This online Boiling Point Calculator allows you to find the boiling point of some common substances at arbitrary pressures using the Clausius-Clapeyron relation.
Definition of Boiling Point
The boiling point of a substance is the temperature at which its vapor pressure equals the surrounding atmospheric pressure, causing the liquid to transition to a gaseous state.
At the molecular level, boiling occurs when the molecules in a liquid gain sufficient kinetic energy to overcome intermolecular forces and escape into the vapor phase in the form of vapor bubbles arising inside the liquid. When a liquid is heated, its vapor pressure increases. Once this vapor pressure equals the pressure exerted by the surrounding environment (usually atmospheric pressure), the liquid begins to boil.
For example, at sea level, where atmospheric pressure is approximately 101.325 kPa (1 atm), pure water boils at 100 °C. However, at higher elevations where atmospheric pressure is lower, water boils at a lower temperature. Conversely, in a pressure cooker, where the pressure is artificially increased, water boils at a higher temperature. This pressure dependence is a critical consideration in many applications, from cooking to industrial distillation.
The boiling point is considered an important physical property of a substance. It is often used to identify compounds and assess purity. A pure compound typically has a sharp boiling point, whereas a mixture or impure substance exhibits a range of boiling temperatures.
The Clausius–Clapeyron Equation
The Clausius–Clapeyron relation is a way to quantify the relationship between the vapor pressure of a substance and its temperature. It is derived from thermodynamic principles and describes the phase boundary between two phases of matter – in this context, liquid and vapor.
The differential form of the Clausius–Clapeyron equation is:
$$\frac{dP}{dT} = \frac{L}{T\Delta v}$$
where:
• \(dP/dT\) is the rate of change of pressure with respect to temperature,
• \(L\) is the molar latent heat of vaporization,
• \(T\) is the absolute temperature (in Kelvin),
• \(\Delta v\) is the change in molar volume between the liquid and vapor phases.
Assuming the vapor behaves as an ideal gas and the volume of the liquid is negligible compared to that of the vapor, the equation can be integrated to yield the more common logarithmic form:
$$ln\left ( \frac{P_2}{P_1} \right ) = -\frac{L}{R}\left ( \frac{1}{T_2}- \frac{1}{T_1} \right )$$
where:
• \(P_1\) and \(P_2\) are the vapor pressures at temperatures \(T_1\) and \(T_2\) respectively,
• \(L\) is the molar enthalpy (heat) of vaporization (in J/mol),
• \(R\) is the universal gas constant (≈ 8.3145 J/mol·K).
This equation enables the estimation of boiling temperatures at pressures other than the standard 1 atm, provided that the heat of vaporization is known and relatively constant over the temperature range.
Calculating the Boiling Point at Arbitrary Pressures
To calculate the boiling point of a substance at a non-standard pressure using the Clausius–Clapeyron equation, one typically rearranges the logarithmic form to solve for the unknown temperature \(T_2\):
$$T_2 = \left [ \frac{1}{T_1} – \frac{R}{L} ln\left ( \frac{P_2}{P_1} \right ) \right ] ^{-1}$$
Here’s how the calculation works in practice:
- Identify known values:
• \(T_1\) – the boiling point at a known pressure \(P_1\) (usually standard atmospheric pressure),
• \(L\) – the molar heat of vaporization,
• \(P_2\) – the desired pressure at which the boiling point is to be determined. - Insert into the equation. Using the known values and constants, the equation is used to compute \(T_2\), the boiling point at the new pressure.
- Convert units if necessary. Ensure temperature is in Kelvin and pressure in consistent units (e.g., kPa or atm), and convert the result to degrees Celsius or Fahrenheit if needed.
The above equation and the algorithm are used in our Boiling Point Calculator. The boiling point values of various substances at normal pressure (1 atm) and the corresponding molar heat of vaporization values are taken from this table.
Let us remind you once again that this method assumes that the heat of vaporization remains constant over the temperature range, which is an approximation. More accurate results may require integrating the exact variation of enthalpy with temperature or using empirical vapor pressure data.
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