is solid carbon dioxide(dry ice) soluble in water
Everything is soluble in everything, the question becomes how soluble? Solubility of carbon dioxide depends on temperature (dry ice is cold), partial pressure of CO2 in the air above, pH, metal impurities etc.
You may want to do some googling or literature searches. Dissolved carbon dioxide is found as carbonic acid/carbonates in water which are not the most soluble compounds but do dissolve to an extent varying with factors such as those stated above.
Carbon dioxide is soluble in water. Although much of the carbon dioxide will escape as a gas when you put dry ice into water, some of the carbon dioxide will dissolve in the water and make the water carbonated.
If your intention is to make sparkling water to drink, don't do it as the Dry Ice is generally contaminated by compressor oils at a few ppm. Food grade CO2 for making sodas is specially refined to be palatable.
Homebrewers have used a technique for carbonation at bottling that uses an addition of corn sugar calculated to add 1-2 volumes of CO2 to the stillbeer. More advanced brewers use fresh sterile wort calculated to do the same thing in a process called krausening. Popped bottles are a sign that some microbial contamination creates enzymatically excess fermentable sugars from the unfermented carbohydrates left in the "still" beer.
Obviously this is not controllable to make a sweet soda,and small amounts of alcohol are the byproduct of the carbonation.
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