Thermodynamics Trick — Calculate Enthalpy of Solution Easily 🔥

 

❓ Question

The hydration energies of $\text{K}^+$ and $\text{Cl}^-$ are $-x$ and $-y~\text{kJ/mol}$ respectively.
If the lattice energy of KCl is $-z~\text{kJ/mol}$, then what is the heat of solution of KCl?

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🧪 Concept Summary

When an ionic solid (like KCl) dissolves in water:

1. Lattice breaks down — ions separate. (Energy absorbed)

2. Ions get hydrated — water molecules surround ions. (Energy released)

These two processes combine to give the enthalpy (heat) of solution $(\Delta H_{\text{sol}})$.

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🖼️ Question Image

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✍️ Step-by-Step Solution

Step 1 — Write the process

$$\text{KCl(s)}\stackrel{\text{dissolve}}{\to }{\text{K}}^{+}(aq)+{\text{Cl}}^{-}(aq)$$

This happens in two stages:

1️⃣ Lattice dissociation (endothermic):

$$\text{KCl(s)} \rightarrow \text{K}^+ (g) + \text{Cl}^- (g) \quad \text{Energy absorbed} = +z~\text{kJ/mol}$$

2️⃣ Hydration (exothermic):

$$\text{K}^+ (g) + \text{Cl}^- (g) \rightarrow \text{K}^+ (aq) + \text{Cl}^- (aq) \quad \text{Energy released} = (-x) + (-y) = -(x+y)$$

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Step 2 — Apply Hess’s Law

Total heat of solution:

$$\Delta H_{\text{sol}} = (\text{Lattice energy}) + (\text{Hydration energy})$$
$$\Delta H_{\text{sol}} = (+z) + [-(x+y)]$$

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Step 3 — Simplify expression

$$\boxed{\Delta H_{\text{sol}} = z - (x + y)}$$

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🧮 Image Solution

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✅ Final Answer

$$\boxed{\text{Heat of solution of KCl } = z - (x + y)~\text{kJ/mol}}$$

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💡 Concept Recap

Process	Description	Sign of Energy	Example
Lattice energy	Energy to break solid ionic bonds	$+z$ (absorbed)	KCl(s) → K⁺ + Cl⁻
Hydration energy	Energy released when ions attract water	$-(x+y)$ (released)	K⁺, Cl⁻ surrounded by H₂O
Net Heat of Solution	$z - (x+y)$	Can be +ve or –ve depending on magnitudes	Exothermic if $x+y > z$

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