Rather than baking soda one should use washing soda, usually found in the laundry aisle.
I have no idea if this will work or not, but if you add citric acid with the baking soda, you will only have salt water. Citric acid is an acid, of course, and baking soda is a base. Acid + base = salt + water + carbon dioxide. You might just as well just use borax plus salt.
Again, I have no idea if this makes an effective cleaner, but I doubt it. If it did, we would all be using it. I might also say that after checking my box of Borax, it recommends using it for many types of household cleaning, but not for dishes or in a dishwasher.
In conclusion, know that any time you mix an acid such as citric acid or vinegar or lemon juice with a base such as baking soda or ammonia, the one neutralizes the other and you are left with salt water.
I've never heard of homemade dish washing soap. Sounds interesting, I guess, but I don't what you're missing. Never tried it.
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