Question

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4. Carlsbad Caverns have limestone formations called stalagmites and stalactites. These form when calcium lons react with bicarbonate ions to form solid calcium carbonate, water and carbon dioxide gas. Forming 1 mole of calcium carbonate performs 2.47 KJ of P.V work (at 1 atm and 298K) and also absorbs 38.95 KJ of heat from the surroundings. Use these values to determine AH and AE for the reaction. Write an equation for the process with the work and energy on the correct sides.

Answer 1

When Ca2+ ions react with HCO32- ions, CaCO3, CO2 and H2O is formed as per the equation shown below-

Ca(HCO3)2 $\rightarrow$ CaCO3 + H2O + CO2

Now, since the system absorb heat from the surrounding it is a endothermic reaction with $\Delta$ H = 38.95kJ

Since heat is taken by the system from the surrounding, work will be donr by the system on the surrounding. Thus, W= - 2.47kJ. ( The negative sign is not magnitude. It just show that work is done on the surrounding)

Now, enthalpy is defined as-

$\Delta$H =$\Delta$E +P$\Delta$​​​​​​​V

E= internal Energy of the system

P$\Delta$​​​​​​​V = Work Done = 2.47kJ

Thus,

$\Delta$​​​​​​​E = 38.95 - 2.47kJ = 36.48kJ

Including this enthalpy change and work done in the equation, the complete equation will be-

Ca(HCO3)2 + $\Delta$ ​​​​​​​H $\rightarrow$ CaCO3 + H2O + CO2 ​​​​​​​+ Work