Question 39 of 50intermediate🔧 ApplyNumerical2 marks

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 1.5×1.5 \times 10^{-3}$$ m aqueous solution required for the above dose.

Correct Answer

The mass of aqueous solution required is approximately 3.21 g (or 3.2 g).

Exercise: EXERCISES | Q: 1.29 | (Page 29)
For More Understanding

Explanation

This is a molality-based calculation where we need to find the mass of solution required to deliver a specific dose. Molality is defined as moles of solute per kilogram of solvent. First, we calculate the molar mass of nalorphene, then find the moles in the given dose, and finally use the molality formula to find the mass of solvent. The total mass of solution is the sum of solute and solvent masses.

Solution Steps

  1. Step 1: Calculate molar mass of Nalorphene (C₁₉H₂₁NO₃) Molar mass = 19(12) + 21(1) + 1(14) + 3(16) = 228 + 21 + 14 + 48 = 311 g mol⁻¹

  2. Step 2: Calculate moles of Nalorphene in the given dose Given dose = 1.5 mg = 1.5×101.5 \times 10⁻³ g Moles of Nalorphene = Mass / Molar mass = (1.5×101.5 \times 10⁻³ g) / (311 g mol⁻¹) = 4.82×104.82 \times 10⁻⁶ mol

  3. Step 3: Use molality to find mass of solvent Molality (m) = Moles of solute / Mass of solvent (in kg) 1.5×101.5 \times 10⁻³ = (4.82×104.82 \times 10⁻⁶) / Mass of solvent (kg) Mass of solvent = (4.82×104.82 \times 10⁻⁶) / (1.5×101.5 \times 10⁻³) = 3.21×103.21 \times 10⁻³ kg = 3.21 g

  4. Step 4: Calculate total mass of solution Mass of solution = Mass of solute + Mass of solvent Mass of solution = 1.5×101.5 \times 10⁻³ g + 3.21 g = 3.2115 g ≈\approx 3.21 g

PreviousNext