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PTCB Concentration Calculations Practice!

Aug 20th, 2022
ptcb concentration calculations

PTCB Concentration Calculations

Pharmacy math is one of the toughest parts of the PTCB exam. As a subtopic, PTCB concentration calculations can be challenging enough. After all, it can be difficult to conceptualize what exactly is going on.

Here, we break concentration calculations down to the most fundamental level – reviewing the three major kinds of question that appear on the PTCB exam.

We learn how to understand what these questions are asking, how you can solve these problems in multiple formats, and – most importantly of all – understanding step-by-step what is going on. You should not enter the PTCB exam unless you understand the math concepts. Memorizing formulae is not enough.

Examiners deliberately include answers that are misleading; often because a simple step was overlooked. Unless you understand how to answer PTCB practice questions in detail, you may get caught out – and that’s not a risk worth taking. That’s one of the weaknesses of memorizing math methods; as it always leaves open the risk that you won’t know how to solve similar problems from a different angle.

Note: before reviewing each explained answer, try to attempt each of these questions yourself first!

Question 1

How many milligrams of magnesium acetate is needed to prepare 400 mL of a 0.05% w/v solution?

The question asks us to find a quantity of magnesium acetate to add to 400 mL of solution. The end concentration of this solution must be 0.05% w/v.

First, note that 0.05% w/v = 0.05 grams per 100 mL of solution.

It is always important to ensure that units are consistent. Therefore, we must convert 0.05 grams to milligrams – which is 50 milligrams.

In other words, there must be 50 mg in each 100 mL of the final 400 mL solution.

If there is 50 mg in 100 mL, then the target 400 mL must contain 200 mg of magnesium acetate.

Another way to solve this PTCB pharmacy calculation problem is to use the following formula at the lower end of this graphic:

Question 2

How many mL of a 1:200 w/v stock solution is used to make 3L of a 1 : 3000 w/v solution?

To solve this question, the best approach is to convert ratios to percentage form:

  • 1 : 200 = ( 1/200 ) x 100 = 0.5% w/v
  • 1 : 3000 = ( 1/3000 ) x 100 = 0.033% w/v

The target volume is 3-liters, which is the same as 3,000 mL (remember: the question is asking us to find the value in milliliters).

Now that we have three of four variables resolved, we can plug these values into the following equation (where C refers to concentration and V refers to volume).

C1 x V1 = C2 x V2

0.033% x 3,000 mL = 0.5% x V2

0.033% x 3,000 mL / 0.5% = V2

99 / 0.5% = V2

V2 = 198 mL

Therefore, when we add 198 mL of a 1 : 200 w/v stock solution to 3-liters, it produces a final concentration of 1 : 3,000 w/v solution.

Question 3

When 200 mL of a 1 : 400 v/v solution is diluted to 800mL, what is the ratio strength v/v?

This question asks us to find the ratio strength (in volume/volume) when 200 mL of a 1 : 400v/v solution is diluted to 800 mL. This is one of the more difficult kinds of PTCB concentration calculations but let’s review it step-by-step, so you can learn exactly what is going on.

First, as always, the starting point must be to convert the ratio into a percentage. It makes life much easier.

  • ( 1/400 ) x 100 = 0.25%

As above, we now have three variables to plug into the concentration-volume equation, namely:

  • Initial 200 mL volume (V1)
  • Initial concentration of 0.25% (C1)
  • Final volume of 800 mL (V2)

Therefore, we must find C2.

C1 x V1 = C2 x V2

0.25% x 200 mL = C2 x 800 mL

( 0.25% x 200 mL ) / 800 mL = C2

C2 = 0.0625%

However, recall that the question asked us to find the ratio strength in v/v. Therefore, we must convert this percentage to a ratio.

Note that all percentages are, by definition, over 100. The same is true of 0.0625%, which is the same as 0.0625 / 100.

0.0625 / 100 is an inconvenient number, therefore, to create a more convenient fraction, we should multiply both the numerator and denominator by 100.

( 0.0625 / 100 ) x 100 = 6.25 / 10,000

Now, we must reduce this fraction to its simplest form to give us the optimum ratio. We achieve this by dividing both the numerator and denominator by 6.25:

(6.25 / 10,000) / 6.25 = 1/1,600

  • 6.25 divides neatly into 6.25 to give us 1 (the ideal ratio format).
  • 10,000 / 6.25 gives us 1,600.

Therefore, the final ratio concentration in its most reduced form is 1 : 1,600 v/v.

That concludes our review of PTCB concentration calculations. We hope you found this guide useful. Be sure to check back to our PTCB Test Prep blog soon for more exclusive content to help you master the pharmacy technician exam. If you’d like to learn how to master PTCB math and every other knowledge domain of the pharmacy technician exam, become a member of PTCB Test Prep today.

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Elaine Walker

Elaine joined PTCB Test Prep in 2017, currently serving as the lead product development manager overseeing both course development and quality improvement. Mrs. Walker is a graduate of California State University and has worked as a pharmacy technician for over twenty years – with particular interests in pediatric pharmacy, extemporaneous compounding, and hospital pharmacy. Over the past 8-years, she has helped prepare thousands of students for the PTCB examination.