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5PY022 Synoptic Calculations session Question 1 What is the concentration, in mmol/L, of a solution prepared by dissolving 4.5 g of anhydrous glucose in water, which is then made up to a final volume of 250 mL? (Mr anhydrous glucose = 180). mmol = mass (mg)/Mr => mmol anhydrous glucose = 4500/180 = 25 mmol (in 250 mL, final volume) To express this in mmol/L, multiple by 4 (as 4 x 250 mL in 1L) => 4 x 25 mmol of glucose = 100 mmol/L Alternative method (once calculated that 4.5 g contains 25 mmol of glucose) If concentration is expressed in mmol/L then N needs to be in mmol and V in litres (250 mL = 0.25 L) => C =N/V = 25/0.25 = 100 mmol/L Answer: 100 mmol/L Question 2 Following on from question 1, how many grams of glucose BP would be required to prepare 250 mL of a solution containing the same concentration of glucose? (Mr glucose BP [glucose monohydrate] = 198). Express your answer to two decimal places. From question 1 there are 25 mmol of anhydrous glucose in 250 mL of prepared solution => therefore need to calculate the mass of glucose BP that contains 25 mmol. As answer is required in grams I am converting 25 mmol to moles => 0.025 moles mass (g) = mol x Mr = 0.025 x 198 = 4.95 grams Answer: 4.95 g Question 3 A patient is instructed to add 50 mL of water to a bottle containing 12.5 mL of a 0.5%w/v solution of antiseptic before use. What is the concentration of antiseptic (in mg/mL) of the resulting solution? Using C1V1 = C2V2 V1 = 12.5 (mL), C1 = 0.5 (%), V2 = 62.5 (mL), C2 is unknown => C2 = (0.5 x 12.5)/62.5 = 0.1 (this will be % w/v as C1 is expressed as a % w/v) Converting % w/v into mg/mL => 100 mg in 100 mL => 1 mg/mL Answer: 1 mg/mL 5PY022 Synoptic Calculations session Question 4 A prescription is received for 60 g of 0.05% w/w Betnovate® cream. The commercially available strengths are 0.1%w/w and 0.025%w/w. How many grams of the 0.025% w/w cream should be added to an appropriate quantity of the 0.1% w/w to make 60 g of 0.05% w/w? Quantity required = 60 g 0.1 0.025 Total parts = 3 0.05 so 1 part = 60/3 = 20 g 0.025 : 0.05 parts total. Divide both by 0.025 to simplify: Require 2 parts of 0.025% 1 : 2 => 2 x 20 = 40 g = 3 parts total Answer: g 0.025%w/v 40 Question 5 A pharmacist prepares a reconstituted solution by adding 78 mL of water to 30 g of a soluble drug powder to produce a final volume of 100 mL. What is the displacement volume (in mL/g) of the drug powder? Express your answer to two decimal places. D.V. due to drug powder = 100 – 78 = 22 mL This D.V. is produced by 30 g of powder => D.V. in mL/g = 22/30 = 0.733333333 mL/g = 0.73 mL/g to 2 d.p. Answer: 0.73 mL/g Question 6 A 9-year-old child is prescribed a cytotoxic injection at a dose of 300mg/m2. The child weighs 36 kg and is 1.44m tall. The injection is available as a solution containing 100mg/mL. How many millilitres of the injection will provide one dose? => BSA = √ (36 x 144)/3600 = √1.44 = 1.2 m2 Dose = 300 x 1.2 = 360 mg API (mg) Volume of product (mL) 100 1 360 ? ? = 1x 360 = 3.6 mL 100 Answer: 3.6 mL Question 7 A baby requires an antibiotic suspension for an infected wound. She weighs 3.5 kg and has been prescribed a dose of 80 mg/kg/day, given in divided doses every six hours, for seven days. The strength of the suspension is 125 mg in 5 mL. How many millilitres of suspension would you need to supply to ensure that there is sufficient to complete the course? Express your answer to the nearest whole millilitres. TDD = 80 x 3.5 = 280 mg/day, given in 4 divided doses => 1 dose = 70 mg. Check if measurable dose: API (mg) Volume of product (mL) 125 5 70 ? ? = 5 x 70 = 2.8 mL (measurable with a suitable 125 oral syringe) Baby needs 2.8 )mL) x 4 (times a day) x 7 (days) = 78.4 mL => need to supply 79 mL Answer: 79 mL 5PY022 Synoptic Calculations session Question 8 Drug K has a displacement volume of 0.07 mL/5 mg. The nurse adds 12.3 mL of water for injection to a vial containing drug K (as a powder) and this produces a final volume of 20 mL. How many milligrams of drug K does the vial contain? D.V. due to drug powder in vial = 20 (final volume) – 12.3 (volume of WFI) = 7.7 mL mL Drug K has a D.V. of 0.07 mL/ 5 mg therefore by simple proportion: DV (mL) mg of drug K 0.07 5 ? = 5 x 7.7 = 550 mg 0.07 7.7 ? Answer: 550 mg Question 9 A patient is prescribed 1 L of 1.26% w/v sodium bicarbonate as an infusion to be given over 6 hours. How many millimoles of sodium bicarbonate will the patient have received at the end of the infusion? (Mr NaHCO3 = 84). 1.26% w/v => 1.26 g in 100 mL => 12.6 g in 1 L = 12600 mg mmol = mass(mg)/ Mr = 12600/84 = 150 mmol of sodium bicarbonate Answer: 150 mmol Question 10 How many grams of a suitable diluent should to be added to 20%w/w benzyl peroxide cream to prepare 2.5 kg of 4%w/w benzyl peroxide cream? Using alligation: Using C1M1 = C2M2 20 0 4 M1 = 4 (%) x 2500 (grams) = 500 g 4 : 16 20 (%) 1 : 4 = 5 parts total 500 g is the mass of 20% cream required 2.5 kg = 2500 g 5 parts total => 1 part = 2500/5 = 500 g. Need 4 parts diluent => 4 x 500 = 2000 g => need 2500 - 500 = 2000 g of suitable diluent OUT Answer: 2000 g Question 11 A 72-year-old man has been prescribed a potassium permanganate soak to treat exuding eczema on his hand. How many milligrams of potassium permanganate are required to make 750 mL of a 1 in 8,000 solution for soaking his hand? Express your answer to two decimal places. 1 in 8000 => 1 g API in 8000 mL => 1000 mg in 8000 mL By simple proportion: Potassium permanganate (mg) Volume of product (mL) 1000 8000 ? 750 Answer: ? = 1000 x 750 = 93.75 mg 8000 93.75 mg 5PY022 Question 12 An adult cough mixture contains the following active ingredients: Dextromethorphan hydrobromide 6.5 mg Diphenhydramine 14.0 mg in a suitable syrup base to 5.0 mL Synoptic Calculations session The pharmacist in the manufacturing unit calculates that they need 325 grams of dextromethorphan for the batch that is currently being manufactured. How many litres of cough mixture are being prepared? Scaling factor for dextromethorphan = 325000(mg)/6.5 (mg) = 50,000 => final volume being produced = 50,000 x 5 (mL) = 250,000 mL = 250 L Alternative method (scaling up by simple proportion): dextromethorphan (mg) Volume of product (mL) 6.5 5 325000 ? ? = 5 x 325000 = 250,000 mL = 250 L 6.5 Answer: 250 L