Calculating alcohol percentage after diluting with a sugar syrup

Just for context on my experience; I make a lot of limoncello at the little Italian bar I manage.

In future I advise adding your water first, and then stirring the granulated sugar through afterwards. I know making a syrup is easier in many ways, and involves considerably less stirring, but unless you've got detailed notes on your various concentrations, as you experienced, things can get confusing very quickly, and you can end up with a drink that is either far higher or lower proof than you intend.

The Proof-then-sweeten method gives you a bit more control in two main ways;

1. You can accurately calculate the ABV of your final product using either measuring jug OR scales, as (in theory) you know your initial ABV and Vol, and when adding water you can measure either by weight or vol for a known result. This will make your (V1C1)/(V2C2) Calc far easier.

2. You can then measure your overall weight of the lemon oil/ethanol/water solution and add sugar to this solution on the scales. Then, by tasting as you add and dissolve sugar bit by bit, you can figure out a g/L sugar concentration that suits your tastebuds.
   Jot this down! It will give you a good baseline to work towards the next time you make a limoncello, and save you from having to go through the somewhat tedious add/measure/stir/taste/repeat process again.

Remember, every batch will be a little different, because the lemons you get may vary from tree to tree, season to season. Sometimes I end up with a huge amount of really oily skin from 3kg of lemons, sometimes it can be quite waxy and dry. Once you have your target g/L sweetness, try and replicate that in various batches, but come in just short to begin with so that you can taste and make sure you don't over sweeten and have time to taste your way up to full sweetness. I usually aim to land about 50g or 1/2 Cup (overall, not 50g/L) short of my intended g/l and then work up to where I like it.

Because of course, you can always add more sugar, but it can be very hard to reduce the sweetness without thinning the flavour if you add too much.

I know this is kind of answering a parallel question, but I hope this helps yourself or someone else.

Because alcohol concentration is measured in terms of volume, the key question in this is:

What is the volume of 1kg of sugar syrup?

Assuming dissolving the sugar in water doesn't change the total volume much, your liter of sugar syrup weighs 1kg + 800g = 1.8kg. Assuming it was perfectly mixed, the kilogram you added was only 1/1.8 = 0.555... = 55.6% water.

So your total volume should be 1.556 liters.

That said, if I'm wrong you can also measure the volume you actually have and use that amount.

Now in terms of alcohol, one liter of that total 1.556 liters was 96% alcohol, so you total ABV should be

   1L * 0.96ABV
------------------ = 0.6169 ABV = 61.69%
1.556L (or actual)

Again, adjust for your total volume if necessary. But it should be close to 62%.

Edit: it should be noted, per the discussion in the comments, that the volume may change with the ABV. However, this should be fairly minimal and likely offset/limited by the sugar in the syrup you added.

There doesn't seem to be a lot of data on mixing alcoholic substances with anything but pure water for dilution, so giving an exact answer without running an experiment would be difficult. That said, the method above should be a fairly good estimate given everything I've seen.