The temperature of hot metal decreases when immersed in cold water, in turn increasing the temperature of the water. Therefore the heat released by the metal must equal the heat gained by the water, assuming that no heat is lost to the surrounding environment or the calorimeter. The following equation shows that the heat lost from a system is negative and the heat gained is positive:-q(metal) = q(metal)-mmetal x cmetal x Tmetal = mwater x cwater x TwaterSince the experiment was conducted in a calorimeter, then all the heat lost by the metal is gained by water, whose specific heat capacity is 4.81 J/g˚C. The following equation shows how the molar mass of the metal can be approximated once the specific heat capacity has been found: cmetal x MMmetal 25 J/mol˚C where MMmetal, is the molar mass of the metal. This estimate was proposed by Dulong and Petit, demonstrating that one mole of all metals had more or less the same capacity to absorb heat. The same rule applies in a neutralization reaction; the heat developed in the reaction in the reaction must be equal to the heat absorbed by the solution but of opposite sign. The following equation shows this
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