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 a 92 proof ethanol-water solution? Assume the density ofethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), is \(0.79 \mathrm{~g} / \mathrm{cm}^{3}\) and the density of water is \(1.0 \mathrm{~g} / \mathrm{cm}^{3}\)

Short answer

The molarity of ethanol in a 92 proof ethanol-water solution is approximately 7.88 M.

Step-by-step solution

Calculate the percent by volume of ethanol in the solution

The given proof is 92. Since the term proof is defined as twice the percent by volume of ethanol, we have: Percent by volume (ethanol) = (Proof) / 2 Percent by volume (ethanol) = 92 / 2 = 46%

Convert the percent by volume to an actual volume

Assume that we have a 100 mL ethanol-water solution. In this case, 46% of it is ethanol. So, the volume of ethanol in the solution is: Volume (ethanol) = (46%) • (100 mL) Volume (ethanol) = 46 mL

Calculate the mass of ethanol in this volume

Recall that the density of ethanol is 0.79 g/cm^3. To find the mass of ethanol in this volume, apply the following formula: Mass (ethanol) = (Density of ethanol) • (Volume of ethanol) Mass (ethanol) = (0.79 g/cm³) • (46 mL) = (0.79 g/cm³) • (46 cm^3) Mass (ethanol) = 36.34 g

Calculate the molarity of ethanol in the solution

Finally, we need to find the molarity of the ethanol solution. First, recall that the molar mass of ethanol (C₂H₅OH) is approximately 46.07 g/mol. So, we can calculate the moles of ethanol present in the 100mL solution as follows: Moles (ethanol) = (Mass of ethanol) / (Molar mass of ethanol) Moles (ethanol) = 36.34 g / 46.07 g/mol ≈ 0.788 mol Since the total volume of the solution is 100 mL (0.1 L), we can find the molarity of the solution by dividing the moles of ethanol by the volume of the solution in liters: Molarity (ethanol) = (Moles of ethanol) / (Volume of the solution in liters) Molarity (ethanol) = 0.788 mol / 0.1 L ≈ 7.88 M Thus, the molarity of ethanol in a 92 proof ethanol-water solution is approximately 7.88 M.

Key concepts

Proof Definition in Chemistry

In chemistry, the term 'proof' refers specifically to a measure of the strength of an alcoholic beverage. It is a standard used to quantify the alcohol content in spirits, with proof being double the percentage (by volume) of alcohol in the solution. For example, an alcoholic beverage that is 50% ethanol by volume is 100 proof. This is an important concept because it simplifies the communication and understanding of the concentration of ethanol in various solutions.

Percent by Volume

Percent by volume is a common unit used to express the concentration of a solution. It represents the volume of a solute (in this context, ethanol) divided by the total volume of the solution, multiplied by 100 to convert it to a percentage. For instance, if a solution contains 30 mL of ethanol in a 100 mL solution, its concentration is said to be 30% by volume. This is crucial in many applications such as pharmacology, brewing, and even for calculating the molarity of a substance in solution.

Density to Mass Conversion

The density of a substance is its mass per unit volume. Knowing the density is essential for converting between volume and mass, which is a common task in chemistry. For example, if the density of ethanol is 0.79 g/cm³, this means that 1 cm³ of ethanol weighs 0.79 g. To find the mass of a given volume, you multiply the volume of the substance by its density. This step is vital when you start with a volumetric measure (like milliliters) and need to find the mass to calculate moles for molarity.

Calculating Molarity

Molarity, often represented by the letter M, is the number of moles of a solute per liter of solution. It is a measure of the concentration of a solution. To calculate molarity, you need to know two things: the number of moles of solute and the volume of the solution in liters. The formula is: \( Molarity (M) = \frac{moles \; of \; solute}{volume \; of \; solution \; in \; liters} \). Understanding molarity is fundamental for reacting solutions in stoichiometry, for preparing laboratory solutions, and for stoichiometric calculations in chemical reactions.

Molar Mass of Ethanol

Molar mass is the mass of one mole of a substance. For ethanol (C2H5OH), which consists of 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom, the molar mass is calculated by summing the atomic masses of all the atoms in the molecule. Carbon has an atomic mass of 12.01 g/mol, hydrogen 1.01 g/mol, and oxygen 16.00 g/mol. Therefore, the molar mass of ethanol is approximately 46.07 g/mol (2*12.01 + 6*1.01 + 16.00). The molar mass is a critical component when converting from mass to moles, which is a frequent requirement in chemistry.