c1v1+c1v2=c3v3 pharm solution question

Question

need a 1.5%(w/v) solution out of:

a) 100mg/5ml (30ml bottle)

b)10mg/5ml (100 ml bottle)

How much of the 10mg/100ml has to be mixed with the 100mg/5ml to obtain the 1.5% solution

Answer 1

The concentration & dilution equation is a great way to figure out how to mix 2 solutions of different concentrations to make a solution of another desired concentration!

For this problem, you are being asked to mix a 1.5% solution using a 10 mg/100 mL solution and a 100 mg/5 mL solution.

In order to use the equation, you need to convert the starting concentrations to percent weight per volume. Percent strength is a way of expressing concentration as "amount per 100"; percent = per cent...ie of 100 based on the Latin word for hundred, centum. You can remember this by thinking of 100 cents in a dollar.

To accomplish this, set up ratio proportions to determine how many grams of substance would be in 100 milliliters of that solution:

10 mg/100 mL: This concentration is already over 100 mL, but the weight needs to be converted to grams. 10 mg x 1 g/1000 mg = 0.01 g. So this solution is 0.01%.

100 mg/5 mL: 100 mg x 1 g/1000 mg = 0.1 g; 0.1 g/5 mL = x g/100 mL, cross multiply to solve for x=2, so this is a 2% solution.

You may find it helpful to identify your variables before constructing the equation. You'll notice there are two unknown numbers; the volume of the first solution (V1) and the final volume (V3), but you can't solve an equation with 2 variables. Set x as the variable you are solving for, so V1, and we know V3 will be the combined volume of both solutions, so we can express that at 5 mL+x

C1: 0.01% C2: 2% C3: 1.5%

V1: x V2: 5 mL V3: x+5 mL

So our equation is:

(0.01)(x) + (2)(5) = (1.5)(x+5)

0.01x + 10 = 1.5x + 7.5

2.5 = 1.49x

x = 1.68 mL