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Chapter 4: Problem 78

Glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is a substance used extensively in the manufacture of cosmetics, foodstuffs, antifreeze, and plastics. Glycerol is a water-soluble liquid with a density of \(1.2656 \mathrm{~g} / \mathrm{mL}\) at \(15^{\circ} \mathrm{C}\). Calculate the molarity of a solution of glycerol made by dissolving \(50.000 \mathrm{~mL}\) glycerol at \(15^{\circ} \mathrm{C}\) in enough water to make \(250.00 \mathrm{~mL}\) of solution.

Short Answer

Expert verified
The molarity of the glycerol solution is calculated as follows: First, find the mass of glycerol by multiplying the density and volume: \(mass = (1.2656 \mathrm{~g/mL})(50.000 \mathrm{~mL})\). Next, convert the mass to moles using the molar mass of glycerol, \(92.09 \mathrm{~g/mol}\): \(moles = mass ÷ molar \ mass\). Finally, calculate the molarity by dividing the number of moles by the total solution volume in liters (\(0.25000 \mathrm{~L}\)): \(Molarity = (moles)/(0.25000 \mathrm{~L})\).

Step by step solution

01

Calculate mass of glycerol

Given, the density of glycerol is 1.2656 g/mL, and the volume of dissolved glycerol is 50.000 mL. To find the mass of glycerol, use the formula: mass = density × volume. So, mass of glycerol = (1.2656 g/mL)(50.000 mL)
02

Convert mass to moles

To convert the mass of glycerol to moles, divide the mass by the molar mass of glycerol (which is the sum of the molar masses of its constituent elements, i.e., \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\)). The molar mass of glycerol is \(3(12.01)+8(1.01)+3(16.00) = 92.09 \mathrm{~g/mol}\). Now, the number of moles of glycerol = mass ÷ molar mass.
03

Calculate the molarity

The molarity is calculated by dividing the number of moles by the total solution volume in liters. The total volume of the solution is given as 250.00 mL, which is equal to 0.25000 L. Then, calculate the molarity as: Molarity = (number of moles)/(total solution volume in L) Put together the previous steps to find the molarity of the glycerol solution.

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Most popular questions from this chapter

Label each of the following substances as an acid, base, salt, or none of the above. Indicate whether the substance exists in aqueous solution entirely in molecular form, entirely as ions, or as a mixture of molecules and ions. (a) HF, (b) acetonitrile, \(\mathrm{CH}_{3} \mathrm{CN},\) (c) \(\mathrm{NaClO}_{4},\) (d) \(\mathrm{Ba}(\mathrm{OH})_{2}\).

Lanthanum metal forms cations with a charge of \(3+.\) Consider the following observations about the chemistry of lanthanum: When lanthanum metal is exposed to air, a white solid (compound \(\mathrm{A}\) ) is formed that contains lanthanum and one other element. When lanthanum metal is added to water, gas bubbles are observed and a different white solid (compound \(\mathrm{B}\) ) is formed. Both \(\mathrm{A}\) and \(\mathrm{B}\) dissolve in hydrochloric acid to give a clear solution. When either of these solutions is evaporated, a soluble white solid (compound C) remains. If compound \(\mathrm{C}\) is dissolved in water and sulfuric acid is added, a white precipitate (compound D) forms. (a) Propose identities for the substances \(\mathrm{A}, \mathrm{B}, \mathrm{C},\) and \(\mathrm{D} .(\mathbf{b})\) Write net ionic equations for all the reactions described. (c) Based on the preceding observations, what can be said about the position of lanthanum in the activity series (Table 4.5\() ?\)

(a) How many milliliters of a stock solution of \(6.0 \mathrm{M} \mathrm{HNO}_{3}\) would you have to use to prepare \(110 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{HNO}_{3} ?\) (b) If you dilute \(10.0 \mathrm{~mL}\) of the stock solution to a final volume of \(0.250 \mathrm{~L}\), what will be the concentration of the diluted solution?

(a) Calculate the molarity of a solution that contains \(0.175 \mathrm{~mol}\) \(\mathrm{ZnCl}_{2}\) in exactly \(150 \mathrm{~mL}\) of solution. (b) How many moles of \(\mathrm{HCl}\) are present in \(35.0 \mathrm{~mL}\) of a \(4.50 \mathrm{M}\) solution of nitric acid? (c) How many milliliters of \(6.00 \mathrm{M} \mathrm{NaOH}\) solution are needed to provide \(0.325 \mathrm{~mol}\) of \(\mathrm{NaOH} ?\)

A solution of \(100.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{KOH}\) is mixed with a solution of \(200.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{NiSO}_{4}\). (a) Write the balanced chemical equation for the reaction that occurs. (b) What precipitate forms? (c) What is the limiting reactant? (d) How many grams of this precipitate form? (e) What is the concentration of each ion that remains in solution?
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