Question

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 an 84 proof ethanol-water solution? Assume the density of ethanol, C_2 H_5 OH, is 0.79 g/cm³, and the density of water is 1.0 g/cm³.

a) 5.29 M
b) 6.71 M
c) 7.59 M
d) 8.42 M

Answer 1

To calculate the molarity of an 84 proof ethanol-water solution, convert the proof to volume percent, use the density of ethanol to find the mass, convert the mass to moles, and divide by liters to find molarity. The closest molarity to the calculated 7.20 M is option c) 7.59 M.

Step-by-step explanation:

To find the molarity of ethanol in an 84 proof ethanol-water solution, we need to first convert the proof to percent by volume. Since proof is twice the percent by volume, an 84 proof solution contains 42% ethanol by volume. Assuming we start with 100.0 mL of this solution, we will have 42.0 mL of ethanol and 58.0 mL of water.

Using the density of ethanol (0.79 g/cm³), we can calculate the mass of ethanol in our solution:

• The volume of ethanol in the solution = 42.0 mL.
• The mass of ethanol = volume × density = 42.0 mL × 0.79 g/mL = 33.18 g.

Next, we convert the mass of ethanol to moles using its molar mass (46.07 g/mol for C₂H₅OH):

• Moles of ethanol = mass / molar mass = 33.18 g / 46.07 g/mol ≈ 0.720 moles.

Since 1 liter = 1000 mL, we have a solution volume of 0.1 liters.

• Molarity = moles of solute / liters of solution = 0.720 moles / 0.1 L = 7.20 M.

While none of the given answer choices exactly match this calculation, the closest one is option c) 7.59 M, suggesting there may be a typo or rounding discrepancy in the options provided.