Molar heat capacities are often reported instead of mass-based heat capacities. Crystalline magnesium oxide has a molar heat capacity of 37.2Jmol−1K−1 at temperatures near 25 °C.
A materials scientist cools a 2.60 mol sample of solid MgO from 415 K to 298 K in a sealed calorimeter.
(a) Show, by appropriate unit analysis, how to express the given molar heat capacity as a mass-based quantity in Jg−1K−1.
(b) Calculate the amount of thermal energy released by the MgO sample during the cooling process, expressing your result in kilojoules.
(c) Suppose the same energy released in part (b) were used to warm a 150. g block of nickel that is initially at 298 K. Using an accepted specific heat capacity for nickel of 0.444Jg−1K−1, determine the final temperature of the nickel block, assuming no energy is lost to the surroundings.
(d) Evaluate whether the assumption that the heat capacities of MgO and Ni remain constant over the temperature ranges involved introduces significant error into the results. Support your evaluation qualitatively.