The chemical process that is happening is called fermentation.
Step-by-step explanation:
Grapes contain a lot of carbohydrates, specially maltose. Maltose is a disaccharide, composed of two molecules of glucose. This maltose, when acted upon by yeast produces ethanol. The process going in is called fermentation. Here one molecule of glucose undergoes the process of glycolysis which leads to formation of two molecules of pyruvate.
These pyruvates are acted upon by alcohol dehydrogenase to form two molecules of ethanol and two molecules of carbon dioxide. Thus we can see bubbles coming out of the solution. Yeasts die as the alcohol concentration reaches around 13 to 14% v/v.