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Chapter 4: Problem 67

(a) How many grams of ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\), should you dissolve in water to make \(1.00 \mathrm{~L}\) of vodka (which is an aqueous solution that is \(6.86 \mathrm{M}\) ethanol)? (b) Using the density of ethanol \((0.789 \mathrm{~g} / \mathrm{mL})\), calculate the volume of ethanol you need to make \(1.00 \mathrm{~L}\) of vodka.

Short Answer

Expert verified
(a) To make 1.00 L of vodka with 6.86 M ethanol, you need to dissolve 315.56 g of ethanol in water. (b) To make 1.00 L of vodka, you need 400 mL of ethanol (approximately).

Step by step solution

01

Calculate the moles of ethanol required for 1.00 L of vodka.

To find out how many grams of ethanol are needed, first, we have to find the number of moles of ethanol required to make 1.00 L of vodka. The molarity (M) is the number of moles of solute (in this case, ethanol) per liter of solution. Therefore, for 6.86 M of ethanol, we have: Moles of ethanol = molarity × volume of the solution Moles of ethanol = \(6.86 \, \text{moles/L} \times 1.00 \, \text{L}\)
02

Calculate the mass of ethanol required for 1.00 L of vodka.

Now that we have the moles of ethanol required, we can find the mass by using the molecular weight of ethanol. The molecular weight of \(\mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{OH}\) is approximately 46 g/mol. So, to find the mass of ethanol needed, we multiply the moles of ethanol by its molecular weight: Mass of ethanol = moles of ethanol × molecular weight of ethanol Mass of ethanol = moles of ethanol × 46 g/mol
03

Calculate the volume of ethanol required for 1.00 L of vodka using the density.

Now that we have the mass of ethanol, we can calculate its volume using the given density (0.789 g/mL). To find the volume, we need to divide the mass by the density: Volume of ethanol = mass of ethanol ÷ density Volume of ethanol = mass of ethanol ÷ 0.789 g/mL Now we can calculate the mass and volume of ethanol required to make 1.00 L of vodka using the given molarity and density of ethanol.
04

Answers

(a) Mass of ethanol required: Moles of ethanol = \(6.86 \, \text{moles/L} \times 1.00 \, \text{L} = 6.86 \, \text{moles}\) Mass of ethanol = \(6.86 \, \text{moles} \times 46 \, \text{g/mol} = 315.56 \, \text{g}\) So, to make 1.00 L of vodka with 6.86 M ethanol, you need to dissolve 315.56 g of ethanol in water. (b) Volume of ethanol required: Volume of ethanol = \(315.56 \, \text{g} ÷ 0.789 \, \text{g/mL} = 400 \, \text{mL}\) (approximately) Therefore, to make 1.00 L of vodka, you need 400 mL of ethanol.

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