ap chem: q rxn, q soln, and Calorimeters

[kwona]

I have water and an unknown metal. I know the masses of both, as well as the temperature changes. I know the specific heat of water, but I have to determine the specific heat of the unknown metal. There is a equation that goes as follows: q rxn = -(q soln + (C * delta T)). The q rxn would stand for heat the metal absorbed/released and q soln absorbed/released. C is (q cal / delta T). 

m water - 100 g

m metal - 5.332 g

cp water - 4.184

cp metal - n/a

delta t water - 5.5

delta t metal - 23.5

I heated up the water and kept the metal at room temperature, so I think I would switch up the equation so that it goes like this: 

q soln = -(q rxn + (C * delta T)... first of all, is that right? In addition, because the specific heat of the metal (rxn) is unknown, i replaced it with the variable X. So broken up it would look like this: 

m water * cp water * delta T water = -((m metal * X * delta T metal) + (C * delta T)).... But if I use a variable in the equation, then according to basic algebra I would distribute the negative to the q and C * T making them both negative. After, I would add C * T to the q soln which would be negative, giving me a positive value. In the end, my X or specific heat of the metal would equate to -6.6, which is very inaccurate given that most specific heats are below 1 J/g * C. 

How can I fix my calculations? 

Edited October 23, 2019 by kwona