  # Pharmacy Math Question

I feel stupid asking this, math is not my strong point.

1) Prepare 240mL of a 20% solution from a 50% solution you have in stock. How much concentrate will you use? How much diluent?

Can someone show me the steps on how to do it and not just give me the answer. I’m still learning so give me a break!

Thanks,
Fuzz

Alright, you could approach it like this. You need a 240 ml of 20% solution. How much “stuff” is there in that quantity at that concentration? 0% is no stuff, 100% is pure stuff, etc. So, 20% of 240 ml is 48 ml of pure stuff. Now, if you had the pure stuff (100% solution) at hand, and you mixed 48 ml of that with 192 ml of diluent (0% solution), you would have what you need - a total of 240 ml of which 48 ml (i.e. 20%) is stuff.

Now, you don’t have pure stuff at hand, you only have 50% stuff solution. You still need to get 48 ml of pure stuff in the final mix. How much 50% stuff solution does it take to get 48 ml of pure stuff. Well, since it’s half diluted, you need twice as much, so 96 ml of 50% solution will contain the 48 ml of stuff, plus 48 ml of diluent. Now, you still need to fill up to 240 ml. So, 240-96=144. You need to add 144 ml of diluent (0% stuff) back to get the volume you need.

Q1C1=Q2C2

Q1=total quantity 1 240ml
C1=total Concentration 1 20%
Q2=total quantity of 2 =X
C2=total concentration of 2 50%

240*.2=.5Q2

Solve for Q2

At first it was hard to understand but I got it! Thanks. Just to make sure.

240mL x 0.2% = 48mL of pure (100%) solution needed to make a 240mL of 20% solutions

We have half pure solution so need twice as much.

48mL x 2 = 96mL of concentrate needed from 50% solution.

240mL - 96mL = 144mL of diluent/solvent needed.

96mL Concentrate
144mL Diluent

Thanks again.

[quote]Justayoungen wrote:
Q1C1=Q2C2

Q1=total quantity 1 240ml
C1=total Concentration 1 20%
Q2=total quantity of 2 =X
C2=total concentration of 2 50%

240*.2=.5Q2

Solve for Q2[/quote]

Yeah I was solving for x as well. However, your set up worked unlike mine did.
x = 240 mL
0.5% 0.2%