(a) How many grams of ethanol, CH3CH2OH, should you dissolve in water to make 1.00 L of vodka (which is an aqueous solution that is 6.86 M ethanol)? (b) Using the density of ethanol (0.789 g/mL), calculate the volume of ethanol you need to make 1.00 L of vodka.

Verified step by step guidance

1. (a) To find the grams of ethanol needed, start by using the molarity formula: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \). Here, \( M = 6.86 \) M and the volume of the solution is 1.00 L.
2. (a) Calculate the moles of ethanol required: \( \text{moles of ethanol} = M \times \text{volume of solution} = 6.86 \times 1.00 \).
3. (a) Use the molar mass of ethanol (\( C_2H_5OH \)) to convert moles to grams. The molar mass is calculated as: \( 2(12.01) + 6(1.01) + 16.00 = 46.08 \text{ g/mol} \).
4. (a) Multiply the moles of ethanol by the molar mass to find the mass in grams: \( \text{mass} = \text{moles} \times 46.08 \text{ g/mol} \).
5. (b) To find the volume of ethanol needed, use the density formula: \( \text{density} = \frac{\text{mass}}{\text{volume}} \). Rearrange to find volume: \( \text{volume} = \frac{\text{mass}}{\text{density}} \). Use the mass from part (a) and the given density of ethanol, 0.789 g/mL.

Key Concepts

Molarity (M)

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this question, the molarity of ethanol in vodka is given as 6.86 M, indicating that there are 6.86 moles of ethanol in every liter of the solution. Understanding molarity is essential for calculating the amount of solute needed to achieve a desired concentration.

Mass and Molar Mass

To convert moles of a substance to grams, one must use the molar mass, which is the mass of one mole of that substance expressed in grams per mole. For ethanol (C2H5OH), the molar mass is approximately 46.07 g/mol. This concept is crucial for determining how many grams of ethanol are required to achieve the specified molarity in the solution.

Density

Density is defined as mass per unit volume and is typically expressed in grams per milliliter (g/mL) for liquids. The density of ethanol is given as 0.789 g/mL, which allows for the conversion of mass to volume. This concept is important for calculating the volume of ethanol needed to achieve the desired mass for the vodka solution.