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This question does not really contain enough information to be properly answered. We don't know the percentage of other ingredients (mainly sugar is important) in the bottle. The density of alcohol is less than water and the density of sugar is more than water. In the end, a good bottle of wine should have a density close to that of water. With a density slightly less than water it tends to be a dry wine, and with a density slightly greater it tends to be a sweeter wine (which makes sense since sugar is heavier than water, so a greater weight implies more sugar.)

To attempt to answer your question we must make some assumptions about water and sugar content. On this website [1] the author claims that dry wine has a sugar percentage of about 0.25% and a sweet wine can be as high as around 0.9-1.1%. We'll use the author's example of Yellow Tail Merlot which has 0.5% sugar.

dH20 - density of water is 1000 grams/liter

dEthanol - density of ethanol is 789 grams/liter

dSugar - density of sucrose (the sugar in wine) is 1587 grams/liter

If the wine is 13% alcohol and 0.5% sugar, then the water content is 86.5% water.

Therefore:

.13*789+.005*1587+.865*1000 = 975.5 grams/liter

so that would be a rough estimate of your density. I can't make any claims as to how realistic this value is; wine contains many other ingredients that will impact the density, but now you can at least calculate a rough estimate for yourself, if you can figure out the sugar content for your specific wine.

An important note:

The wine industry doesn't use density; they use specific gravity. The specific gravity of a liquid or solid is the ratio of the density of the liquid or solid to the density of liquid water:

Specific Gravity = density of Material X / density of H2O

Specific gravity is technically unitless, but some people create units for it anyways. Check out wikipedia for more details.

[1] http://www.queencitynews.com/modules.php?op=modload&name=News&file=article&sid=6386

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