Measurement

Abstract

Emphasis is placed on understanding the measurements, the operation of prescription balances, and the responsibility of the operator to carry out measurements as accurate as possible in order to avoid causing human casualties. The concept of measurement is explained first by an extensive description of accuracy versus precision of measured values. You can use the exact quantitative definition described in this chapter to classify measurements as accurate and/or precise, and you can further perfect your skills by solving the carefully selected multiple-choice, true or false, fill in the gaps, or computational problems. A connection to the pharmaceutical field is made through various examples that demonstrate that, as with all other applied sciences, appropriate units should accompany a meaningful measurement. It is also explained that measurements are obtained with laboratory instruments, and as such, they are always accompanied by an error. The magnitude of the error or uncertainty in a measurement is dependent not only on the analytical instrument but also on the skills and knowledge of the operator. The impact of accurate dose measurements in the livelihood of patients is also demonstrated, thus explicitly denoting that it is the responsibility of every scientist to be aware of measurement uncertainties.

Exercises

• 1.1 How is accuracy different from precision?

• 1.2 Write a definition of the sensitivity requirement of a balance equal to 6 mg.

• 1.3 Mark the statements below as True or False:

  • (a) A precise measurement is always accurate.

  • (b) An accurate measurement is always precise.

  • (c) Only accurate measurements are precise.

  • (d) Only precise measurements are accurate.

  • (e) Measurements that have exactly the same value are precise.

  • (f) Measurements that have exactly the same value are accurate.

  • (g) Precise measurements have values close to each other even if none of them is near the true or correct value.

  • (h) Accurate measurements have values close to each other even if none of them is near the true or correct value.

  • (i) An experimental measurement can be precise or accurate but not both.

  • (j) An average value of a set of measurements is said to be precise if it is near the true (or ideal or correct) value.

  • (k) An average value of a set of measurements is said to be accurate if it is near the true (or ideal or correct) value.

• 1.4 Fill in the blanks:

  • (a) A measurement which is very close to the true value is designated as _____________.

  • (b) _____________ is defined as the closeness of measurements to each other.

• 1.5 The sensitivity requirement of a balance is 6 mg. Calculate the smallest weight that would lead to a maximum potential error of 5%.

  • (Answer: 120 mg)

• 1.6 The minimum allowable weight of a balance is 135 mg. What is the SR of the balance if the maximum allowable error is 5%?

  • (Answer: cannot be determined)

• 1.7 A student measured five times the same tablet (true weight = 90 mg) using the same analytical balance (SR = 1.4 mg). Given the set of values below, choose the correct statement:

  90.1

  88.1

  90.8

  88.8

  91.3

  This set of measurements can best be described as:

  • (A) Accurate and precise

  • (B) Accurate but not precise

  • (C) Precise but not accurate

• 1.8 A student measured five times the same tablet (true weight = 90 mg) using the same analytical balance (SR = 1.4 mg). Given the set of values below:

90.1

88.1

90.8

88.8

91.3

• (a) How many measurements should be discarded to render her data precise?

• (b) How many measurements can be considered as accurate?

  • (Answer: (a) only one; either the 88.1 or the 91.3 but not both; (b) all of them but the 88.1)

• 1.9 A prescription balance weighing 0.120 g of drug is more precise than a balance weighing 0.1208 g. True or False?

• 1.10 A student measured the weight of a capsule (true value = 69.70 g) on a balance with SR = 0.2 g, three times, 66.79 g, 66.70 g, and 66.69 g. Can these measurements be designated as accurate?

• 1.11 You are preparing an o/w emulsion for oral administration. Addition of 1 mL (23 drops) of vanillin per 10 L of emulsion is recommended to mask the bad odor of the drug. Due to a stream of air from the ventilation system, the drops are prematurely cutoff from the glass pipet. As a result, 23 drops are equivalent to 0.83 mL. Calculate the error and % error in the measurement.

  • (Answer: −0.17 mL; −17%)

• 1.12 You need to make 1 L of 9% NaCl. You weigh out 90 g NaCl but instead of dissolving the salt with water and diluting it up to 1 L of solution, you dissolved it with 1 L of water, thus making a total volume of 1035 mL. Calculate (a) the error and % error incurred in the volume measurement, (b) the error and % error in NaCl concentration.

  • (Answer: (a) 35 mL; 3.5%; (b) –3.04 g/L, − 3.4%)

• 1.13 A prescription calls for 8.940 g of KCl dissolved in 120 mL of syrup for a patient who is treated for hypokalemia. The signa of the prescription is “i tbsp p.o. b.i.d. p.c.” If potassium chloride was weighed out with a 0.5% error, what is the true weight of KCl? How much KCl is contained in each dose?

  • (Answer: 8.9847 g; 1.1231 g)

• 1.14 You are preparing 20 doses of codeine phosphate for cough relief. Each dose is 15 mg of codeine phosphate in one teaspoonful of cherry syrup. Codeine phosphate was weighed with a 1% error. What is the sensitivity requirement of the balance?

  • (Answer: 3 mg)

• 1.15 A dermatologist prescribed 50 g of 0.5% w/w hydrocortisone ointment. You used a class III prescription balance that has a sensitivity of 6 mg to weigh hydrocortisone powder. Calculate the % error introduced in the measurement.

  (Hint: 0.5% w/w hydrocortisone = 0.5 g of hydrocortisone in 100 g of ointment)

  • (Answer: 2.4%)

• 1.16 ℞

  Menthol		0.15
  Phenol liquefied		0.5
  ZnO
  Talc	aa	4.0
  Propylene glycol		11.0
  2-Propanol		3 fξ

  (Assume: 1 fξ = 30 mL)

  Specific gravity of: 2-propanol = 0.79; phenol = 0.95; propylene glycol = 1.25.

  Ingredient quantities are in grams unless otherwise specified. In preparing the antiseptic lotion above, you weighed ZnO with a 1.5% error. What is the actual amount of ZnO in the lotion?

  • (Answer: 4.06 g)

• 1.17 Calculate the actual volume transferred if the error associated with measuring 24 mL using a 100 mL graduated cylinder is 3%.

  • (Answer: 24.72 mL)

• 1.18 A prescription for earache relief calls for 8.33 mg of ethyl aminobenzoate per mL of glycerin. You are using a balance that has an SR of 4 mg. How many mL of the ear drop formulation should you prepare if the error in the active ingredient should not exceed 10%?

  • (Answer: 4.80 mL)

• 1.19 Calculate the desired volume if the resultant error after “accurately” transferring 6.7 mL were −0.30 mL.

  • (Answer: 7.00 mL)

• 1.20 Thirty doses of a drug were weighed on a balance that has an SR of 5 mg. The error associated with the measurement was 2%. How much drug is in a single dose?

  • (Answer: 8.33 mg)

1.1.1 Additional Exercises

• 1.21 What is the error and % error in the measurement if the actual volume measured is 0.3 mL smaller than the theoretical value?

  • (Answer: −0.3 mL)

• 1.22 Using a high precision spectroscopic method, the actual amount of drug W was found to be 0.15 times bigger than the desired one in a compounded prescription. What is the error and % error incurred in the original weighing?

  • (Answer: 15%)

• 1.23 Calculate the SR of a balance if a 10 mg weight deflects the pointer two divisions from the zero point of the index (neglect human error). What would you do to ensure that the SR you calculated is the correct one?

  • (Answer: 5 mg)

• 1.24 A medical dropper delivers 0.05 mL/drop of purified water when is held vertically. At 20° angle, the dropper delivers 0.045 mL/drop. Unfortunately, you calibrated the dropper at a vertical position but you measured the water for the prescription holding the dropper at a 20° angle.

  • (a) What is the volume error and % error for 3.4 mL volume?

  • (b) Which number is not affected by the value of the desired total volume, the error or the % error?

  • (c) What is the error and % error for 13.6 mL volume?

  • (d) Calculate the error and % error associated with 34 drops.

    • (Answer: (a) –0.34 mL, −10%; (b) % error; (c) –1.36 mL, −10%; (d) –0.17 mL, −10%)

• 1.25 Guaifenesin was weighed on a balance that has a sensitivity requirement of 7 mg and dissolved in 140 mL of cherry syrup. The error in the weighing was 10%. Calculate the concentration in mg/mL and mol/L of the drug in the syrup (MW = 198.21).

  • (Answer: 0.5 mg/mL; 0.00252 mol/L)

• 1.26 You have prepared 120 mL of 4.2% w/v boric acid eyewash solution. When the solution was tested using an HPLC (high-performance liquid chromatography) instrument, the concentration of boric acid was found to be 4.3% w/v.

• (a) How much boric acid did you use to prepare the wash solution?

• (b) Assuming no error in the HPLC analysis, what is the error and % error associated with the weighing of boric acid?

  (Hint: 4.2% w/v boric acid = 4.2 g of boric acid in 100 mL of solution)

  • (Answer: (a) 5.16 g; (b) 0.12 g, 2.38%)

• 1.27 Purified water was placed in a graduated cylinder and weighed on a balance. Using as density of purified water 1 g/mL, it was found that a 1.25% error occurred for measuring 23 mL of water. What is the actual volume of water in the graduated cylinder?

  • (Answer: 23.29 mL)

• 1.28 Isotonic saline was prepared by diluting 100 mL of 9% w/v NaCl stock solution to 1 L with water.

  • (a) What is the actual volume of 9% NaCl used if the % error associated with the transfer of the stock solution was 3.33?

  • (b) What is the actual concentration of the final solution?

    (Hint: 0.9% w/v NaCl = 0.9 g of NaCl in 100 mL of solution)

    • (Answer: (a) 96.67 mL; (b) 0.87%)

• 1.29 You were asked to dissolve 1 g of lyophilized drug powder with 1 mL sterile saline solution. Because you ran out of 1 mL syringes, you used the much higher capacity 10 mL syringe and you actually transferred 1.1 mL. Calculate (a) the % error in the volume measurement; (b) the final concentration in g/mL; (c) % error in drug concentration.

  • (Answer: (a) 10%; (b) 0.909 g/mL; (c) −9.09%)

• 1.30-32 Instructions for preparing antibiotic solution from lyophilized powder are usually supplied in a package insert as shown below.

• AMPICILLIN SODIUM

• PACKAGE INSERT

• DIRECTIONS FOR USE

  Use only freshly prepared solutions. Intramuscular or intravenous injections should be administered within 1 h after preparation, since the potency may decrease significantly after this period.

  Intramuscular Administration—Reconstitute as directed in the table below with sterile water for injection, USP, or bacteriostatic water for injection. Shake well until dissolved.

Vial size	Diluent to be added	Approximate available volume	Average concentration
125 mg	1.2 mL	1.0 mL	125 mg/mL
250 mg	1.0 mL	1.0 mL	250 mg/mL
500 mg	1.8 mL	2.0 mL	250 mg/mL
1 ga	3.5 mL	4.0 mL	250 mg/mL
2 g	6.8 mL	8.0 mL	250 mg/mL

1. ^aThe 1 g vial should be reconstituted only with sterile water for injection or bacteriostatic water for injection

• 1.30 The directions for intramuscular injection required reconstitution of a 2 g vial with 6.8 mL of sterile water for injection. You did not carefully read the table and added 8 mL which is the volume written in the adjacent column. What is the error and % error introduced in the measurement of volume?

  • (Answer: 1.2 mL; 17.65%)

• 1.31 Addition of 1 mL of sterile water in a 250 mg ampicillin sodium vial should make the concentration of antibiotic equal to 250 mg/mL. The concentration in the vial analyzed by high-performance liquid chromatography (HPLC) was found to be 232 mg/mL.

  • (a) Calculate the actual volume of the solution in the vial.

  • (b) What is the error and % error in ampicillin sodium concentration?

    • (Answer: (a) 1.078 mL; (b) 18 mg/mL, −7.2%)

• 1.32 During reconstitution of 250 mg vial of ampicillin sodium, backpressure caused 0.22 mL of sterile water for injection to spill out. What is the concentration of the antibiotic in the reconstituted vial?

  • (Answer: cannot be calculated)