Question 1.14: A patient requires an injection of 0.012 g of a pain killer ...

Fundamentals of General, Organic and Biological Chemistry in SI Units

A patient requires an injection of 0.012 g of a pain killer available as a 15 mg /mL solution. How many milliliters of solution should be administered?
ANALYSIS Knowing the amount of pain killer in 1 mL allows us to use the concentration as a conversion factor to determine the volume of solution that would contain the desired amount.
BALLPARK ESTIMATE One milliliter contains 15 mg of the pain killer, or 0.015 g. Since only 0.012 g is needed, a little less than 1.0 mL should be administered.

exa 1,14

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STEP 1: Identify known information.	Dosage = 0.012 g Concentration = 15 mg/mL
STEP 2: Identify answer and units.	Volume to administer = ?? mL
STEP 3: Identify conversion factors. Two conversion factors are needed. First, g must be converted to mg. Once we have the mass in mg, we can calculate mL using the conversion factor of mL/mg.	$1 mg = .001 g \Rightarrow \frac { 1 mg}{ 0.001 g} \\ 15 mg/mL\Rightarrow \frac {1 mL} {15 mg}$
STEP 4: Solve. Starting from the desired dosage, we use the conversion factors to cancel units, obtaining the final answer in mL.)	$(0.012 \cancel{g} ) \left(\frac { 1 \cancel {mg}} {0.001 \cancel {g}} \right) \left( \frac { 1 mL}{ 15 \cancel{mg}} \right) = 0.80 mL$

BALLPARK CHECK Consistent with our initial estimate of a little less than 1 mL.

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