To calculate the number of moles of ethanol in a 750-mL bottle of wine that is approximately 12% ethanol by volume, we can follow a series of steps.
Step 1: Calculate the volume of ethanol in the wine
Since the wine is 12% ethanol by volume, we can find the volume of ethanol in a 750-mL bottle of wine.
\[ \text{Volume of ethanol} = \text{Total Volume of wine} \times \text{Percentage of ethanol} \]
\[ \text{Volume of ethanol} = 750 , \text{mL} \times 0.12 = 90 , \text{mL} \]
Step 2: Convert the volume of ethanol to grams
Next, we need to convert the volume of ethanol to grams using the density of ethanol. The density of ethanol is given as \(0.789 , \text{g/mL}\).
\[ \text{Mass of ethanol} = \text{Volume of ethanol} \times \text{Density of ethanol} \]
\[ \text{Mass of ethanol} = 90 , \text{mL} \times 0.789 , \text{g/mL} = 71.01 , \text{g} \]
Step 3: Convert grams of ethanol to moles
Finally, we convert the mass of ethanol to moles using the molar mass of ethanol, which is \(46.06 , \text{g/mol}\).
\[ \text{Moles of ethanol} = \frac{\text{Mass of ethanol}}{\text{Molar mass of ethanol}} \]
\[ \text{Moles of ethanol} = \frac{71.01 , \text{g}}{46.06 , \text{g/mol}} \approx 1.54 , \text{moles} \]
Conclusion
In a 750-mL bottle of wine that is approximately 12% ethanol by volume, there are approximately 1.54 moles of ethanol present.
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