Question

Al₂(CO₃)₃ (s) è Al₂O₃ (s) + 3 CO₂ (g)           ∆H = +579 kJ            

a. What kind of chemical reaction is taking place? Is it endo- or exothermic? Explain how you know both answers.

b. Predict the change in enthalpy for each of the following reactions:

          1. 5 Al₂(CO₃)₃ (s) è 5 Al₂O₃ (s) + 15 CO₂ (g)           ∆H = ??

          2. 3 Al₂O₃ (s) + 9 CO₂ (g) è 3 Al₂(CO₃)₃ (s)             ∆H = ??

          3. Write the balanced thermochemical equation that will have ∆H = -2316 kJ

c. How much heat is required to react 5.00 grams of the aluminum carbonate?

d. If 5250 kJ of heat is added to aluminum carbonate, how many grams of aluminum oxide will be produced?

e. Using the enthalpies of formation found in the appendix of your textbook and the thermochemical equation above, calculate the enthalpy of formation of solid aluminum carbonate

Answer 1

During the course of exothermic reaction, heat is generated and hence enthalpy change is -ve. When deltaH is +ve, the reaction is endothermic. so the reaction Al2(CO3)3 --------->Al2O3(s)+3CO2(g), deltaH= 579 Kj ---- (1) is endothermic reaction as deltaH is +ve.

when reaction-1 is multiplied with 5, the equation becomes 5Al2(CO3)3 (s) ------->5Al2O3(s)+15CO2(g), deltaH= 5*579 = 2895 KJ

when the reaction -1 is reversed, this changes the sign of deltaH also

Al2O3(s)+ 3CO2(g) ---------->Al2(CO3)3, deltaH= -579 KJ (1A)

when Reaction-1A is multiplied with 3, the reaction is 3Al2O3(s)+ 9CO2(g) ------->3Al2(CO3)3, deltaH=-3*579= -1737 Kj

deltaH is required is -2316 so exothermic, -2316/-579 =4 gives the coefficient required to multiply reaction -1A . So multiplying the reaction-1A with 4 gives

4Al2O3(s) +12CO2(g) --------->4Al2(CO3)3, deltaH=-2316 KJ

c) as per the reaction-1, 1 mole of Aluminium carbonate requires 579 KJ of heat for reaction

moles= mass/molar mass 5 gm of Al2(CO3)3 in terms of moles = 5 gm / 234 g/ mole ( molar mas of al2(CO3)3= 0.02137

1 moles requires 579 Kj

0.02137 moles requires 0.02137*579 =12.37 KJ

d) 579 KJ are required per moles of Aluminium carbonate to produce 1 mole of Al2O3

5250 Kj are required per 5250/579 =9.1 moles of Aluminium carbonate produces 9.1 moles of Al2O3.

Molar mass of Al2O3= 102 g/mole, mass of Al2O3 produced= 102*9.1 =928.2 gm

Enthalpy of formation data : Al2O3= -1676.7 Kj/mole , CO2= -393.5 Kj/mole

for reaction-1, deltaH= sum of deltaH of products- sum of deltaH of reactants

579= 1* deltaH of Al2O3+3* deltaH of CO2- deltaH of Al2(CO3)3

579= 1* (-1676.7)+3*(-393.5)- deltaH of Al2(CO3)3

deltaH of Al2(CO3)3= -3436.2 KJ/mole