Exposing the mattress to natural sunlight will help permanently remove the smoke smell.
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Take the mattress outdoors and expose it to sunlight for an entire day.
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Bring the mattress back indoors and sprinkle baking soda over the entire surface. Allow the baking soda to absorb into the mattress for one day.
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Vacuum up the baking soda from the mattress with an attachment. Flip the mattress over, and apply baking soda to the other surface. Allow the baking soda to set for one day.
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Vacuum up the baking soda with the vacuum attachment. Mix 2 cups of hydrogen peroxide with 3 tbsp. baking soda together in a spray bottle.
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Spray the solution over areas of the mattress where the smoke smell remains. Allow the mattress to air-dry.