1. Understand the Relationship
* Boiling Point and Pressure: The boiling point of a liquid is the temperature at which its vapor pressure equals the surrounding atmospheric pressure.
* Clausius-Clapeyron Equation: This equation relates vapor pressure to temperature. We can use a simplified form for small temperature ranges:
```
ln(P₂/P₁) = - (ΔHvap / R) * (1/T₂ - 1/T₁)
```
where:
* P₁ and P₂ are the vapor pressures at temperatures T₁ and T₂
* ΔHvap is the enthalpy of vaporization
* R is the ideal gas constant (8.314 J/mol·K)
2. Gather Information
* Normal Boiling Point: The normal boiling point of methylene chloride is 40.1 °C (313.25 K) at 760 mmHg (standard pressure).
* Enthalpy of Vaporization (ΔHvap): This value is typically found in a reference table. For methylene chloride, it's approximately 29.9 kJ/mol.
3. Set up the Equation
* P₁: 760 mmHg (normal boiling point)
* T₁: 313.25 K (normal boiling point)
* P₂: 670 mmHg (given pressure)
* T₂: This is what we want to find (boiling point at 670 mmHg)
4. Solve for T₂
```
ln(670 mmHg / 760 mmHg) = - (29.9 kJ/mol / 8.314 J/mol·K) * (1/T₂ - 1/313.25 K)
```
* Simplify and solve for 1/T₂:
```
1/T₂ ≈ 0.00318 K⁻¹
```
* Calculate T₂:
```
T₂ ≈ 314.5 K
```
5. Convert to Celsius
* T₂ ≈ 314.5 K - 273.15 = 41.35 °C
Therefore, the boiling point of methylene chloride at 670 mmHg is approximately 41.35 °C.
