Nalorphine, a relative of morphine, is used to combat withdrawal symptoms in heroin users. How many milliliters of a 0.40% (m/v) solution of nalorphine must be injected to obtain a dose of 1.5 mg?

Verified step by step guidance

1. Step 1: Understand the problem. You are tasked with determining the volume (in milliliters) of a nalorphine solution with a concentration of 0.40% (m/v) that contains a dose of 1.5 mg of nalorphine. Recall that % (m/v) means grams of solute per 100 mL of solution.
2. Step 2: Convert the dose of nalorphine from milligrams to grams. Use the conversion factor: 1 mg = 0.001 g. This is necessary because the concentration is given in terms of grams.
3. Step 3: Write the relationship for the concentration of the solution: \( \text{Concentration} = \frac{\text{Mass of solute (g)}}{\text{Volume of solution (mL)}} \times 100 \). Rearrange this equation to solve for the volume of solution: \( \text{Volume of solution (mL)} = \frac{\text{Mass of solute (g)} \times 100}{\text{Concentration (% m/v)}} \).
4. Step 4: Substitute the known values into the rearranged equation. Use the mass of nalorphine in grams (from Step 2) and the concentration of the solution (0.40% m/v).
5. Step 5: Perform the calculation to determine the volume of solution in milliliters. Ensure that your units are consistent throughout the calculation.

Key Concepts

Concentration (m/v) Solutions

The concentration of a solution can be expressed in mass/volume (m/v) percentage, which indicates the mass of solute per 100 mL of solution. In this case, a 0.40% (m/v) solution means there are 0.40 grams of nalorphine in 100 mL of the solution. Understanding this concept is crucial for calculating the volume needed to achieve a specific dose.

Dosage Calculation

Dosage calculation involves determining the appropriate amount of a drug to administer based on the desired therapeutic effect. In this scenario, the goal is to find out how many milliliters of nalorphine are required to deliver a dose of 1.5 mg. This requires converting the desired dose into a compatible unit with the concentration of the solution.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, it is necessary to convert milligrams (mg) to grams (g) since the concentration is given in grams per 100 mL. This step is essential for ensuring that the calculations align with the units used in the concentration of the nalorphine solution.