A doctor prescribes 12 mg of a medication, but the medication available is in a concentration of 0.006 g per 5 mL. How much mL should be given to the patient?

Steps to Solve

1. Convert the prescribed dose from mg to g

First, we need to convert the dose from milligrams (mg) to grams (g). We know that:

$$1 \text{ g} = 1000 \text{ mg}$$

Therefore, to convert 12 mg to grams:

$$ \text{Dose in grams} = \frac{12 \text{ mg}}{1000} = 0.012 \text{ g} $$

2. Understand the concentration of the medication

The concentration of the medication is given as 0.006 g per 5 mL. This means in every 5 mL of this medication solution, there are 0.006 g of the medication.

3. Calculate the amount of mL needed for the prescribed dose

To find out how many mL are needed for the prescribed dose of 0.012 g, we can set up a proportion based on the given concentration:

From the concentration, we know:

$$ 0.006 \text{ g} \text{ is in } 5 \text{ mL} $$

Set up the equation using the ratio for the unknown volume ($V$) needed for 0.012 g:

$$ \frac{0.006 \text{ g}}{5 \text{ mL}} = \frac{0.012 \text{ g}}{V} $$

Now we can cross multiply to solve for $V$:

$$ 0.006 \cdot V = 0.012 \cdot 5 $$

4. Solve for V

Now, calculate:

$$ V = \frac{0.012 \cdot 5}{0.006} $$

Now simplify the expression:

$$ V = \frac{0.060}{0.006} = 10 \text{ mL} $$

Therefore, the final volume of the medication required is 10 mL.