 50 mL of a saturated solution?

23. Plot the following information on linear graph paper. This information was developed by selecting 5 standard concentrations, performing a chemical test and measuring the results of the chemical reaction on an instrument.

Standard Concentration of

1.5 mg/dL and instrument value of 0.110

3 mg/dL and instrument value of 0.221

6 mg/dL and instrument value of 0.439

9 mg/dL and instrument value of 0.667

12 mg/dL and instrument value of 0.879

24. Plot the following information on semilog graph paper with concentration on the log axis.

  Standard Concentration             Instrument Value        
  1 mg/dL                            95%                     
  3 mg/dL                            65%                     
  5 mg/dL                            45%                     
  8 mg/dL                            25%                     
  10 mg/dL                           12%                     
  30 mg/dL                           10%                     

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