Pierino's suggestion to place an open box of baking soda in the fridge is a good one, but don't use that box of baking soda in your cooking. Keep a separate box for use in cooking in your cupboard where it will stay dry and odor-free.
It's not recommended here is something I looked up about it:
How do I store my baking powder, baking soda or corn starch? Can I refrigerate or freeze?
A. Baking powder, soda or cornstarch should be stored in a dry cupboard away from heat and excess moisture. You should only measure with a dry utensil and replace the lid promptly after each use. Storage in a refrigerator or freezer is not recommended, as the condensation that can accumulate will make the powder react in the can, rendering it useless.
One of the best uses for baking soda is to stick it your refrigerator with the lid partially torn back to absorb funky odors in there. Replace it every one or two months.
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How do I store my baking powder, baking soda or corn starch? Can I refrigerate or freeze?
A. Baking powder, soda or cornstarch should be stored in a dry cupboard away from heat and excess moisture. You should only measure with a dry utensil and replace the lid promptly after each use. Storage in a refrigerator or freezer is not recommended, as the condensation that can accumulate will make the powder react in the can, rendering it useless.