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% W/W

(Percent weight/weight) This is used when the active ingredient and the base are both in the same unit of weight, grams.
By definition, 1% = 1gm of active ingredient per 100 grams of total product. (1% = 1gm/100gm) 

% V/V

(Percent volume/volume) This is used when the solute (the active drug) and the solvent (the inactive base) are both in the same unit of volume, milliliters.
By definition, 1% = 1ml of active ingredient per 100ml of total product. (1% = 1ml/100ml) 

% W/V

(Percent weight/volume) This is used when the solute (the active drug) is in the unit of weight, grams, and the solvent is in the unit of volume, milliliters.
By definition, 1% = 1gm of active ingredient per 100ml of total product. (1% = 1gm/100ml) 

In either of the cases, the process is the same. To determine the percentage strength, divide the amount of active ingredient by the total weight, or volume, of the product, then multiply by 100.

(Active Ingredient <g or ml> ÷ Total Preparation <g or ml>) x 100 = percentage concentration


If 1.4g of phenol is mixed with 9.0g of glycerin, what is the percentage concentration of phenol in the product?

First find the total weight of the product:
1.4 + 9.0 = 10.4g Plug your values into the formula and solve: 1.4/10.4 x 100 = 13.0% w/w 

4g of KCl is dissolved in enough of a sweetened base to make a total of 25.0ml. What is the percent concentration of the final preparation?

4/25 x 100 = 16% w/v


10.0ml of glycerin is dissolved in enough water to make 73ml of final solution. Calculate the percentage strength of glycerin.

10/73 x 100 = 14% v/v


Percentage Concentration Answers
42.0g KCL is added to enough of a sweetened vehicle to equal 1 liter. Calculate the resulting percentage concentration of KCl. 
42.0/1000 x 100 = 4.2% w/v


13g Hydrocortisone is added to 60g of cold cream. Calculate the resulting percentage concentration of Hydrocortisone.

13/73 x 100 = 17.8% w/w


23.0ml of "Drug A" is added to 65ml of water. Calculate the resulting percentage concentration of "Drug A".

23/88 x 100 = 26.1% v/v


45.0g of "Drug B" is mixed with 100g of an inactive ointment base. Calculate the resulting percentage concentration of "Drug B".

45 + 100 = 145
45/145 x 100 = 31.0% w/w 

3.0g of "Drug C" is added to enough alcohol to make a total of 30ml of solution. Calculate the resulting percentage strength of "Drug C".

3/30 x 100 = 10% w/v


Percentage Concentration Answers
How much propranolol must be used to make 240ml of a 3% suspension? 
3g/100ml = x/240ml
x = 7.2gm 

How much KCl would be needed to make 450ml of a 20% solution?

20g/100ml = x/450ml
x = 90g 

How much hydrocortisone powder would be needed to make 60g of a 10% cream?

10g/100g = x/60g
x = 6g 

How much diazepam would be needed to make 360ml of a 0.5% suspension?

0.5g/100ml = x/360ml
x = 1.8g 

How much NaCl would be needed to make 1000ml of a 0.9% solution?

0.9g/100ml = x/1000ml
x = 9g 

Alligation Answers
A prescription calls for an 80% concentration of "Cream A". Your pharmacy stocks "Cream A" in the 95% and 10% commercially available strengths. Calculate the amount of each to make 300g of the final product. 
95% > 70/85 x 300 = 247g
10% > 300  247 = 53g 

A prescription calls for 240ml of a 30% solution of "Drug B". "B" is commercially available in strengths of 80% and 20%. How much of the 20% solution will be needed to make the final product?

50/60 x 240 = 200ml of 20%


Ratio Concentration Answers
An order for an injection of 4mg of epinephrine comes to the pharmacy. The pharmacist has drawn up the appropriate volume of 1:100 epinephrine into a syringe. How much should he have used? 
1:100 = 10mg/ml
1ml/10mg = x/4mg x = 0.4ml 

The physician has given you an order for 800ml of a 1:1000 solution of KMnO4 solution. How much KMnO4 will be required?

1:1000 = 1mg/ml
1mg/1ml = x/800ml x = 800mg 