Calcualte ΔH° in kilojoules for the synthesis of lime (CaO) from limestone (CaCO3), the key step in the manufacture of cement. CaCO3(s) → CaO(s) + CO2(g) ΔH°f [CaCO3(s)] = -1207.6 kJ/mol ΔH°f [CaO(s)] = -634.9 kJ/mol ΔH°f [CO2(g)] = -393.5 kJ/mol

Verified step by step guidance

1. Identify the chemical reaction: CaCO_3(s) \rightarrow CaO(s) + CO_2(g).
2. Use the formula for the standard enthalpy change of reaction: \( \Delta H^\circ = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants}) \).
3. List the standard enthalpies of formation: \( \Delta H^\circ_f [CaCO_3(s)] = -1207.6 \text{ kJ/mol} \), \( \Delta H^\circ_f [CaO(s)] = -634.9 \text{ kJ/mol} \), \( \Delta H^\circ_f [CO_2(g)] = -393.5 \text{ kJ/mol} \).
4. Calculate the sum of the standard enthalpies of formation for the products: \( \Delta H^\circ_f [CaO(s)] + \Delta H^\circ_f [CO_2(g)] \).
5. Subtract the standard enthalpy of formation of the reactant from the sum of the products: \( (\Delta H^\circ_f [CaO(s)] + \Delta H^\circ_f [CO_2(g)]) - \Delta H^\circ_f [CaCO_3(s)] \).

Key Concepts

Enthalpy of Formation (ΔH°f)

The enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial value in thermodynamics, allowing chemists to calculate the energy changes associated with chemical reactions. In this question, the ΔH°f values for CaCO3, CaO, and CO2 are provided, which are essential for determining the overall reaction enthalpy.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps, regardless of the pathway taken. This principle allows for the calculation of reaction enthalpies using known ΔH°f values. In the context of the given reaction, Hess's Law enables the determination of ΔH° for the decomposition of CaCO3 into CaO and CO2 by using the enthalpy values of the products and reactants.

Standard State Conditions

Standard state conditions refer to the set of specific conditions (usually 1 atm pressure and a specified temperature, typically 25°C) under which thermodynamic measurements are made. These conditions provide a reference point for comparing the enthalpy of substances. In this question, the ΔH°f values are given under standard state conditions, which is essential for accurately calculating the enthalpy change for the reaction.