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In a small bowl, combine 2 tablespoons (20 g) of cream of tartar with enough water to make a thick paste. Stir them together to completely incorporate the two ingredients. To make larger quantities, add more cream of tartar and water and mix it into a paste.  Cream of tartar, otherwise known as potassium bitartrate, is an acidic by-product of winemaking that can be used to clean and scrub metal, ceramic, stone, and other surfaces.  This paste is good for scrubbing soot and fireplace buildup from brick. In a small bowl, combine 2 ounces (59 ml) of liquid dish soap and 2 ounces (57 g) of salt. Mix them together to make a paste. Add just enough water to make the mixture creamy and spreadable. The cleaner should have the consistency of paint or pancake batter.  To make larger quantities, mix equal parts soap and salt, by weight, in a larger container. Add enough water to make the mixture spreadable. In this cleaner, the salt will act as an abrasive, and the soap will wash dirt and grease from the bricks. In a small bucket, combine 2 tablespoons (30 ml) of liquid dish soap, 1 tablespoon (15 ml) of ammonia, and 1 tablespoon (9.5 g) of pumice powder. Add hot water in small increments, until you can stir the mixture into a loose paste.  Pumice powder is a mild abrasive that can be purchased in art stores, craft shops, and beauty supply stores. Never mix ammonia with bleach or other cleaners. Use a cheese grater to grate a bar of Fels-Naptha soap into a medium bucket. Add 12 cups (2.8 L) of boiling water and stir the mixture until the soap is dissolved. Set the mixture aside to cool for at least an hour. Add 1 cup (235 ml) of ammonia and 1 pound (454 g) of pumice powder to the bucket. Stir the mixture to fully combine all the ingredients.  Fels-Naptha soap is a powerful laundry soap that’s often used to pretreat stains. This is a heavy-duty cleaner that will kill mold, and scrub soot and buildup from brick. In a large bucket, combine 2 tablespoons (30 ml) oxygen bleach with 4 cups (940 ml) of water. Stir the mixture for a few minutes to dissolve the oxygen bleach in the water.  Oxygen bleach is different from chlorine bleach, and it’s not as corrosive or damaging. This cleaner is good if you need to remove mold or mildew from brick, because the oxygen bleach will kill the mold.

Summary:
Combine cream of tartar and water to make a cleaning paste. Make a soap and salt paste. Mix ammonia with soap and pumice. Try a naphtha soap and ammonia solution. Combine oxygen bleach powder with water.