Problem 2.1.8

 

Determine heat of formation of water at 350 Kelvin.  Heat of formation at 298 Kelvin is given as minus 57,798 calories per mole.  Ideal gas heat capacity is equal to a plus bT plus cT2, where values of a, b, and c are given.

 

Solution: 

 

The enthalpy of formation is defined as the isothermal enthalpy change in a synthesis reaction from the elements in their standard states.  In such a reaction scheme, the elements are assumed initially to be at reaction temperature, at 1 atmosphere, and in their most stable phases, e.g., diatomic oxygen as an ideal gas, carbon as a solid in the form of beta-graphite, etc.  Ordinarily one need not be concerned with the numerical values of the enthalpy of formation of the constituent elements, since, to obtain a standard enthalpy of reaction, the enthalpy of formation of all elements cancel.  Reported enthalpies of formation are normally available only at 298 K.  At other temperatures, delta Hfo(T) is equal to delta Hfo(298 K) plus integral from 298 to T of delta Cpo dT where delta Cpo is equal to the sum of the heat capacities of the compound and the constituent elements, each element in its standard state, and each multiplies by the appropriates stoichiometric multiplier nu.  This multiplier, nu, is negative for reactants and positive for products.

 

Integration constant, delta Ho can be found as deltaHf298 – (a time 298 plus b/2 2982 plus c/3 T3).  This value is equal to minus 2.52 time 105 joules per mole.  Now at 350 Kelvin, delta H can be found be using this value of temperature, and it is equal to minus 2.40 time 105 joules per mole.