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4. Special cases

Often it is necessary to prepare solutions from chemicals that are less than 100% pure. To prepare solutions from these impure chemicals, first choose the volume and molarity of the resulting solution you require. Multiply the solution’s volume by its molarity. The product (n) is the number of moles of pure chemical needed to produce that solution. Mpure × Vpure = npure Because the percent purity of chemicals sold commercially is measured by mass, first calculate the mass of the pure chemical needed to make the solution. Multiply the number of moles of pure chemical times the gram formula weight of the chemical. mass of pure chemical = npure × gram formula weight (1) mass of pure chemical = Mpure × Vpure × gram formula weight The mass of the impure chemical times the percent purity equals the mass of the pure chemical. Divide the mass of pure chemical by the percent purity to yield the mass of the impure chemical. mass of impure chemical × percent purity = mass of pure chemical (2) mass of impure chemical = mass of pure chemical/percent purity Substitute the expression for mass of pure chemical from equation (1) into equation (2). mass of impure chemical = Mpure × Vpure × gram formula weight/percent purity For example, what mass of potassium hydroxide that is 85.9% pure is needed to prepare 1.0 L of a 0.25 M solution of potassium hydroxide? The gram formula weight of potassium hydroxide is 56.11 g/mol. mass of impure chemical = Mpure × Vpure × gram formula weight/percent purity = 0.25 M × 1.0 L × 56.11 g/mol ÷ 0.859 = 16 g If the chemical in question is a liquid, then one more calculation is required. Divide the mass of impure chemical by its density to yield the volume of chemical. volume of impure = mass of impure chemical in g/density of impure chemical in mL chemical in grams per milliliter Again, combine the previous equations. volume of impure chemical = Mpure × Vpure × gram formula weight/ (percent purity × density) For example, what volume of hydrochloric acid that is 37.1% pure is needed to prepare 1.0 L of a 0.10 M solution of hydrochloric acid? The gram formula weight of hydrochloric acid is 36.46 g/mol and the density of 37.1% hydrochloric acid is 1.200 g/mL. volume of impure chemical = Mpure × Vpure × gram formula weight/(percent purity × density) = 0.10 M × 1.0 L × 36.46 g/mol ÷ (0.371 × 1.200 g/mL) = 8.2 mL