Calculations

REMEMBER FOR ALL PHAY0001 CALCULATIONS

YOU MAY NEED TO REFER TO BNF

Miss KD has been prescribed Piriton syrup, 5mg TDS, for 4/7. What would be the total quantity dispensed?

60mL

How much of thioridazine 100mg/5mL and 25mg/5mL should be mixed together to get 300mL of thioridazine with a concentration of 50mg/5mL?

• x + y = 300mL

• x = 300 - y

• Total mg = 3000mg » as conc is 50mg per 5mL (300/5 × 50)

• (x/5 × 100) + (y/5 × 25) = 3000mg

• 20x + 5y = 3000

• 20(300-y) + 5y = 3000

• y = 200mg

• x = 100mg

• so 200mL of 25mg/5mL thioridazine and 100mL of 100mg/5mL thioridazine

You have been asked to make 200mL of 50:50 rose water and witch hazel, how much rose water concentrate do you use? (Rose water = 1 part concentrate + 39 parts water)

• 100mL rose water, 100mL witch hazel

• Rose water = 1/40 dilution

• So to make 100mL of rose water, the amount of concentrate required = volume of rose water / total parts

• 100/40 = 2.5mL

The total daily dose of cefalexin for a child is 35mg/kg of body weight and it should be given every 4 hours. Your patient is a 6 year old child weighing 40kg. What is the nearest dose that should be given every 4 hours? Do not refer to BNF.

Total daily dose = 35 × 40 = 1400mg

Number of doses = 24/4 = 6

Dose per hour = 1400 /6 = 233.3mg

Prescription asks for erythromycin tablets to be given 500mg qds for 10 days. You only have 250mg tablets in stock. How many do you dispense and what is the dosage?

• Total mg = 20,000mg

• Number of 250mg tablets = 80 tablets

• 1 500mg 4 times a day = 2 250mg 4 times a day

• 80mg, two qds

How much potassium permanganate is required to produce 100mL of a solution, such that when 5mL is diluted to 1L it produces a 1 in 1000 solution?

• 1 in 1000 solution = 1g of potassium permanganate in 1000mL of solution = 0.001g/mL

• C1V1 = C2V2

• C1 × 5mL = 0.001 × 1000

• C1 = 0.2 g/mL

• 0.2 × 100 = 20g

What does double strength mean?

1 parts concentrate, 19 part water

How much orange flower water concentrate is required to make 200mL of double strength orange flower water?

• Double strength = 1 part concentrate, 19 parts water

• 1/20 × 200 = 10mL

A patient is 5 feet and 6 inches tall. What is their height in metric units?

• 1 foot = 304mm

• 1 inch = 25.4 mm

• (5 × 304) + (6 × 25.4) = 1672.4mm

What does it mean by U100 insulin syringes

100 units in every mL

A Parkinson’s disease patient is on apomorphine. He is discharged from hospital with a supply of apomorphine 20mg/2mL ampoules (vial containing the medicine) and 1mL U100 insulin syringes with needles. He requires a subcutaneous dose of 1.5mg. How many UNITS will he draw up each time to provide the equivalent dose in mg?

• U100 = 100 units per mL

• Apomorphine concentration = 20mg/2mL = 10mg/mL

• Volume patient needs = 1.5/10 = 0.15mL

• 100 units = 1mL, so 15 units = 0.15mL

• 15 units

What is half life?

The time taken for plasma concentration to decrease by half

A drug overdose patient has been admitted to hospital. The half life of the drug is 16 hours. The plasma concentration was 64mcg/mL when measured. After 24 hours what would you expect an approximate plasma concentration to be?

• Half life = time taken for plasma concentration to decrease by half

• Number of half lives in 24 hours = 24/16 = 1.5 half lives

• Plasma concentration halves per half life

• So plasma concentration after 1.5 half lives = 24mcg/mL

The doctor has prescribed 500mL of 1.8% sodium chloride to a patient. The nurse informs you they only have 500mL sodium chloride 0.9% bags and 30% sodium chloride 10mL ampoules available. The 500mL is to be run over 2 hours.

1. What volume of sodium chloride 0.9% should be used to make up the 1.8% solution. Give your answer to 1dp.

2. What volume of sodium chloride 30% should be used to make up the 1.8% solution. Give your answer to 1dp.

3. How should the nurse make this solution up practically?

4. What should the nurse set the rate of infusion at in mL/hr?

1. V1 = volume of 0.9% sodium chloride

   V2 = volume of 30% sodium chloride

   V1 + V2 = 500mL

   V2 = 500 - V1

   (C1 x V1) + (C2 x V2) = 1.8 × 500

   (0.9 x V1) + (30 x V2) = 900

   (0.9 x V1) + (30 x (500 - V1)) = 900

   0.9V1 + 15000 - 30V1 = 900

   14100 = 29.1V1

   V1 = 484.5mL of 0.9% NaCl

2. 500 - 484.5 = 15.5mL

3. • Use the 500mL 0.9% sodium chloride bag and remove 15.5mL of solution

   • Replace with 15.5mL of sodium chloride 30%

4. 250mL/hr

What weight of timolol is contained in a pack of 30 timolol 0.2mL unit dose eye drops 0.25%

0.25% = 0.25g in 100mL

15mg

Work out the amount of water that is to be added to 20mg potassium permanganate to produce a 1 in 150 solution

Final volume = 20mg x 150 = 3000mg = 3g = 3mL

Amount of water to add = 3mL = 0.003L

Elimination half life equation

t_1/2 = ln(2) x change in time / ln(original concentration / new concentration)