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# GPhC registration exam: concentrations calculations masterclass

Are you confident with conversion of units, the various definitions of concentration, as well as the concept of displacement volume ahead of your General Pharmaceutical Council (GPhC) registration exam?

The GPhC registration exams are now imminent, so here is a quick masterclass to help you polish up on your understanding of concentrations. Please don’t panic. If you concentrate, you will ace those concentrations calculations.

In its simplest terms, concentration refers to the weight or volume of a drug substance divided by the amount or volume of the mixture in which it is dissolved or suspended. This ratio can be expressed in various forms (which you should know and be able to convert from one form to another) such as percent (%), parts per million (ppm), 1 in X and mg/mL. Additional symbols are added in front of the concentration units to indicate whether the drug is a solid-in-solid (thus weight in weight - w/w), solid-in-liquid (weight in volume - w/v) or liquid-in-liquid (volume in volume - v/v).

The first important point in concentration calculations is to fully understand the conversion of units and the key definitions of concentration units as summarised in Table 1. Please note that this is not an exhaustive list. Also note that standard international (SI) units are used in pharmacy practice to avoid confusion.

Table 1. Unit conversion and concentration units in common pharmacy practice

 Unit conversion Concentration definition 1 kg = 1000 g 1 g = 1000 mg 1 mg = 1000 microgram 1 mcg = 1000 ng 1 litre = 1000 mL 1 dL = 100 mL 1 mL = 1000 microlitre % (w/v) = g / 100 mL % (w/w) = g / 100 g 1 in X = 1 g in X mL 1 ppm (w/w) = 1 g / 1 million g 1 ppm(w/v) = 1 g / 1 million mL or 1mg / 1000 mL 1 ppm (v/v) = 1 mL / 1 million mL

Second, you need to be fluid in converting from one concentration type to another, for instance, converting 1 in X to percent (%) if required. Third, you should adopt uniform units if the question has different units for various parameters given. Fourth, always be mindful of displacement volumes for some solid drugs. The displacement volume is the volume occupied by the powder after mixing with the liquid, so this needs to be incorporated into the final volume when calculating concentration.

With these four tips in mind, let’s see how you can apply them into solving the questions that follow below. Remember, there are many ways to tackle these questions, so feel free to use a method that works best for you.

## Question 1:  Expressing concentration as 1 in X, adrenaline injection

A child weighing 21kg has received 0.21 mL of adrenaline at a dose of 10 mcg/kg by intravenous infusion. What is the concentration of the adrenaline expressed as 1 in X where X is a whole number? Write the value of X only.

This calculation should be straightforward. The key points are: understanding the conversion of units and the definition of 1 in X. We set out our calculation as below, but feel free to use your own method.

1. Calculate dose:

Dose given = 10 mcg/kg x 21kg = 210mcg

But we know 1 in X means 1g in X mL, so the dose needs conversion from (mcg) to (g).

2. Conversion of (mcg) to (g)

210mcg = 0.210mg = (0.210/1000) = 0.00021g

3. Calculate concentration:

Concentration = (0.00021) g/ 0.21 mL = 0.001 g/ mL

Multiply numerator and denominator by 1000/1000

Concentration = 1g / 1000mL = 1 in 1000

Correct answer: 1 in 1000 and value of X = 1000

## Question 2: Concentration expressed as parts per million (ppm)

A bottle of carmellose eye drops has its strength labelled as 5 mg/mL. Express this strength in parts per million (ppm).

As before, the key to getting the correct answer is understanding the definitions of parts per million and converting units. We set out the calculations as below:

1. Define parts per million

Look at the units, mg/mL indicate that this relates to a (w/v) preparation.

So, parts per million = 1g / 1000 000mL

2. Convert to mg/ml to g/ml to match the ppm definition

5 mg/ml= 0.005 g/mL

3. Multiply denominator and numerator by 1000 000

(0.005g / 1mL) x 1000 000/1000 000

= 5000g / 1000 000mL

= 5000 ppm

## Question 3: Concentration expressed as mg/mL

A 67-year-old man weighing 85kg is due to receive AmBisome (amphotericin B) dispersion for infusion at a dose of 3 mg/kg/day in dextrose 5% (w/v) solution for infusion. To reconstitute one AmBisome vial, 12mL of sterile water for injection is added to the AmBisome Liposomal 5mg Powder for dispersion. The displacement volume for the 50mg powder is 0.5mL. The volume of the reconstituted vial(s) equivalent to the prescribed dose is further diluted 1 in 20 with 5% (w/v) dextrose.

What is the final concentration of AmBisome in the final 5% (w/v) dextrose solution expressed as mg/mL? Give your answer to one decimal place.

This calculation is tricky as there are a few key pieces of information to consider and put together. The key points are understanding the conversion of units, dilution and displacement volume. We will illustrate all these points in the calculations below.

1. Calculate dose

Daily dose is 85kg x 3 mg/kg/day = 255 mg/day

2. Calculate initial concentration after adding 12mL sterile water for injection

Amount of AmBisome in vial = 50mg

Total volume after dilution = 12mL + 0.5mL = 12.5mL;

After mixing in vial, concentration = 50mg / 12.5mL

3. Calculate amount of AmBisome in (mg) to be withdrawn for further dilution

The volume to be withdrawn for further dilution should equate the daily dose of 225 mg/day.

Volume of reconstituted AmBisome (mL) required to give 255 mg/day = 255mg / (50mg / 12.5ml) = 63.75mL.

So, 63.75mL is further diluted 1 in 20, meaning that it is diluted 20 times.

The final volume is therefore 63.75mL x 20 = 1275mL.

4. Calculate final concentration

Concentration = 255mg / 1275mL = 0.2 mg/mL

## Question 4: Manipulation of concentration for dextrose infusions

You are required to aseptically prepare a non-standard concentration of dextrose X % (w/v) infusion. The instructions require you to remove 50mL from a 500mL bag of dextrose 5% (w/v) infusion fluid (A) and then add 20mL of dextrose 50% (w/v) infusion fluid (B) into A and mix well.

What is the final percentage concentration (% w/v) of dextrose? Give your answer to one decimal place.

This is another tricky question as it requires knowledge of both concentrations and dilutions. Follow the key information in the scenario carefully. The calculations are set out below using the algebra method.

After removing 50mL from 500mL of 5% (w/v) infusion fluid (A);

Amount of glucose in g = 5g / 100mL x (500 - 50)= 5g / 100mL x 450mL = 22.5g

20ml of 50% glucose contains = 50g / 100mL x 20mL = 10g

Total weight of glucose in g = 22.5g + 10g = 32.5g

Concentration as % (w/v) = 32.5g / 470mL x 100% = 6.914893617% rounded to 6.9%.

## Question 5: Calculation of concentration after dilution

A sterile diluent was added to a vial containing 0.5mg (epoprostenol sodium) for injection powder and mixed to make up the final reconstituted mixture of 5mL. Then, 3mL of this mixture was withdrawn and added to sufficient sterile diluent to make it up to 100mL. Calculate X, the concentration of epoprostenol sodium in the final 100mL mixture expressed as nanogram/millilitre (ng/mL).

This question is straightforward requiring you to follow the dilution process and work out the amount of drug that is finally diluted to 100mL at the end. Be mindful of the requested units of ng/mL and convert accordingly. Our steps are as follows:

1. Amount of drug in 5mL of initial mixture

0.5mg / 5ml = 500mcg / 5mL = 500 000ng / 5mL

Amount of drug in 3mL = 500 000ng / 5mL x 3mL= 300 000ng

2. Calculate concentration

Concentration in 100mL = 300 000ng / 100mL= 3000 ng/mL

## Conclusion

As you can see from these examples, it’s important to be confident with conversion of units, the various definitions of concentration, and the concept of displacement volume. You may have seen from these examples that some topics overlap eg dilutions, concentrations and infusions. As before, practice makes perfect. Please do not hesitate to give us feedback.

Good luck in your upcoming exams!

Authors:

Luso Kumwenda: MSc Community Pharmacy (Cardiff), B Pharm Hons (Zimbabwe), Independent Prescriber, MRPharms, Mentor at UKBPA & RPS

Prof David R. Katerere: PhD Pharmaceutical Science (Strathclyde), Tshwane University of Technology, Platform Research Chair – Pharmaceutical and Biotech Advancement in Africa (PbA2)

Acknowledgements: The questions were kindly provided by: Focus Pre-Reg Revision

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 or trainee pharmacist. The concentrations calculations depicted here cannot be viewed to reflect the calculations in real practice. Please consult the relevant smpc and clinical guidelines to inform your concentrations calculations in practice. The views in this article are our own and do not represent the views of any organisations we are associated with. Table

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