Pharmaceutical Calculations practice exam 1 worked answers PDF

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Dr Jan Daly...

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A GPHC-APPROVED CALCULATOR IS PERMITTED FACULTY OF SCIENCE AND ENGINEERING SCHOOL OF PHARMACY FORMATIVE EXAMINATION PAPER ______________________________________________________________ Module Code : 5PY022 Examination title: Pharmaceutical Calculations Sitting: Formative paper 1 Date: December 2020 Year leader: Dr Ayman Antoun Reyad Examiner: Dr Jan Daly Time Allowed: 1 hour ______________________________________________________________ Instructions to candidates: This is a closed book examination. The assessment consists of 20 ‘fill in the box’ questions to be completed in 1 hour. Print your name and student number clearly in the space provided at the bottom of this page. Attempt ALL questions. The pass mark is determined by cut-scoring and there is no negative marking. Write your final answer in the ‘Answer’ section at the bottom of each question, using the pre-printed answer grid. Your final answer must be written in the answer grid using a pencil. If you wish to change an answer, rub out your first solution carefully, taking care not to smudge across the boxes, then re-write your answer clearly. The decimal point is already placed on the answer grid. When completing the answer grid use the pre-entered decimal point to guide you. For example if the answer is 118 tablets, fill in the answer as shown below. For whole numbers, do not enter zeros after the decimal point.

Decimal points are provided. If the answer contains a decimal point, use the decimal point that is pre-entered. For example if the answer to a question is 450.5 g, fill in the answer as shown below.

Do not use commas. For example if the answer is four hundred and thirty thousand units, write this as 430 000 as shown below.

However, if the answer is less than 1, then enter a ‘leading’ zero, e.g. write 0.15 mL as shown below

It is an examination requirement that you show a logical working out process to arrive at a computed answer. Accordingly, even where a submitted answer is correct, it will not be awarded a mark in the absence of a logical working out method with supporting numerical data. Read the questions carefully, and ensure that all answers are expressed in the units specified in the answer box

Student name: …………Worked answers……………

Student number: ………N/A…………….. 1

A calculator is permitted. Write your final answer for each question clearly in the ‘Answer’ box Question 1 Disinfectant D is available as a 90%v/v stock solution. The local community hospital asks you to prepare 5.25 L of 0.06% v/v disinfectant solution for cleaning hard surfaces. How many mL(s) of the stock solution are required? Give your answer to 1 decimal place Using C1V1 = C2V2 convert 5.25 L to mL (so using same units) => 5250 mL

90 x V1 = 0.06 x 5250 => V1 = (0.06 x 5250)/90 = 315/90 = 3.5 mL

Answer:

mL(s)

Question 2 An injection is available as a 1 in 8000 solution. The dose for a child is 87.5 micrograms. How many mL(s) of injection will contain a child’s dose? Give your answer to 1 decimal place. By definition 1 in 8000 => 1 g in 8000 mL = 1,000,000 micrograms in 8000 mL By simple proportion: API (micrograms) Volume of product (mL)

1,000,000 8000

87.5 ?

Answer:

? = 8000 x 87.5 = 0.7 mL 1,000,000

mL(s)

Question 3 You receive a prescription for 200 mL of an oral solution containing sodium bicarbonate 2 mmol/5 mL, which you will prepare using a commercially-available solution of sodium bicarbonate 4.2%w/v. How many mL(s) of the 4.2%w/v solution would you need to prepare the prescription item? (Mr for sodium bicarbonate is 84). If 2 mmol/5 mL => 4 mmol/10 mL => 8 mmol/20 mL => 80 mmol in 200 mL = 0.08 moles Mass = mol x Mr = 0.08 x 84 = 6.72 g of sodium bicarbonate required By definition 4.2% w/v => 4.2 g in 100 mL By simple proportion: Sodium bicarbonate Volume of product (mL)

4.2 100

6.72 ?

Answer:

? = 100 x 6.72 = 160 mL 4.2

mL(s) 2

Question 4 A child, weighing 14.4 kg, is being treated in hospital for suspected pneumonia with benzylpenicillin at a dose of 200 mg/kg/day, given in divided doses every four hours. Single vials of benzylpenicillin contain 600 mg in 2 mL. How many mL(s) will provide one dose? Give your answer to 1 decimal place. Total daily dose for this child = 200 (mg) x 14.4 (kg) = 2880 mg, given every 4 hours (=6 divided doses)  each dose = 2880/6 = 480 mg By simple proportion: benzylpenicillin Volume of product (mL)

600 2

480 ?

? = 2 x 480 = 1.6 mL 600

Answer:

mL(s)

Question 5 Mr J asks to buy cough linctus for himself, his mother, and his two children aged seven and ten; sufficient for five days. The dosage instructions are: adults, the elderly and children over 12 years – take two 5 mL spoonsful; children 6 -12 years – take one 5 mL spoonful. Repeat after 4 hours, but not more than 4 doses in 24 hours. If each bottle of linctus contains 250 mL, how many bottle(s) would you sell Mr J? To ensure sufficient is supplied assume all individuals will require the maximum recommended dose: Adult dosing (2 people): 2 x 10 mL (dose) x 4 (doses) x 5 (days) = 400 mL Child dosing (2 < 12) : 2 x 5 mL (dose) x 4 (doses) x 5 (days) = 200 mL Total 600 mL

Each bottle contains 250 mL => need to sell 3 bottles

Answer:

bottle(s)

3

Question 6 Antiseptic C is available as a 1 in 20 solution which is further diluted before use. How many mL(s) of this solution would you use to prepare 3.5 L of a 0.75% w/v solution for use as a skin cleanser? First convert both expressions of conc. to the same units: 1 in 20 => 1 g in 20 mL => 5 g in 100 mL = 5% w/v Using C1V1 = C2V2 convert 3.5 L to mL (so using same units) => 3500 mL

5 x V1 = 0.75 x 3500 => V1 = (0.75 x 3500)/5 = 2625/5 = 525 mL

Answer:

mL(s)

Question 7 You are required to supply eight suppositories each containing 500 mg of aminophylline, using theobroma oil as the suppository base, and a mould size of 4 g. You decide to prepare ten suppositories to allow for any wastage during preparation. How many gram(s) of the suppository base do you require? Give your answer to 2 decimal places. The displacement value for aminophylline in theobroma oil is 1.3 Total number of suppositories to prepare = 10 Each will contain 500 mg aminophylline => total amount of aminophylline required = 500 x 10 = 5000 mg = 5 g Amount of base required (unmedicated) = 10 x 4 = 40 g of theobroma oil By definition (displacement value) 1.3 g of aminophylline will displace 1 g of base => by simple proportion

Displacement API (g) Base (g)

1.3 1

so ? = 1 x 5 = 3.846…… g 1.3

5 ?

=> amount of base needed = 40 – 3.846 ……g = 36.15 grams to 2 decimal places

gram(s)

Answer:

4

Question 8 Keflex® capsules contain cefalexin monohydrate but the dose is expressed in terms of anhydrous cefalexin. How many milligram(s) of the monohydrate, equivalent to 500 mg of anhydrous cefalexin, does each capsule contain? Mr cefalexin monohydrate = 365, Mr anhydrous cefalexin = 347. Express your answer to the nearest whole number. By simple proportion: monohydrate (mg) anhydrous (mg)

365 347

? 500

so ? = 365 x 500 = 525.936….. mg 347

= 526 mg to nearest whole number

Answer:

mg

Question 9 A patient is prescribed ‘Hear-Clear’ ear drops for use in both ears to facilitate the removal of ear wax. The usage instructions are to ‘instil five drops per ear, twice daily, for ten days’. Assuming the dropper delivers 20 drops per mL and that a bottle of ‘Hear-Clear’ contains 8 mL, how many bottle(s) will you need to supply? Total drops administered = 5 (drops) x 2 (ears)x 2 (twice a day) x 10 (days) = 200 drops If each 1 mL produces 20 drops then total mls administered = 200/20 = 10 mL Each bottle contains 8 mL  need to supply 2 bottles

Answer:

bottle(s)

Question 10 A particular brand of an oral antibiotic powder for reconstitution has a displacement volume of 4.8 mL/g of antibiotic A. You are required to prepare 100 mL of reconstituted suspension, which contains 250 mg of antibiotic A in each 5 mL dose after reconstitution. How many mL(s) of water should be added to the powder in the container to produce a final volume of 100 mL? Total antibiotic A present in bottle = 250 mg (in 5 mL) x 20 (number of 5 mL doses in 100 mL) = 5000 mg = 5 g D.V. of antibiotic A = 4.8 mL/g => D.V. for 5 g = 4.8 x 5 = 24 mL  the antibiotic powder will displace 24 mL. Final volume of reconstituted suspension is 100 mL  volume of water required to reconstitute = 100 – 24 = 76 mL

Answer:

mL(s) 5

Question 11 Miss N has been prescribed drug V by her hospital consultant, to be reviewed in 3 weeks’ time. She requires 300 mg o.d. on days 1 and 2, then 300 mg b.d. on days 3, 4 and 5, followed by 300 mg t.d.s. thereafter. The hospital consultant requests 4 weeks supply in total. How many tablet(s) should be supplied if each tablet contains 150 mg of drug V? Each individual dose is 300 mg = 2 x 150 mg tablets

Dose (tabs)

Frequency (per day)

Days

Total Tablets

2

1

2

4

2

2

3

12

2

3

23

138 154

Answer:

tablet(s)

Question 12 A 7-year-old boy, weighing 20 kg, has been admitted to hospital for emergency surgery. At the initiation of anaesthesia he is given an intravenous injection of fentanyl at a dose of 2 micrograms/kg, followed by a further dose of 1.25 micrograms/kg at a later stage in the operation. The fentanyl injection contains 0.1 mg/2 mL. How many mL(s) of fentanyl injection will he have received in total? Give your answer to 1 decimal place. First convert to the same units: dose is in micrograms => injection contains 100 micrograms/2 mL Initial dose required = 2 (micrograms) x 20 (kg) = 2nd dose

40 micrograms

= 1.25 (micrograms) x 20 (kg) = 25 micrograms Total 65 micrograms

By simple proportion: API (micrograms) Volume of product (mL)

100 2

65 ?

? = 2 x 65 = 1.3 mL 100

Answer:

mL(s) 6

Question 13 You receive a prescription from the skin clinic for 30 grams of 0.4% w/w hydrocortisone cream, to treat a baby with eczema. 1% w/w hydrocortisone cream is available in the pharmacy, which may be diluted with a suitable base. How many gram(s) of the diluent base are required to prepare this prescription? I’m using alligation to do this but the dilution equation would work equally well. Diluent base = 0% API

1

0 0.4

0.4 2

0.6 3

I divided both 0.4 and 0.6 by 0.2 to create whole numbers

Answer:

I am making 30 g of 0.4% Total parts = 5, so 1 part = 30/5 = 6 g I need 3 parts of diluent to 2 parts 1%  Need 3 (parts) x 6 (g) = 18 g base

gram(s)

Question 14 How many micromole(s) of an active pharmaceutical ingredient are contained in 5 mL of solution, given that the Mr is 50 and the solution is 1 in 8,000 (w/v)? Give your answer to 1 decimal place By definition: 1 in 8000 = 1 g in 8000 mL => 1,000,000 micrograms in 8000 mL

As I want micromoles I will convert to micrograms

By simple proportion: API (micrograms) Volume of product (mL)

1,000,000 8000

? 5

? = 1,000,000 x 5 = 625 micrograms 8,000

Micromoles = mass (micrograms)/Mr = 625/50 = 12.5 micromoles

Answer:

micromole(s)

7

Question 15 How many mL(s) of water should be added to a 12.5 %w/v concentrated ‘stock’ solution of disinfectant to prepare 750 mL of a 0.25% w/v solution? I am going to use alligation again to solve this question Water is the diluent used to reduce the concentration of the stock solution; it contains 0% API

12.5

0

0.25 0.25 1

I am preparing 750 mL of 0.25% Total parts = 50, so 1 part = 750/50 = 15 mL 12.25 I divided both 0.25 and 12.25 I need 49 parts of diluent to 1 parts of stock 49  Need 49 (parts) x 15 (mL) = 735 mL water by 0.25 to create whole numbers

Answer:

mL(s)

Question 16 A doctor has prescribed 150 mL of a solution containing 30 mg/mL of drug R for Mr TR. The dispensary has solutions containing 4% w/v and 1% w/v of drug R available. How many of mL(s) of the 1% w/v solution should be mixed with an appropriate quantity of the 4% w/v strength to prepare 150 mL of a solution containing 30 mg/mL of drug R? This requires the alligation alternate method as there are three different concentrations. First express all concentrations in the same units. I will convert 30 mg/mL to a % as there is only one calculation involved to do this. 30 mg/mL => 300 mg in 10 mL => 3000 mg in 100 mL = 3% Enter the values into the alligation grid

4

1

I am preparing 150 mL of the 3% solution of drug R Total parts = 3, so 1 part = 150/3 = 50 mL I need 1 part of 1% to 2 parts 4%  Need 1 (parts) x 50 (mL) = 50 mL of 1% w/v

3 2

1

mL(s) of 1% w/v

Answer:

8

Question 17 A pharmaceutical product is available as bottles containing 50 mL of a 6 % w/v solution of the active pharmaceutical ingredient (API). Before first use the patient is instructed to add 30 mL of water to the bottle, mix well, and then use it as a skin cleanser. What is the concentration of API (in mg/mL) in the solution that the patient applies to their skin? Give your answer to 1 decimal place. There are numerous ways of approaching this calculation. From first principles: 50 mL of a 6 % w/v solution will contain 3 g of API = 3000 mg

After dilution by the patient this 3000 mg will be in a final volume of (50 +30) = 80 mL By simple proportion: API (mg) Volume (mL)

3000 80

? 1

so ? = 3000 x 1 = 37.5 mg/mL 80

Answer:

mg/mL

Question 18 Drug K has a displacement volume of 0.08 mL/5 mg. You add 38 mL of water to a bottle containing drug K (as a powder for reconstitution) and this produces a final volume of 50 mL. How many milligram(s) of drug K does the bottle contain? Difference between final volume and volume of water added = 50 - 38 = 12 mL (which is the displacement due to the powder). The D.V. for 5 mg is 0.08 mL By simple proportion: API (mg) Displacement Volume (mL)

5

?

0.08

12

so ? = 5 x 12 = 750 mg 0.08

Answer:

mg

9

Question 19 Master J’s medication chart comes down from the paediatric ward with a take-home prescription for drug D at a dose of 20 micrograms/kg three times a day for 7 days. You contact the ward and are told that Master J, age 10, weighs 32 kg. Drug D is available as an oral solution containing 0.1 mg/mL. How many mL(s) of the oral liquid would you dispense to ensure sufficient for 7 days’ supply? Give your answer to the nearest whole mL. First work out the volume for each dose to ensure it can be accurately measured Each dose = 20 (micrograms) x 32 (kg) = 640 micrograms. Solution contains 0.1 mg/mL = 100 micrograms/mL By simple proportion: API (micrograms) Volume (mL)

100 1

640

so ? = 1 x 640 = 6.4 mL 100

?

This volume is measurable using a suitably calibrated oral syringe. Total doses required = 6.4 (mL/dose) x 3 (times a day) x 7 (days) = 134.4 mL  supply 135 mL to nearest whole mL to ensure sufficient for 7 days.

Answer:

mL(s)

Question 20 A child is prescribed 600 micrograms of a potent diuretic as an oral dose. It is available in the hospital pharmacy as a solution containing 4 mg/mL. Following the hospital’s local policy you measure 5 mL of this solution and dilute it to 20 mL with water before sending the resulting solution to the paediatric ward. How many mL(s) of the diluted solution provides one dose for this child? Give your answer to 1 decimal place. Read the question carefully to ensure that you understand the dilution that was done. Using C1V1 = C2V2 C1 = initial concentration of diuretic = 4 (mg/mL) V1 = 5 (mL) C2 = unknown V2 = 20 (mL)

4 x 5 = C2 x 20 => C2 = (4 x 5)/20 = 1 Original solution was expressed in mg/mL so diluted solution contains 1 mg/mL = 1000 micrograms/mL By simple proportion: API (micrograms) Volume (mL)

1000 1

600 ?

so ? = 1 x 600 = 0.6 mL 1000

Answer:

mL(s) 10

Correct format for answers in GPhC-style answer grid

1

3 .

5

mL(s)

11

2

0 .

7

mL(s)

3

1

6

1 5

4

.

tablet(s)

12

1

.

mL(s)

13

1 8

.

mL(s)

14

1 2

.

3

5

.

mL(s)

mL(s)

3

mL(s)

0

.

4

1

.

5

3 .

bottle(s)

15

5

mL(s)

16

5 0

.

5 gram(s)

17

3

7

.

mg

18

7 5

0

.

mg

bottle(s)

19

1 3

5

.

mL(s)

mL(s)

20

0

.

6

5 2

7

3

8

5 2

9

10

.

6 .

6

.

2 .

7 6

6

.

1

11

7

grams

5

5

6

micromoles

mg/mL

mL(s)...