A particular beer is 6.50 % ethanol by volume (C2H6O). If a single bottle of beer contains 750.0 mL of beer , what quantity in moles of ethanol (C2H6O) are present in the bottle? The density of ethanol is 0.789 g ethanol/mL ethanol
The Correct Answer and Explanation is :
To calculate the quantity in moles of ethanol (C₂H₆O) present in the bottle of beer, we will follow these steps:
1. Determine the volume of ethanol in the beer:
The beer is 6.50% ethanol by volume, meaning that 6.50% of the total volume of beer is ethanol. The total volume of the beer bottle is 750.0 mL.
[
\text{Volume of ethanol} = \frac{6.50}{100} \times 750.0 \, \text{mL} = 48.75 \, \text{mL}
]
Thus, the volume of ethanol in the beer bottle is 48.75 mL.
2. Convert the volume of ethanol to mass:
Next, we need to convert the volume of ethanol to mass using its density. The density of ethanol is given as 0.789 g/mL. The mass of ethanol in the beer bottle is:
[
\text{Mass of ethanol} = \text{Density of ethanol} \times \text{Volume of ethanol}
]
[
\text{Mass of ethanol} = 0.789 \, \text{g/mL} \times 48.75 \, \text{mL} = 38.47 \, \text{g}
]
So, the mass of ethanol in the bottle is 38.47 grams.
3. Convert mass of ethanol to moles:
To calculate the number of moles of ethanol, we use its molar mass. The molecular formula for ethanol is C₂H₆O, and its molar mass is:
[
\text{Molar mass of ethanol} = (2 \times \text{atomic mass of C}) + (6 \times \text{atomic mass of H}) + (1 \times \text{atomic mass of O})
]
Using the atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, O = 16.00 g/mol):
[
\text{Molar mass of ethanol} = (2 \times 12.01) + (6 \times 1.008) + (1 \times 16.00) = 46.08 \, \text{g/mol}
]
Now, we can calculate the number of moles of ethanol:
[
\text{Moles of ethanol} = \frac{\text{Mass of ethanol}}{\text{Molar mass of ethanol}} = \frac{38.47 \, \text{g}}{46.08 \, \text{g/mol}} \approx 0.834 \, \text{mol}
]
Final Answer:
The quantity of ethanol (C₂H₆O) present in the bottle is approximately 0.834 moles.
Explanation:
This calculation follows a systematic approach: first, we determine the volume of ethanol in the beer, then we convert it to mass using the density of ethanol, and finally, we convert the mass to moles using the molar mass of ethanol. Each step ensures that we accurately calculate the number of moles in the given beer bottle.