Lime is made commercially by decomposition of limestone `CaCO_(3)`. What is the change in internal energy when 1.00 mole of solid `CaCO_(3)` (V = 34.2 ml) absorbs 177.9 kJ of heat and decomposes at `25^(@)C` against a pressure of 1.0 atm to give solid CaO. (Volume = 16.9 ml) and `CO_(2)` (g) (V = 24.4 L)

Explanation

To find the change in internal energy (ΔU) for the decomposition of calcium carbonate (CaCO₃) into calcium oxide (CaO) and carbon dioxide (CO₂), we will use the relationship between enthalpy change (ΔH) and internal energy change (ΔU). The relevant equation is:

\[ \Delta H = \Delta U + \Delta N_g RT \]

Where:
- ΔH is the change in enthalpy (given as 177.9 kJ)
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