The solubility of NaCl in water decreases with increases in temperature.

Answer

To determine whether the statement "The solubility of NaCl in water decreases with an increase in temperature" is correct, we can analyze the dissolution process and the thermodynamic principles involved.

### Step-by-Step Solution:

1. **Understanding the Dissolution of NaCl**:
- When sodium chloride (NaCl) is added to water, it dissolves and dissociates into sodium ions (Na⁺) and chloride ions (Cl⁻).
- The dissolution process can be represented as:
\[ \text{NaCl (s)} \rightarrow \text{Na}^+ (aq) + \text{Cl}^- (aq) \]

2. **Enthalpy of Dissolution**:
- The enthalpy change (ΔH) for the dissolution of NaCl is positive, indicating that the process is endothermic. This means that heat is absorbed when NaCl dissolves in water.

3. **Solubility Product (Ksp)**:
- The solubility product (Ksp) is a constant that reflects the solubility of a salt in a saturated solution. For NaCl, we can express the relationship between Ksp and temperature using the van 't Hoff equation:
\[ \ln Ksp = -\frac{\Delta H}{RT} + \frac{\Delta S}{R} \]
- Here, ΔS is the entropy change, R is the universal gas constant, and T is the temperature in Kelvin.

4. **Effect of Temperature on Ksp**:
- Since ΔH is positive (endothermic), increasing the temperature (T) will affect the Ksp value.
- As temperature increases, the term \(-\frac{\Delta H}{RT}\) becomes less negative (or more positive), leading to an increase in Ksp.

5. **Conclusion on Solubility**:
- If Ksp increases with temperature, it implies that the solubility of NaCl in water also increases with an increase in temperature.
- Therefore, the statement that "the solubility of NaCl in water decreases with an increase in temperature" is **incorrect**.

### Final Answer:
The solubility of NaCl in water **increases** with an increase in temperature, making the original statement incorrect.

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