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Chapter 13: Problem 35

What volume of glycerol,\(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\) \((d=1.26 \mathrm{g} / \mathrm{mL})\)must be added per kilogram of water to produce a solution with 4.85 mol \% glycerol?

Short Answer

Expert verified
To prepare a solution with 4.85 mol % glycerol by adding it to a kilogram of water, approximately 62.4 mL of glycerol is required.

Step by step solution

01

Determine the Molar Mass of Glycerol

The molar mass of glycerol, which has the chemical formula \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH})\mathrm{CH}_{2} \mathrm{OH}\), is found to be \(92.09 \mathrm{g/mol}\); this can be calculated by adding up the molar masses of individual atoms.
02

Calculation of Moles in 4.85% of 1kg of water

First, calculate the total moles in solution when 4.85 mol % of glycerol is added to 1 kg (or 1000 grams) of water. We know that mol percent (mol%) is defined by the number of moles of the solute (glycerol) per 100 moles of the total solution. Therefore, if 'x' moles of glycerol constitute 4.85% by mole, then the total moles in the solution will be \(x/0.0485\). The moles of water can be found by the formula weight of water (1kg) divided by the molar mass of water (18.015 \(g/mol\)), which equals \(1000/18.015\) moles. To solve for 'x', we set up the equation \(x/0.0485 = x + 1000/18.015\) then solve for 'x'.
03

Determine the Mass of Glycerol

The mass of glycerol can be found by multiplying the moles of glycerol 'x' (found in step 2) by the molar mass of glycerol.
04

Determine the Volume of Glycerol

The volume of glycerol can be found by using the density formula, Density = Mass/Volume. We can rearrange this to Volume = Mass/Density. therefore we find the volume of glycerol by dividing the mass of glycerol (found in step 3) by the given density of glycerol (1.26 \(g/mL\)).

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Most popular questions from this chapter

Briefly describe each of the following ideas or phenomena: (a) Henry's law; (b) freezing-point depression; (c) recrystallization; (d) hydrated ion; (e) deliquescence.

The most likely of the following mixtures to be an ideal solution is (a) \(\mathrm{NaCl}-\mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}-\mathrm{C}_{6} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{7} \mathrm{H}_{16}-\mathrm{H}_{2} \mathrm{O} ;\) (d) \(\mathrm{C}_{7} \mathrm{H}_{16}-\mathrm{C}_{8} \mathrm{H}_{18}\)

Use the concentration of an isotonic saline solution, \(0.92 \% \mathrm{NaCl}(\mathrm{mass} / \text { volume }),\) to determine the osmotic pressure of blood at body temperature, \(37.0^{\circ} \mathrm{C}\). [Hint: Assume that \(\mathrm{NaCl}\) is completely dissociated in aqueous solutions.]

A typical commercial grade aqueous phosphoric acid is \(75 \% \mathrm{H}_{3} \mathrm{PO}_{4}\) by mass and has a density of \(1.57 \mathrm{g} / \mathrm{mL}\) What is the molarity of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) in this solution?

Under an \(\mathrm{O}_{2}(\mathrm{g})\) pressure of \(1.00 \mathrm{atm}, 28.31 \mathrm{mL}\) of \(\mathrm{O}_{2}(\mathrm{g})\) dissolves in \(1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C} .\) What will be the molarity of \(\mathrm{O}_{2}\) in the saturated solution at \(25^{\circ} \mathrm{C}\) when the \(\mathrm{O}_{2}\) pressure is 3.86 atm? (Assume that the solution volume remains at \(1.00 \mathrm{L}\).)
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