To find the enthalpy change for the process MgCl₂(s) -> MgCl₂(aq), we can use the Hess's law, which states that the enthalpy change of a reaction is equal to the sum of the enthalpy changes of the individual steps that make up the reaction.
Here are the steps to calculate the enthalpy change for the given process:
Step 1: Write down the given equations and their enthalpy changes:
1. MgCl₂(s) -> Mg²⁺(g) + 2Cl⁻(g) ΔH₁ = +2490 kJ/mol
2. Mg²⁺(g) -> Mg²⁺(aq) ΔH₂ = -1920 kJ/mol
3. Cl⁻(g) -> Cl⁻(aq) ΔH₃ = -360 kJ/mol
Step 2: Notice that the overall equation we are looking for has solid (s) MgCl₂ on the left side and aqueous (aq) MgCl₂ on the right side. To achieve this, we need to combine equations 2 and 3 in a way that cancels out the product Mg²⁺(aq) and Cl⁻(g).
Step 3: Multiply equation 2 by 2 to balance the number of Cl⁻:
2 × (Mg²⁺(g) -> Mg²⁺(aq)) => 2Mg²⁺(g) -> 2Mg²⁺(aq) [Multiply enthalpy change by 2 as well]
This gives us the desired number of Mg²⁺(aq) and Cl⁻(g).
Step 4: Add equations 2 and 3 together:
2Mg²⁺(g) + Cl⁻(g) -> 2Mg²⁺(aq) + Cl⁻(aq) [Add the enthalpy changes of the equations]
Step 5: Write the final equation:
MgCl₂(s) -> 2Mg²⁺(aq) + Cl⁻(aq)
Step 6: Add the enthalpy changes of the individual steps to get the enthalpy change for the overall equation:
ΔH_total = ΔH₁ + ΔH₂ + ΔH₃
ΔH_total = (+2490 kJ/mol) + (-1920 kJ/mol) + (-360 kJ/mol)
ΔH_total = 210 kJ/mol
Therefore, the enthalpy change for the process MgCl₂(s) -> MgCl₂(aq) is 210 kJ/mol.