Final answer:
To find the moles of ethanol in a 750-mL bottle of wine, calculate the volume of ethanol using the alcohol percentage, convert that volume into mass using the density of ethanol, and finally convert the mass to moles using the molar mass of ethanol. The result is approximately 1.54 moles of ethanol.
Step-by-step explanation:
To calculate the number of moles of ethanol in a 750-mL bottle of wine with 12% alcohol by volume (12% alc/vol), we first need to determine the volume of ethanol present in the wine. Since the wine is 12% ethanol by volume, this means that there are 12 mL of ethanol for every 100 mL of wine. Therefore, a 750-mL bottle of wine contains 0.12 × 750 mL = 90 mL of ethanol. Next, we use the density of ethanol, 0.789 g/mL, to find the mass of ethanol in grams: mass = density × volume = 0.789 g/mL × 90 mL = 71.01 g. Finally, we convert the mass of ethanol into moles using the molar mass of ethanol, which is 46.06 g/mol. The number of moles = mass / molar mass = 71.01 g / 46.06 g/mol = 1.54 moles. Therefore, in a 750-mL bottle of wine, there are approximately 1.54 moles of ethanol present.