Final answer:
To find the proof of tequila, first the mass of ethanol is calculated using molar mass and moles provided, then converted to volume using density. The volume percentage of ethanol in the bottle is determined and doubled to find the alcohol proof, which is approximately 102 proof.
Step-by-step explanation:
To determine the proof of the tequila, we need to calculate the volume percentage of ethanol in the bottle. First, we calculate the mass of ethanol using its molar mass (46.07 g/mol) and the given moles of ethanol in the bottle (3.26 moles).
Mass of ethanol = number of moles × molar mass = 3.26 moles × 46.07 g/mol = 150.19 g
Next, since the density of ethanol is given as 0.785 g/mL, we can find the volume of ethanol:
Volume of ethanol = mass / density = 150.19 g / 0.785 g/mL = 191.4 mL
Now we need to establish what portion of the bottle's total volume is made up of ethanol to find the volume percentage:
Volume percentage = (volume of ethanol / total volume of solution) × 100% = (191.4 mL / 375 mL) × 100% = 51.04%
The alcohol proof is twice the percentage of alcohol by volume:
Alcohol proof = 2 × volume percentage = 2 × 51.04% = 102.08 proof
Therefore, the tequila is approximately 102 proof. Note that in actual practice, volume contractions upon mixing may slightly alter these calculated values.