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The other 95% of vinegar will be water.
If the fizzing has stop the reaction is over (or near over).
I see your problem - there is solid but you can still smell vinegar. So what's going on?
Vinegar has a pretty potent smell so the vinegar might only be around in trace amounts.
The white solid might also be calcium acetate formed in the reaction, rather than the added calcium carbonate. While calcium acetate is more soluble in water (34.7 g/100 mL) than calcium carbonate (0.15 g/100 mL) your solution might be saturated. According to Wikipedia calcium acetate has a solubility of 34.7 g/100 mL so if you've made more than 35 g per 100 ml of water it will begin to precipitate from solution.
To test the solid you could scoop some out and add fresh vinegar - if it fizzes then it contains calcium carbonate if not, then it will be calcium acetate.
The other problem will be as the vinegar and calcium carbonate are used in the reaction, the reaction will slow down. This is because the reagents will become more dilute and so will find it more difficult to find each other - you could try to heat the reaction up a little, maybe in an old sauce pan. Can't see how this can damage the calcium acetate or carbonate, and has the advantage that it will tend to boil off any remaining vinegar.
Excess vinegar seems to be a worse option than excess calcium carbonate.
I tried the reaction using antacid tablets, the problem is that these tablets contain sugar and I think kaolin (and spearmint flavour!). The problem with the kaolin is that I've had the same problem – a white precipitate and yet a slight whiff of spearmint/vinegar. I should have used sugar free tablets! I also saw in the local DIY shop that you can by pure calcium carbonate, next time I will used that!
Therefore:
(1) try heating the solution in a saucepan and still if it still has that fizz! At least this should get rid of the remaining vinegar.
(2) Also scoop out a little of the white solid and test it with some fresh neat vinegar to see if it still fizzes.
Hope that helps
CH
kishke - not sure what is going on with your eggshells, but becareful with that glacial acetic acid!!