Calcium chloride is a drying agent

Calcium chloride is a drying agent, although often used only for gases. It is also widely sold for melting ice on sidewalks in cold climate areas. It is effective to a lower temperature then salt. 

Now, for treatment of insect bites, and not just mosquito, but the ones that can be deadly: 

Calcium chloride is essential for the proper functioning of nerve and muscle, where it has a major influence on stimulation thresholds and the release of neurotransmitters. Calcium chloride can be administered as adjunctive therapy in a number of conditions, including the following: insect bites or stings such as Black Widow Spider bites. 

The exact mechanism of black widow venom is not completely understood. There is an oversimplified view in the prehospital setting that black widow venom is essentially a calcium channel blocker similar to Cardizem. The common belief is that calcium gluconate or calcium chloride is the best treatment.