In this tutorial, I'm going to show you four effective steps for solving any pharmaceutical calculations question, and we are starting right now.
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Pharmaceutical Calculations: 4 Effective Steps for Solving Any Question
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Let's get right to it and look at the four effective steps that you need to solve any pharmaceutical calculations question.
STEP 1 - Understanding the Problem
Step number one involves understanding the problem. When you get a pharmaceutical calculations question, the question is composed of words, and these words describe a specific scenario, and it's your duty to be able to take those words and accurately interpret those words and reconstruct the actual scenario that the examiner had in mind.
What I mean by that is if we take a look at this particular scenario, if I said I am thinking of a four-legged creature, these are words that I just showed you. And in your mind, you begin to quickly imagine some possible answers. So perhaps you may have thought about a dog or a cat or maybe a horse or perhaps a lion. Now, the issue with this particular phrase that has been given is it's incomplete. So there are so many different answers.
But if I said on top of that, that it is the fastest animal in the world. So I'm thinking of a four-legged creature, and this four-legged creature is the fastest animal in the world. Now your mind begins to go through and scan all the four-legged creatures that you know and begins to automatically sort them out in how fast they can run.
And if you actually knew the answer to this, then the solution to this question would be a cheetah. If you didn't know that the cheetah was the fastest animal in the world, then it wouldn't matter that I gave you the second clue to this particular question.
It's the same thing for a pharmaceutical calculations question. You get a bunch of words and it's your duty to be able to take those words and begin to, in your mind, reconstruct what those words actually mean to help you understand the problem, to use the right calculation steps to get the answer. And it is doing this accurately that actually indicates your understanding of the problem.
So how do you ensure that you have the right understanding of the problem? There are a few things you could do.
The first one is to carefully read and thoroughly consider the problem prior to engaging in any computation. So before you actually take the pen to paper and begin to add, subtract, and divide, you need to carefully consider what the problem is actually about.
On top of that, an understanding of the purpose and goal of the problem and the types of calculations that are required will provide the needed direction and confidence that is needed.
First, you read the question carefully, you think about it, and then you begin to ask yourself a few questions that help you glean what the main objective of the problem is.
Then once you have determined that, you begin to think about the various calculation steps that you could do to help you achieve that particular objective in the problem.
There are a few questions you could also ask that would enhance this process. The first one is, what is the unknown in the question? You ask yourself that question. What are you looking for? Is it the quantity in milliliters or the milliequivalents or the milliosmoles? You need to know what you're looking for, that is your unknown.
The second thing that could help is what data have you been given? You look in the question and see what is the data that you have.
The third thing is what is the condition? Basically, what this means is how do you actually link up that data that has been provided to help you determine the unknown?
The fourth question you could ask is, is it possible to actually satisfy the condition? Is it possible to actually link the data that has been provided in such a way that you can actually get to your answer?
The next question you could ask is, is the condition sufficient to determine the unknown? The data that has been provided and how you want to link it, is it enough to help you get the answer?
Now, let's take these questions and use a pharmaceutical calculations example and see how these questions can actually help improve your understanding of the problem.
So in this example, it says how many milliosmols per 100 mL are represented by a 5% ,250 mL potassium chloride solution. The molecular weight of Calcium Chloride is 74.5 g/mol.
We start off by analyzing the question. Our goal here is not to put pen to paper, but simply to understand the question some more. What exactly is this question about? And understanding the question is literally about 50% to 60% of solving the problem.
So one of the questions we want to ask is, what is the unknown? What are we looking for? In this question, the unknown is the number of milliosmols in 100 mL. It's not asking for osmolarity, it's not asking for how many milliosmols is in 500 mL. Indeed, it's asking for the number of milliosmols in 100 mL. Now that's important. That is our unknown. That is what we are looking for.
So the next question we can ask in analyzing the question so we have a deeper understanding of the problem is, what are the data? Now, this example question is a fairly short one, and so some of the data is actually very prominent. We can see it very easily.
But what exactly is the data that is provided in the question? We have the percentage strength, we have the molecular weight of potassium chloride, and also we have number of particles.
Now, nowhere in the question do you see the term number of particles, but that is implied because you are solving an osmolarity calculations type question, and you would need a number of particles when you go to your equation.
So the number of particles will come from the number of species that are released by the potassium chloride salt when in an aqueous environment. So that is implied, which means having a background understanding of the topic is also pertinent for you to understand the critical data that can be used in the computation.
The next trigger question that you could ask is, what is the condition? By the condition here we mean, how are you going to link or connect the data that you've identified in the previous question that you asked to be able to get to the unknown, to solve the unknown?
So we can do that in this example by linking the percentage strength, the molecular weight, the number of particles, the milliosmols per liter, which is also your osmolarity, and the milliosmols per 100 mL, which is your unknown. Now you can link all this data in such a way that you end up being able to accurately determine the number of in 100 mL.
The next question you can ask during the analysis of the question is, is it possible to satisfy the condition? Is it possible to link percentage strength, molecular weight, number of particles, per liter to determine the milliosmols per 100 mL? The answer to that question is yes, for this example.
The next trigger question we can ask is, is the condition sufficient to determine the unknown? In this example question, the answer to that would be yes, because we can appropriately connect percentage strength, molecular weight, the number of particles, milliosmols per liter in such a way that we would be ultimately able to determine the number of millimols per 100 mL.
So by going through these five trigger questions and answering those appropriate or really, we've been able to analyze the question in such a way that we really understand what the problem is here. Our unknown is the number of milliosmols per 100 mL. The data that we have is the percentage strength, molecular weight, number of particles, milliosmols per liter. We are going to connect those pieces of information in such a way that we will end up being able to determine the number of milliosmols per 100 mL.
STEP 2 - Devising a Plan
But how do we do that? We need a plan, and that's the second step. Step number two is devising a plan.
The main goal in devising a plan here is to be able to find the connection between the data and the unknown. The plan I'm referring to here is a series of specific calculation steps done in a certain specified sequence so that ultimately you get your answer. That's the plan we're referring to.
So there are a few questions we could ask that will help us in devising the plan. The first one is, have you seen the question before? Because if you've seen the question before, you probably have solved it before. And so you have some framework as to the types of calculations that you need to perform and the order in which you need to perform them.
Now, if you have not seen the question before, have you seen the same question in a slightly different form? Is the question similar to something you've seen in your practice where maybe the numbers would change or the concentration was changed from percentage strength to ratio strength? Have you seen the same question in a slightly different form?
So if you have not seen the question before and you've not seen the same question in a slightly different form before, then the next thing you could also ask is, do you know a related problem? Or do you know a concept that could be useful?
And actually, the more practice questions you solve, the more likely you're going to have a good repository of related problems, concepts, and similar types of problems that you've seen that when you come across a question in the future, you have a good frame of reference to solve the question. So I highly encourage you to do a lot of practice problems with the goal of getting familiar with why the variety of examples is practical in your preparation.
So what if you have not seen the question before? You have not seen the same question in a slightly different form? You do not know a related problem? You don't know a concept that readily comes to mind? Then what you could do is actually look at the unknown and think of a familiar problem having the same or similar unknown. Using this approach, you're actually looking at what your final target is, what your unknown is, and trying to craft a pathway to get to that.
Perhaps you're looking for a quantity in grams and you don't know a useful equation. Perhaps you could even draw upon the use of dimensional analysis and track your units and see whether you could arrange the data in such a way that the units cancel out appropriately to end up with your quantity in grams. So you could use this approach to help you make a connection between the data and the unknown and help you develop a very good plan to get to your answer.
So now let's actually apply this approach using an example calculations question to see how we could develop the plan. So the example question is still the same as what was used earlier. It says how many milliosmols per 100 mL are represented by a 5%, 250 mL Potassium Chloride Solution. Molecular Weight of Potassium Chloride is equal to 74.5 g/mol.
So here I'm going to show you using some of the strategies that we discussed earlier, how you could come up with a good plan to solve this question. Remember, a plan is a series of well-defined calculation steps in a certain specified sequence such that when you go through all of those steps, you end up with the answer.
STEP 2 - Plan A
So in this example calculation, I'm going to give you two plans. The first one is plan A, and it states to start off with the osmolarity equation. That's the first thing we will do.
After we've written down the osmolarity equation, we will go ahead and determine the mass concentration of potassium chloride in grams per liter in the solution. Now, we will soon find out why we need the grams per liter.
The next step will be to determine the number of particles of potassium chloride.
The fourth step will be to determine the osmolarity, which is milliosmols per one liter of the solution.
And then once we know the osmolarity, we are going to use proportion to determine the milliosmols in 100 mL.
So these are the five steps. We will go step one, step two, step three, step four, and by the time we get to step five, the solution to the question would unveil itself.
STEP 2 - Plan B
The alternative plan, which is plan B, will look like this. First, we'll start off with the milliosmol equation. And then we will determine the amount of potassium chloride in milligrams in 100 mL of the solution. And then we'll go ahead and determine the number of particles of potassium chloride.
And finally, we will determine the milliosmols in 100 mL. So plan A has five steps and plan B has four steps. And if you go through each step of each plan, you end up being able to determine the number of milliosmols in 100 mL.
So I showed these two plans because there are multiple ways you could solve a pharmaceutical calculations question. But as you do a lot more practice and have a deeper understanding of the question, you end up being able to develop the most efficient plan, which would allow you to get your answer in the fewest number of steps.
STEP 3 - Implementing the Plan
Now let's take a look at the next step. Step three is implementing the plan. In step one, we understood the problem. Step two, we devised the plan. Step three, we need to execute and implement the plan.
Now, this involves performing the necessary calculations for each of the steps that are in your plan, and you want to do it in such a way that you're using the most appropriate method, you're being efficient and you really understand what you're doing.
So I'm going to use the same example from previous to illustrate how you could implement plan A and plan B for this question which was devised in step two.
STEP 3 - Plan A
So we start with plan A. The first step was to start with the Osmolarity Equation. And the Osmolarity Equation actually states that mOsm/L is equal to g/L divided by the Molecular Weight, times the number of particles, times 1,000. So that was the first step.
Then we move on to the next step. In the next step, we said we wanted to determine the mass concentration of potassium chloride in grams per liter in the solution. And the reason we wanted to determine the mass concentration of KCL in grams per liter is because in the osmolarity equation, you have milliosmols per liter, being equal to grams per liter, divided by the molecular weight. So we need a g/L piece, and we do not have g/L provided in the question explicitly.
So how we do this is we take the percentage concentration, which is 5%, which means you have 5g of potassium chloride in 100 mL of solution.
That should be equal to some quantity in grams divided by 1,000 ml. And the 1,000 mL comes in because 1,000 mL is equal to 1 liter.
So we solve for X, and X is going to be equal to 5 g divided by 100 mL, times 1,000 mL, and that should be equal to 50 g.
Then we move on to step three. And in step three, what we want to do is determine the number of particles of potassium chloride. And so the way we find number of particles for potassium chloride is when you put potassium chloride in an aqueous environment, potassium chloride is a salt in an aqueous environment is going to dissociate into a potassium cation and a chloride anion.
We have one potassium cation and one chloride anion, a total of two particles. So the number of particles here is two. So we are done with step three, we move on to step four.
Now in step four, we want to determine the osmolarity of the solution. And so milliosmols per liter is going to be equal to g/L, which we determined to be 50, divided by the molecular weight, which was 74.5, times the number of particles, which is 2, times 1,000.
And if you do that, you end up with 1,342.28 mOsm/L.
Now, our goal is to determine milliosmols per 100 mL, and that's where step five becomes pertinent. So in step five, we determine the milliosmols in 100 mL. So we take the answer from step four, which was 1,342.28 mOsm/L, which would be per 1,000 mL. And we set that equal to some quantity in mOsm divided by 100 mL, because that's the volume of solution we are interested in.
We solve for the unknown, which is X. So X equals 1,342.28 mOsm, divided by 1,000 mL, times 100 mL.
The milliliters cancel out and you end up with 134.23 m/L. And that would be your answer.
So once again, after we understood the problem, we devised a five step plan, and by completing each step, we ended up having the solution to the question.
STEP 3 - Plan B
Now, let's see what it would look like for Plan B. So in Plan B, the first step was to start with the milliosmol equation. The milliosmol equation states that milliosmol is equal to millimol, times number of particles.
And the millimole is equal to milligrams divided by molecular weight.
So we can say milliosmols equals milligrams, divided by molecular weight, times the number of particles. So that's our equation.
In step two, we wanted to determine the amount of potassium chloride in milligrams in 100 mL of the solution.
Now, the reason we wanted to determine the amount in milligrams is because our equation, milliosmols is equal to milligrams, divided by molecular weight, times number of particles. So we need the amount of potassium chloride in milligrams.
So the way we do that is to take the percentage strength, which is 5%.
And so 5 g in 100 mL, should be equal to some quantity in grams times 100. So basically the hundreds will cancel out.
But if you solve for X, you end up with 5 g divided by 100 mL, times 100 mL. The milliliters cancel out and you end up with 5g.
Now we need the amount in milligrams, so we take the grams and we convert that to milligrams. So 1 g equals 1,000 mg. The grams cancel out and you end up with 5,000 mg.
So now we move on to step three. And in step three, we determine the number of particles of potassium chloride.
And the way you do that is to take the potassium chloride and when you put potassium chloride in an aqueous environment, it would dissociate into a potassium cation and a chloride anion. We have one potassium cation, one chloride anion, and that will mean that we have two particles in the solution. So the number of particles will be equal to two.
So now we move on to step four. So in step four, we determine the milliosmols in 100 mL. The way we do that is to take the equation, milliosmols equals weight in milligrams. So the weight of potassium chloride in 100 mL of the solution was 5 g, which was 5,000 mg. We divide that by the molecular weight, which is 74.5, we multiply that by number of particles, which is two, and that gives us 134.23 milliosmols, which is the same answer as what we got in plan A.
So that's how you go about implementing the plan. The key thing is to make sure that for each step you are performing your calculations correctly. If you do that, you end up with the right answer.
STEP 4 - Double Check the Answer
And so the last step is to double-check the answer. And here there are just two important points I want to put across.
The first thing is before you assume the answer is correct, the problem should be read again. So you want to read the question again and you want to check all the calculations for the each of the steps that you had in your plan. You double-check it.
Now, the reason you want to do this is that sometimes you may have punched the number incorrectly in your calculator, or you may have written down the decimal in the wrong place. So all of this is just to ensure that the work that you did in steps one, two, and three are validated.
And so the next point is to consider the reasonableness of the answer in terms of the numeric value. And this includes the proper position of a decimal point and the units of measure.
So for example, if your unknown is supposed to be quantity in grams, and for some reason, at the end of your manipulation, you end up with quantity in milliliters, you know something is off right there. And that will help you go back and evaluate each step and make sure that your calculation was done correctly for each step that you had in your plan.
So those are the four effective steps for solving any pharmaceutical calculations question.
So I hope you found this tutorial useful. Thank you so much, and I will see you in the next blog.
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