Pharmaceutics Dilution Problems

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A series of problems with detailed answers.

**Problem 1**

Acid 1: 5% w/v

Acid 2: 10% w/v

Flexible Collodion q.s. 100 mL (FYI: collodion is a flammable, syrupy solution applied to skin)

How many mL of an 85% w/w solution of Acid 1 with a specific gravity of 1.21 should be used in preparing the prescription?

**Problem 2**

Acid 1: 5% w/v

Acid 2: 10% w/v

Flexible Collodion q.s. 100 mL (FYI: collodion is a flammable, syrupy solution applied to skin)

How many mL of an 85% w/v solution of Acid 1 with a specific gravity of 1.21 should be used in preparing the prescription?

**Problem 3**

Drug “X” solution is prepared by dissolving 750 g of Drug “X” in sufficient volume of solvent to make 1000 mL of solution. If the specific gravity of this solution is 1.5, how many milliliters of solvent are used?

**Problem 4**

A bottle of drug solution is labeled as 96.5% w/v. If the specific gravity of the solution is 1.71, what is its concentration in % w/w?

**Problem 5**

A prescription calls for 60 mL of a 1.5% (w/v) spirit using drug “X”. Since the water solubility of “X” is only 2 g/L, ethanol as a co-solvent is used to ensure that the preparation will be a homogenous solution. The solubility of “X” in ethanol is 1 g/5 mL.

a) What is the volume fraction of ethanol in this preparation?

b) How many milliliters of USP alcohol (95% v/v) are needed for the preparation of this topical solution?

**Problem 6**

The solubility of drug “Y” in a particular solvent is 2 g/120 mL. The density of the solvent is 0.786 kg/L. The molecular weights of “Y” and the solvent are 888.88 g/mol and 60.10 g/mol, respectively.

a) What is the molality of the saturated solution?

b) What is the molarity of the saturated solution if its density is 0.86 g/mL?

**Problem 7**

How many grams of HNO3 must be added to 8.5 L of water to make a 75 mM solution? MW of HNO3 = 63 g/mol

**Problem 8**

100 g of ointment of Dug “Y” was prepared by using 70 g of vehicle. Drug “Y” is an oil. If the specific gravity of the oil is 0.90, how many milliliters of oil “Y” was needed for this preparation?

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