5.4.6 Hess's Law of Heat Summation [1840]

The heat change for a reaction is the same whether the reaction takes place in one step or several steps. Illustration: Shop takings for the day. One can total the takings at morning tea, lunch, afternoon tea and closing - or simply at closing - the result will be the same.

S(s) + 11/2 O2(g) = SO3(s) H = - 395 kJ mol-1 Form SO3 in one step S(s) + 11/2 O2(g) = SO3(s) H = - 395 kJ mol-1 If it is formed in two stages. S(s) + O2(g) = SO2(g) H = - 297 kJ mol-1 SO2(g) + 1/2 O2(g) = SO3(s) H = - 98 kJ mol-1 Total S(s) + 11/2 O2(g) = SO3(s) - 395 kJ mol-1 This can be used to calculate the heat of reaction for reactions which are difficult or even impossible to measure directly.

Find the heat of formation of CO C(s) + 1/2 O2(g) = CO(g) One cannot do this directly because some CO2 is always going to be formed. The following two equations can be worked out directly by experiments. C(s) + O2(g) = CO2(g) H = - 393 kJ mol-1 CO(g) + 1/2 O2(g) = CO2(g) H = - 283 kJ mol-1

If we arrange as in the previous example I. e If we arrange as in the previous example I.e. as a two stage process – making CO first and then converting the CO to CO2 we get :- C(s) + 1/2 O2(g) = CO(g) H = - ??? kJ mol-1 CO(g) + 1/2 O2(g) = CO2(g) H = - 283 kJ mol-1 C(s) + O2(g) = CO2(g) H = - 393 kJ mol-1 The unknown must be - 110 kJ mol-1 C(s) + 1/2 O2(g) = CO(g) H = - 110 kJ mol-1

Calculate the heat of formation of Fe2O3 given the following information. 2 Fe + O2 = 2 FeO ΔH = - 280 kJ 4 FeO + O2 = 2 Fe2O3 ΔH = -300 kJ 2 Fe + 1½ O2 = Fe2O3

* ½ Calculate the heat change for the reaction 2 Fe + 1½ O2 = Fe2O3 Equations given 2 Fe + O2 = 2 FeO ΔH = -280 kJ 4 FeO + O2 = 2 Fe2O3 ΔH = -300 kJ OK * ½ Write modified equations 2 Fe + O2 = 2 FeO ΔH = - 280 kJ 2 FeO + ½ O2 = Fe2O3 ΔH = - 150 kJ 2 Fe + 1½ O2 = Fe2O3 ΔH = - 430 kJ

If the heat of formation of Al2O3 is – 1596 kJ mol-1 If the heat of formation of Al2O3 is – 1596 kJ mol-1. and the heat of formation of Cr2O3 is – 1134 kJ mol-1, calculate the heat of reaction for 2 Al(s) + Cr2O3(s) = Al2O3(s) + 2 Cr(s)

2 Al(s) + Cr2O3(s) = Al2O3(s) + 2 Cr(s) 2 Al(s) + 11/2 O2(g) = Al2O3(s) -1596 2 Cr(s) + 11/2 O2(g) = Cr2O3(s) -1134

Calculate the heat change of the following reaction C2H4(g) + H2(g) = C2H6(g) Given that the heat of combustion of ethene [C2H4], hydrogen [H2] and ethane [C2H6] are -1393, - 286 and – 1561 kJmol-1 respectively

Calculate the heat of reaction for the for HCOOH(l) = CO(g) + H2O(l) Given the following heats of formation C(s) + ½ O2(g) = CO(g) ΔH = -111 kJmol-1 H2(g) + ½ O2(g) = H2O(l) ΔH = - 285.8 H2(g) + O2(g) + C(s) = HCOOH(l) ΔH = - 424.7 Answer + 27.9 kJ mol-1

Calculate the heat of reaction for the following equation 2H2S + SO2 = 3S + 2 H2O H2(g) + S(s) = H2S(g) ΔH = - 21 S(g) + O2(g) = SO2(g) ΔH = - 297 H2(g) + ½ O2(g) = H2O(g) ΔH = - 286 Answer = - 233

2H2S + SO2 = 3S + 2 H2O (rev *2)H2(g) + S(s) = H2S(g) ΔH = - 21 (Rev) S(g) + O2(g) = SO2(g) ΔH = - 297 (*2) H2(g) + ½ O2(g) = H2O(g) ΔH = - 286 2 H2S(g) = 2 H2(g) + 2 S(s) ΔH = + 42 SO2(g) = S(g) + O2(g) ΔH = +297 2 H2(g) + O2(g) = 2 H2O(g) ΔH = - 572 Answer = -233