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Chapter 10: Problem 96

The term proof is defined as twice the percent by volume of pure ethanol in solution. Thus, a solution that is \(95 \%\) (by volume) ethanol is 190 proof. What is the molarity of ethanol in a 92 proof ethanol-water solution? Assume the density of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) is \(0.79 \mathrm{g} / \mathrm{cm}^{3}\) and the density of water is \(1.0 \mathrm{g} / \mathrm{cm}^{3}\)

Short Answer

Expert verified
The molarity of ethanol in a 92 proof ethanol-water solution is approximately \(7.88\, M\).

Step by step solution

01

Calculate the volume percentage of ethanol in the solution

The problem states that the proof of a solution is defined as twice the percent by volume of pure ethanol in the solution. Given that the solution we are working with is 92 proof, we will find the volume percentage of ethanol in the solution by dividing 92 by 2: \[Volume \, Percentage \, of \, Ethanol = \frac{92}{2} = 46 \%\]
02

Use the densities to calculate mass percentages

We are given the density of ethanol (\(0.79 \, g/cm^3\)) and the density of water (\(1.0 \, g/cm^3\)). We can use these densities to find the mass percentages of ethanol and water in the solution: \[Mass \, Percentage \, of \, Ethanol = 0.46 * 0.79\] \[Mass \, Percentage \, of \, Water = 0.54 * 1.0\]
03

Convert mass percentages to actual masses

Assume we have 100 mL of the solution. We can find the mass of ethanol and water in the 100 mL solution: \[Mass \, of \, Ethanol = 100 * 0.46 * 0.79 = 36.34 \, g\] \[Mass \, of \, Water = 100 * 0.54 * 1.0 = 54 \, g\]
04

Convert the mass of ethanol to moles

The molar mass of ethanol is approximately \(46.07\, g/mol\). We can use this to convert the mass of ethanol into moles: \[Moles \, of \, Ethanol = \frac{36.34}{46.07} = 0.788 \, moles\]
05

Calculate the volume of the solution

We have assumed 100 mL of the solution and therefore the total volume is equal to 100 mL. Now, convert the volume from mL to L: \[Total \, Volume = 100 \, mL * \frac{1 \, L}{1000 \, mL} = 0.1 \, L\]
06

Determine the molarity of ethanol in the solution

Now, we can determine the molarity of ethanol in the solution: \[Molarity \, of \, Ethanol = \frac{Moles \, of \, Ethanol}{Total \, Volume} = \frac{0.788}{0.1} = 7.88 \, M\] The molarity of ethanol in the 92 proof ethanol-water solution is approximately \(7.88\, M\).

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