APCAT+-+Calculations+Walkthrough

=Calculations Walkthrough=

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Quick Tips
//read the question very carefully!//
 * often you might skim through the question and forget a key word (calculate the __daily__ dose - meaning you may need to read the prescription for how often the patient needs to take a medication)
 * in other cases the question might give you too much information **(Dopamine 200 mg in 500 mL** of normal saline at 5 μg/kg/min is ordered for a 70Kg patient . What is the final **concentration of solution in μg/mL**? - half of this question is there just to distract you!)

//remember correct units!//
 * a useful tip from the below document is to write out your 'final line' with the units required from the question before writing your answer
 * make your units consistent or they won't carry through the equation properly

//if in doubt (and have time left), double-check your answer!//
 * if changing the concentration of a product, it helps to calculate the final concentration from your answer to make sure you're right

//random but useful facts//:
 * isotonicity is 0.9% NaCl (0.9g/100mL)
 * NaCl equivalent is the osmotic pressure provided by 1 g of active ingredient - i.e. multiply amount in grams of active ingredient by its NaCl equivalent to calculate the amount of NaCl provided and hence required to achieve isotonicity
 * ratio strengths are expressed as 1 in //r -// where 1 unit of active ingredient is in //r// units of diluent
 * parts per million (ppm) would be a ratio of //x// in 1 000 000 (i.e. 1 g in 1 000 000mL)
 * percentage strengths is the amount of ingredient in 100 parts of a product (v/w and w/v are expressed in mL/100g and g/100mL, respectively - i.e 0.9% w/v = 0.9g/100mL)

Useful Resources
[|Calculations used when compounding medications] pretty useful guide - proportion calculations, isotonicity, diluting and concentrating (both algebriac and alligation methods) [|Introduction to pharmaceutical calculations]

**increasing the concentration of a product**
//general description of this equation://
 * the numerator represents the amount of active ingredient, denominator represents the total amount in the preparation (you want this ratio to equal the number on the right side of the equal sign (0.1 = 10%)
 * left-hand side of the fraction represents what you are adding (indicated by x and 0.2x, which is the concentration of active ingredient you are adding) and the right-hand side is what is already there.

//**referring to question 13b) of the [|Selected Calculations (Ansel)]**// **//file://**
 * the zinc cream currently contains 2g of zinc oxide and 62g of other excipients (the 2 and 64 [62+2] in the equation)
 * the cream is currently at 3.1% but we want to change it to 10% (the 0.1 in the equation) using a 20% zinc oxide ointment (the x on the denominator [this is the total amount we are adding] and the 0.2x, representing that the ointment we are adding only contains 20% w/w of our active ingredient)
 * if you solve for x, you will find that it contains the correct answer of 44g!


 * //referring to question 4 of the// //[|NFEC Preparation Guide 2008]//** //**file:**

How many mL of alcohol 90% v/v must be added to 200 mL of alcohol 20% v/v, to produce alcohol 70% v/v?//



//general description of this equation://
 * same as the previous equation, apart from the fact that this question involves a concentration and volume of the active ingredient already there
 * we start with 200mL of 20% alcohol (0.2 x 200) and want to make to a final concentration of 70% (0.7) using 90% alcohol (0.9x)
 * solve for x and you come up with the correct answer of 500mL!

//**referring to question 14**// //**of the [|Selected Calculations (Ansel)]**// **//file://**

//How many grams of coal tar should be added to 925g of zinc oxide paste to prepare an ointment containing 6% of coal tar?//



//general description of this equation://
 * much simpler, as there is no active ingredient (coal tar) already present in the preparation
 * solve for x and you come up with the correct answer of 59g!

Alligation

 * //referring to question 1//** **//of the//** [|**//Calculation Questions//**] **//file://**

//How much glycerin (wt/mL 1.26) should be added to water (wt/mL 1.0) to produce 5 litres of solution of wt/mL 1.05?//

Desired concentration/strength = 1.05

Work out the differences of the concentration/strength of the two products to the desired strength and assign the difference to the opposite product: //glycerin//

//water//

The total amount required is divided by the sum of these differences:

This number is then used to determine how much of each product is required: //glycerin//

//water//

Backtracking can be done to check your answer: 5L of solution of wt/mL 1.05 will weigh:

0.96 L of glycerin at 1.26g/mL:

4.04 L of water at 1g/mL:

Total solution will weigh: **
 * Graphical representation of the alligation method:

Isotonicity
//**referring to question 17**// //**of the [|Selected Calculations (Ansel)]**// **//file://**

Ephedrine Sulfate 0.3g (NaCl equivalent = 0.23) Purified Water 30mL Make isotonic by adding NaCl

First work out the amount of NaCl in 30mL to make it a solution of 0.9% NaCl: media type="custom" key="4209397"

Then work out how much of the osmotic pressure is already provided by the ephedrine sulfate:

The difference of this is how much NaCl needs to be added to make the solution isotonic: media type="custom" key="4209427"


 * //referring to question 20 of the//** [|Selected Calculations (Ansel)] **//file://**

First work out the amount of NaCl in 15mL to make it a solution of 0.9% NaCl:

Then work out how much of the osmotic pressure is already provided by the oxymetazoline: media type="custom" key="4211037"

The difference of this is how much NaCl needs to be added to make the solution isotonic: media type="custom" key="4211041"

Convert this value by dividing by the NaCl equivalent to calculate how much boric acid needs to be added:

Finally determine how much of a 5% solution of boric acid needs to be added: media type="custom" key="4211059"

Ratio Strengths

 * //referring to question 12 of the//** [|Selected Calculations (Ansel)] **//file://**

//How many mLs of water should be added to a litre of 1:3000 (w/v) solution to make a 1:8000 (w/v) solution?//

Work out how much active ingredient is found in 1 Litre of a 1:3000 (w/v) solution:

Therefore, in a 1:8000 (w/v) solution, work out how much water is used to dissolve 0.333g of ingredient:

From this, work out how much water needs to be added: