Problem

The label for lorazepam is shown below. How many grams of lorazepam are in 1.6 milliliters of this drug? lorazepam $4 \mathrm{mg} / \mathrm{mL} 1 \mathrm{~mL}$ Vial For IM use REFRIGERATE for IV route, see directions For IV use, additional dilution is required; see accompanying information. Usual Dosage: See accompanying information Do not use if solution is discolored or contains a precipitate. There are grams of lorazepam in 1.6 milliliters of this drug. (Type an integer or a decimal.)

Solution

Step 1 :The label indicates that there are 4 milligrams (mg) of lorazepam per milliliter (mL) of the drug.

Step 2 :To find out how many grams of lorazepam are in 1.6 milliliters, we need to multiply the concentration (4 mg/mL) by the volume (1.6 mL).

Step 3 :\(concentration = 4\)

Step 4 :\(volume = 1.6\)

Step 5 :\(amount_{mg} = concentration \times volume = 4 \times 1.6 = 6.4\)

Step 6 :However, the result will be in milligrams, so we need to convert it to grams by dividing by 1000 (since there are 1000 milligrams in a gram).

Step 7 :\(amount_{g} = \frac{amount_{mg}}{1000} = \frac{6.4}{1000} = 0.0064\)

Step 8 :Final Answer: There are \(\boxed{0.0064}\) grams of lorazepam in 1.6 milliliters of this drug.

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