# Tackling displacement volume calculations in the registration exam ## Try our six worked examples to help you practice displacement volume calculations

This article illustrates worked examples of calculation questions that involve the concept of displacement volumes and its implication when preparing injectable dosage forms. It will be necessary for some questions to use resources including the Summary of Product Characteristics (SmPC) or the British National Formulary (BNF) to extract the information needed.

For more worked example calculations, try our calculation questionsincluding extended matching calculation questions and dilution and compounding calculation questions or visit the C+D Community to connect with peers and our pre-reg leads.

Question 1:  A child has been diagnosed with meningitis and is due to receive an intravenous infusion of benzylpenicillin. The prescribed dose is 600mg every six hours. In order to reconstitute a 600mg vial, you need to add sodium chloride solution (0.9% w/v) to the vial to produce a 100mg/mL of benzylpenicillin.

Considering the displacement volume for benzylpenicillin in this vial is 0.4mL, how much sodium chloride solution 0.9% (in mL) should be added to reconstitute the vial? Give your answer to one decimal place.

### Click here for the comments, working out and answer

First determine the final volume of the drug solution. The concentration in the vial is 100mg in 1mL, so 600mg in 6mL. Therefore, the final volume in the vial should be 6mL. The displacement volume can be interpreted as 600mg of benzylpenicillin displaces 0.4mL of diluent, meaning the drug occupies a volume of 0.4mL. Therefore, to achieve a final volume of 6mL, we have to account for the displaced volume, then we add diluent up to 6mL. So 6mL – 0.4mL = 5.6mL of sodium chloride solution (0.9% w/v).

Final answer = 5.6mL of sodium chloride (0.9% w/v)

Question 2: A child is prescribed cefuroxime injection to be administered intravenously over 3-5 minutes. The recommended daily dose is 60mg/kg daily divided into four doses. The child weighs 37kg. In order to prepare the vial, you need to add 7mL of water for injection to a 750mg cefuroxime vial. The displacement volume of the brand of cefuroxime vials you are using is 0.5mL per 750mg.

What volume (in mL) will be administered to the child at each dose? Give your answer to one decimal place.

### Click here for the comments, working out and answer

First calculate the single dose for this child in mg, 60mg/kg so 60mg x 37kg = 2220mg daily. This dose will be divided into four equal doses so 2220mg/4 = 555mg in each single dose. The next step is to determine what volume contains a dose of 555mg. By adding 7mL of water for injection and considering the volume occupied by the drug, ie the displacement volume (0.5 mL), the total volume of the reconstituted vial will be 7mL + 0.5mL= 7.5mL. 750mg in 7.5mL, so 555mg in 5.55mL. Note that the question specifies to give the answer to one decimal place, so make sure you follow the rounding instructions. Therefore, 5.6 mL is the volume of each single dose.

Final answer = 5.6mL

Question 3: You are working in the hospital centralised intravenous additives service unit (CIVAS). You need to prepare 12 doses of 440mg of cefotaxime for the Paediatric Intensive Care Unit. Since the preparation is performed in a sterile environment in CIVAS, the full content of each vial to prepare the batch can be used. You will be using 1g vials of cefotaxime, which need to be reconstituted to a concentration of 200mg/mL. The displacement volume for the brand of vials you are using is 0.6mL per 1g.

How much water for injection (in mL) will you need to use in total to prepare these 12 doses? Give your answer to one decimal place.

### Click here for the comments, working out and answer

Since the preparation is in CIVAS, we can use the full content of vials to prepare the 12 doses. You need to make 12 x 440mg doses so 5280mg = 5.28g in total. Therefore, we need six of the 1g vials. Next step is to reconstitute the vials to produce concentrations of 200mg/mL.  200mg in 1mL so 1000mg in 5mL. This means that each vial needs to be reconstituted to make a final volume of 5mL. 0.6mL is displaced by 1g cefotaxime so 5mL – 0.6mL= 4.4mL water for injection needs to be added to make each vial. Finally, six vials are used in preparation so in total 6 x 4.4mL = 26.4mL water is needed.

Final answer = 26.4mL water for injection

Question 4: A paediatric patient has been prescribed fosfomycin infusion for the treatment of osteomyelitis. The dose is 5g daily to be given in three divided doses. You have available Fomicyt® (fosfomycin) 2g vials that need to be reconstituted and subsequently diluted, according to the instructions given in Fomicyt® SmPC.

What volume (in mL) of the prepared infusion will the patient be receiving for each dose? Give your answer to one decimal place.

### Click here for the comments, working out and answer

First determine the single dose so 5g/3 = 1.667g. Then, find what volume of the reconstituted vial includes this dose. The SmPC in section 6.6 states: “Reconstitute the 2g vials with 20mL of solvent. Shake well to dissolve.” Then: “Transfer the reconstituted contents of 2g vials into an infusion container with further 30mL of solvent.”

Consequently, the total volume of the added fluids (20mL + 30mL) = 50mL. “The displacement value for the solution is 1mL for the 2g pack size”. Considering that 2g of the drug displace 1mL, the final volume of the infusion will be 50mL + 1mL = 51mL.  2g of the drug is in a final volume of 51 ml, so 1.6667 g in 42.5mL.

Final answer = 42.5mL

Question 5: A six-year-old child weighing 20kg requires an intravenous infusion of piperacillin with tazobactam to treat a complicated intra-abdominal infection. The dose prescribed is 112.5mg/kg of piperacillin with tazobactam every eight hours.

According to the SmPC of the generic product of piperacillin/tazobactam (2g/0.25g), 10mL of water for injection should be added to reconstitute the vial. Then the final volume is made up to 50mL with a saline solution (0.9% w/v sodium chloride).

What volume of the saline solution (in mL) is used to make the infusion for each dose? Give your answer to one decimal place.

### Click here for the comments, working out and answer

Note the dose prescribed is expressed as a combination of piperacillin and tazobactam in a ratio of 8:1. First, calculate the single dose for this patient 20kg × 112.5mg/kg every 8 hours so we need = 2250mg =2.25g of the combination for each dose, which is one vial of piperacillin/tazobactam 2g/0.25g.

The SmPC section 6.6 states that “each gram of piperacillin/tazobactam 2g/0.25g Powder for Solution for Infusion has a displacement volume of 0.7mL”. 1 g of the combination displace 0.7mL so 2.25g displace 1.575mL. “Each vial should be reconstituted with 10mL of one of the following diluents: Sterile water for injections”. Therefore, by adding 10mL of water for injections, the volume of the reconstituted vial will be 1.575mL + 10mL = 11.575mL. The targeted volume of the infusion is 50mL, so 50mL - 11.575mL= 38.425mL so the answer to the nearest decimal place is 38.4mL.

Final answer = 38.4mL

Question 6: A 13-year-old girl who weighs 42kg and is 145cm tall is admitted to the hospital having been bitten by an animal. She is prescribed co-amoxiclav intravenous injection. You have available 1.2g co-amoxiclav vials that should be prepared by adding 20mL water for injection to reconstitute the vial.

The displacement volume is 0.9mL per 1.2g of co-amoxiclav of this brand.

 Indications and dose  Prophylaxis of infection from human bites, Prophylaxis from animal bites  By intravenous injection, or by intravenous infusion  For Child 1–2 months  30 mg/kg every 12 hours, intravenous infusion recommended in children less than 3 months of age.  For Child 3 months–17 years  30 mg/kg every 8 hours (max. per dose 1.2 g every 8 hours)

Using the resource given above, calculate how much (in mL) should be administered to this girl for each dose. Give your answer to one decimal place.

### Click here for the comments, working out and answer

The dose for this patient is 30 mg/kg. The child is 42kg so the dose is 30mg × 42kg= 1260mg = 1.26 g. However, the BNFC states 1.2g is the maximum dose every 8 hours. Therefore, the single dose here is 1.2g, which is one vial. Taking the displacement volume into account (0.9 mL), the total volume of the reconstituted vial is 0.9mL + 20mL= 20.9mL, which is how much should be administered to this patient in a single dose.

Final answer = 20.9mL

Disclaimer: The questions and explanations presented here are for educational purposes only and do not replace your training, knowledge and application of professional judgement as a pharmacist, pre-reg or prov-reg pharmacist. The views in this article do not represent the views of any organisations the author is associated with.

This article was peer reviewed by Kate McComiskey, PhD MPSNI 0 Comments
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