Nalorphene (C19H21NO3), similar to morphine, is used to combat withdrawal symptoms in narcotic users. Dose of nalorphene generally given is 1.5 mg. Calculate the mass of 1.5 – 10–3 m aqueous solution required for the above dose.

To determine the mass of a 1.5 × 10⁻³ M aqueous solution of nalorphene required to achieve a dose of 1.5 mg, we need to follow a few logical steps involving molarity, molecular weight, and the relationship between mass and volume. Let's break this down step by step.

Understanding Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. In this case, we have a 1.5 × 10⁻³ M solution of nalorphene. This means that in every liter of this solution, there are 1.5 × 10⁻³ moles of nalorphene.

Calculating Moles of Nalorphene

First, we need to convert the dose of nalorphene from milligrams to grams:

• 1.5 mg = 0.0015 g

Next, we need to find the number of moles of nalorphene in 0.0015 g. To do this, we need the molecular weight of nalorphene (C₁₉H₂₁NO₃). The molecular weight can be calculated as follows:

• Carbon (C): 12.01 g/mol × 19 = 228.19 g/mol
• Hydrogen (H): 1.008 g/mol × 21 = 21.168 g/mol
• Nitrogen (N): 14.01 g/mol × 1 = 14.01 g/mol
• Oxygen (O): 16.00 g/mol × 3 = 48.00 g/mol

Adding these together gives:

• Molecular weight of nalorphene = 228.19 + 21.168 + 14.01 + 48.00 = 311.368 g/mol

Finding Moles from Mass

Now, we can calculate the number of moles of nalorphene in 0.0015 g:

• Moles = mass (g) / molecular weight (g/mol)
• Moles = 0.0015 g / 311.368 g/mol ≈ 4.81 × 10⁻⁶ moles

Calculating the Volume of Solution Needed

Now that we know the number of moles required, we can find out how much volume of the 1.5 × 10⁻³ M solution is needed to provide these moles. Using the formula for molarity:

• Molarity (M) = moles of solute / volume of solution (L)

Rearranging this gives us:

• Volume (L) = moles of solute / Molarity (M)

Substituting the values we have:

• Volume = 4.81 × 10⁻⁶ moles / (1.5 × 10⁻³ moles/L) ≈ 3.21 × 10⁻³ L

Converting Volume to Milliliters

To express this volume in milliliters, we convert liters to milliliters (1 L = 1000 mL):

• Volume = 3.21 × 10⁻³ L × 1000 mL/L ≈ 3.21 mL

Final Result

Therefore, to achieve a dose of 1.5 mg of nalorphene from a 1.5 × 10⁻³ M aqueous solution, you would need approximately 3.21 mL of that solution. This calculation illustrates the relationship between concentration, volume, and mass, which is fundamental in pharmacology and chemistry.