I'm not an expert on mice but I believe they do better in groups rather than alone. Two or three maybe.
I think people do use 10 gallon tanks for mice - according to the calculator on this web page a 10 gallon tank could be ok for up to three mice - but I think it's a minimum size.
Mouse Cage Calculator
It's considered the minimum for a hamster by the ASPCA but most people would consider it too small for a hamster. A 40 gallon breeder tank is a popular size for a Syrian Hamster and a 30 or 40 gallon tank popular for a dwarf hamster in the US (assuming you are in the US?).
Personally I wouldn't get the pet to suit the tank you have. ie I wouldn't get mice just because the tank is ok for them - unless you have really looked into keeping mice. I believe some people can find the smell quite strong with mice and more so than for a hamster.
Bicarbonate of soda wouldn't be good - it could cause serious health issues if ingested. Maybe contact Rene...... for more info on mice
