In order to make manganese dioxide electrodes, you're going to need cobalt nitrate and manganese nitrate to do it. Making cobalt nitrate is fairly easy, but making the manganese nitrate is a little more complicated. But not impossible.
Watch this science video tutorial from Nurd Rage on how to make cobalt and manganese nitrates with Dr. Lithium.
WARNING: These are heavy metals and toxic if mishandled. In addition cobalt is carcinogenic. You MUST wear gloves and preferably additional safety equipment like dust masks and lab coat. A fumehood is recommended too.
Making cobalt nitrate is very easy, just get cobalt carbonate from a pottery supply store and mix it with twice its mass in water. Then add nitric acid until it stops fizzing. That's all! The red solution can be dried to make cobalt nitrate crystals for storage.
Making manganese nitrate is a little more complicated. Manganese dioxide is mixed with oxalic acid, water and nitric acid to produce manganese nitrate. Alternatively you can bubble nitrogen dioxide directly into the manganese dioxide. If the solution is yellow it's because there is some iron contamination. But this is not a problem for making manganese dioxide electrodes.
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