Question

In the following overall chemical reaction, aluminum displaces chromium from chromium(III) oxide and forms aluminum oxide.

2 Al(s) + Cr2O3(s) → 2 Cr(s) + Al2O3(s); ΔH = ?

Find the change in enthalpy for this reaction, using Hess' law and the enthalpy changes for the reactions given below.
(1a) 4 Al(s) + 3 O2(g) → 2 Al2O3(s); ΔH = −3351.4 kJ
(2a) 4 Cr(s) + 3 O2(g) → 2 Cr2O3(s); ΔH = −2279.4 kJ

Answer 1

Change in enthalpy for the reaction is -536 kJ

Step-by-step explanation:

• Overall chemical reaction can be represented a summation of two given elementary steps with slight modification.
• Take reaction (1a) and divide stoichiometric coefficients by 2
• Take reverse reaction (2a) and divide stoichiometric coefficient by 2
• Then add these two modified elementary steps to get overall chemical reaction
• 
  `\Delta H` is an additive property. hence value of
  `\Delta H` will be changed in accordance with modification

`2Al+(3)/(2)O_(2)\rightarrow Al_(2)O_(3).....\Delta H_(1)=(-3351.4)/(2)kJ=-1675.7kJ`

`Cr_(2)O_(3)\rightarrow 2Cr+(3)/(2)O_(2)....\Delta H_(2)=(2279.4)/(2)kJ=1139.7kJ`

--------------------------------------------------------------------------------------------------------------

`2Al+Cr_(2)O_(3)\rightarrow 2Cr+Al_(2)O_(3)....\Delta H=\Delta H_(1)+\Delta H_(2)=-1675.7+1139.7kJ=-536kJ`