It is 'baking' soda (bicarb soda, in British English - or at least, Australian English!), not 'backing'. In this instance, 'household cleaner' sounds more natural to me.

household chores are chores that everyone in the house can do. That is why the phrase is correct. You can also say domestic chores. Household chores is the colloquial way to say it. domestic means of or relating to home. household means in the same family or house. You can ask "how many people are in your household?" But you cannot say "how many people are in your domestic?" As nouns the difference between household and domestic is that household is collectively, all the persons who live in a given house; a family including attendants, servants etc; a domestic or family establishment while domestic is a house servant; a maid; a household worker. As adjectives the difference between household and domestic is that household is belonging to the same house and family while domestic is of or relating to the home.

Hi Niwantha, The answer is "it depends." In your example sentence, only "household" is correct. "Baking soda can be used as a household cleaner." That is, the cleaner is a thing which cleans a household. (The second sentence is awkward, or refers to cleaning a servant = "a domestic.") However, you could say both "I need to do some household chores" (as in, chores around my household) or "I need to do some domestic chores" (as in, chores in the domestic sphere). When in doubt: household is more likely to be correct. Or, just ask on italki! :)