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pharmacy math question

by Magda
(Frisco, tx)

A patient needs IV infusion of 0.9% NaCl. You have a 1L Sterile Water For Injection bag and 4.5% w/v stock solution of NaCl. Considering that there are no volume displacement effects; How much of the 4.5% w/v needs to be added to the 1L SWFI bag to produce the desired concentration?
A. 700mL
B. 250mL
C. 350mL
D. 500mL

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pharmacy math
by: Anonymous

Use an equation, with single missing variable.

What you have = What you want

C - concentration
V - volume

C1 x V1 = C2 x V2

1000(0.00) + X(0.045)= 1000(0.009)

Then do the MATH

0.045X = 9

X = 200mL
Hey anonymous...missed a step
by: Jerry

Yes, you take what you have, and equate it to what you want.

=> First, what do you have:
1000mL of water
That will be written as- 1000(0.0)
and,
you have 4.5% - but don't know how much needed.
This unknown variable will be X(0.045)

=> Next, what you need:
1L of water PLUS unknown amount of X that together contains 0.9% concentration:
[1000 + X](0.009)

Now, put it together:

1000(0.0)+x(0.045)=(.009)[1000+X]

0 + 0.045X = 9 = .009X

Subtract .009X from both sides

.036X = 9

Divide both sides by .036

X = 250

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