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Chapter 11: Problem 104

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 7.888 mol/L.

Step by step solution

01

Calculate Percent by Volume of Ethanol in the Solution

First, we need to find the percent by volume of ethanol in the solution, which we can do by dividing the proof by two. Given: Proof = 92 Percent by Volume of Ethanol = (Proof) / 2 = \(92/2\) = 46% Ethanol is 46% (by volume) in the solution.
02

Establish Ratios of Ethanol and Water

Since we now know that the solution is 46% (by volume) ethanol, we can also determine that it is 54% water. Let the volume of the solution = 100 cm³. Given: Volume of ethanol = 46 cm³ Volume of water = 54 cm³
03

Calculate Masses of Ethanol and Water

Using the given densities, we will now calculate the masses of ethanol and water in the solution. Given: Density of Ethanol = 0.79 g/cm³ Density of Water = 1.0 g/cm³ Mass of ethanol = (Volume of Ethanol) × (Density of Ethanol) = (46 cm³) × (0.79 g/cm³) = 36.34 g Mass of water = (Volume of Water) × (Density of Water) = (54 cm³) × (1.0 g/cm³) = 54 g
04

Calculate the moles of ethanol and water

We need to calculate the moles of ethanol and water based on their molecular weights. Given: Molecular Weight of Ethanol = 46.07 g/mol Molecular Weight of Water = 18.02 g/mol Moles of Ethanol = (Mass of Ethanol) / (Molecular Weight of Ethanol) = \(36.34 \text{g} / 46.07 \text{g/mol}\) = 0.7888 mol Moles of Water = (Mass of Water) / (Molecular Weight of Water) = \(54 \text{g} / 18.02 \text{g/mol}\) = 2.9978 mol
05

Calculate the Molarity of Ethanol in the Solution

Finally, we can calculate the molarity of the ethanol solution by dividing the moles of ethanol by the volume of the solution in liters: Given: Volume of Solution = 100cm³ = 0.1 L Molarity of Ethanol = (Moles of Ethanol) / (Volume of Solution in Liters) = \(0.7888 \text{mol} / 0.1 \text{L}\) = 7.888 mol/L The molarity of ethanol in a 92 proof ethanol-water solution is approximately 7.888 mol/L.

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