Question

100 ml of a 10\\(\frac{1}{2}\\) % solution has been prepared.
a. how many grams of medication is in the 10\\(\frac{1}{2}\\)%
strength solution?
b. how many milliliters of solution are in this 10\\(\frac{1}{2}\\)%
strength solution?
c. express this solution as a simplified ratio.
d. how much pure drug is needed to create 32.5 ml
of this solution?
e. how much pure drug is needed to create 85 ml of
this solution?
f. if you have 60 ml of solution, how many grams of
pure drug will you have in order to keep the 10\\(\frac{1}{2}\\)%?
10\\(\frac{1}{2}\\)% strength solution.
(type an integer or a decimal.)
b. \\(\square\\) milliliters of solution are in this
10\\(\frac{1}{2}\\)% strength solution.
c. the simplified ratio is \\(\square : \square\\).
d. about \\(\square\\) grams of pure drug are need
to create 32.5 ml of this solution.
(round to the nearest tenth as needed.)
e. about \\(\square\\) grams of pure drug are need
to create 85 ml of this solution.
(round to the nearest tenth as needed.)

Explanation:

Step1: Understand the problem (a)

We have a 100 mL solution with a concentration of \(10\frac{1}{2}\%\) (which is \(10.5\%\) or \(0.105\) in decimal). To find the grams of medication, we use the formula: mass = volume × concentration. Here, volume is 100 mL, and we assume the density of the solution is 1 g/mL (so 100 mL = 100 g of solution, approximately for dilute solutions). So mass of medication = \(100 \times 0.105\).
\(100 \times 0.105 = 10.5\) grams.

Step2: Solve part (b)

The problem states that 100 mL of the solution has been prepared. So the volume of the solution is 100 mL.

Step3: Solve part (c)

First, \(10\frac{1}{2}\%=\frac{21}{2}\%=\frac{21}{200}\) as a fraction. So the ratio of medication to solution is \(21:200\) (since \(\frac{21}{200}\) means 21 parts medication to 200 parts solution).

Step4: Solve part (d)

We know the concentration is \(10.5\%\) or \(0.105\). For 32.5 mL of solution, mass of pure drug = volume × concentration. So \(32.5 \times 0.105\).
\(32.5 \times 0.105 = 3.4125 \approx 3.4\) grams (rounded to nearest tenth).

Step5: Solve part (e)

For 85 mL of solution, mass of pure drug = \(85 \times 0.105\).
\(85 \times 0.105 = 8.925 \approx 8.9\) grams (rounded to nearest tenth).

Step6: Solve part (f)

For 60 mL of solution, mass of pure drug = \(60 \times 0.105\).
\(60 \times 0.105 = 6.3\) grams.

Answer:

s:
a. \(\boxed{10.5}\) grams
b. \(\boxed{100}\) milliliters
c. The simplified ratio is \(\boxed{21}:\boxed{200}\)
d. \(\boxed{3.4}\) grams
e. \(\boxed{8.9}\) grams
f. \(\boxed{6.3}\) grams