Without seeing the weapon, I am guessing it is a model 1816 Harpers Ferry Musket, dated 1829. I would imagine it is a conversion from flintlock to caplock. If the area where the flashpan & strike plate (if you aren't knowledgeable about weapons, this would be the area on the right side of rifle where the hammer would come down & ignite the strike plate with a piece of flint & ignite a spark which would go through the flash hole & ignite the powder)is replaced, I am guessing this is a conversion & there should be a brass replacement where the the flashpan once was. On top of the brass replacement should be a small hollow tube called a nipple where the cap would be placed, hence caplock. The 7C marking could be a regiment (7th infantry, company C)marking or, if stamped on the metal, is most likey an assembly code. Many of these conversions were used in the war. You didn't say whether "Missouri" was stamped on the metal or in the wood.
I am dubious about such markings unless it is period carved into the wood & even then, am suspicious as there are unscrupulous sellers who will embellish weapons & ask a commanding price & hope to snare unsuspecting buyers.
Again, someone knowledgeable about Civil War weapons could tell you if Missouri stamped on it is correct or not.