Nalorphine 1C19H21NO3 2, a relative of morphine, is used to combat withdrawal symptoms in narcotics users. How many grams of a 1.3 * 10-3 m aqueous solution of nalor-phine are needed to obtain a dose of 1.5 mg?

검증된 단계별 안내

Convert the desired dose from milligrams to grams by using the conversion factor: 1 mg = 0.001 g.

Use the formula for molarity (M = moles of solute / liters of solution) to express the concentration of the solution in terms of moles of nalorphine per liter of solution.

Calculate the moles of nalorphine required for the dose by using the molar mass of nalorphine (C_{19}H_{21}NO_{3}).

Determine the volume of the solution needed to provide the calculated moles of nalorphine using the given molarity.

Convert the volume of the solution from liters to grams, assuming the density of the aqueous solution is approximately 1 g/mL, to find the mass of the solution needed.

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주요 개념

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Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for calculating how much solute is present in a given volume of solution. In this question, the molarity of the nalorphine solution is given, which allows us to determine how many moles are needed to achieve a specific mass of the drug.

Conversion between mass and moles

To solve problems involving solutions, it is often necessary to convert between mass (grams) and moles. This is done using the molar mass of the substance, which is the mass of one mole of that substance in grams. For nalorphine, knowing its molar mass allows us to convert the desired dose in milligrams to moles, which can then be used in conjunction with the molarity to find the required volume of solution.

Dilution and volume calculations

When working with solutions, understanding how to calculate the volume needed to achieve a certain concentration is essential. The relationship between molarity, volume, and moles is given by the equation M1V1 = M2V2, where M is molarity and V is volume. In this case, once the number of moles needed is determined, the volume of the 1.3 * 10^-3 M solution can be calculated to find out how many grams of nalorphine are required.