Methane (CH4) has a boiling point of -164^∘ C at 1 atm and a vapor pressure of 42.8 atm at -100^

step 1 So for this question, we have to find the heat of vaporization of methane. And I've written down

Methane (CH4) has a boiling point of -164^∘ C at 1 atm and a...

Methane $\left(\mathrm{CH}_{4}\right)$ has a boiling point of $-164^{\circ} \mathrm{C}$ at 1 $\mathrm{atm}$ and a vapor pressure of 42.8 atm at $-100^{\circ} \mathrm{C}$ . What is the heat of
vaporization of $\mathrm{CH}_{4} ?$

Key Concepts

Clausius-Clapeyron Equation

This equation provides a mathematical relationship between the vapor pressure of a substance and its temperature, under the assumption of a constant heat of vaporization over the temperature range. It is used to calculate the enthalpy of vaporization by relating the natural logarithm of the vapor pressure to the inverse of the temperature, thereby allowing the determination of the latent heat involved in the phase change from liquid to vapor.

Enthalpy of Vaporization

This term refers to the amount of energy required to convert one mole of a substance from the liquid phase to the vapor phase at constant pressure. It is a measure of the strength of the intermolecular forces in the liquid, with higher values indicating stronger forces that must be overcome during vaporization.

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a substance when it is in thermodynamic equilibrium with its liquid (or solid) phase. It reflects the tendency of molecules to escape from the condensed phase and is highly dependent on temperature. Understanding vapor pressure is essential for studying phase changes and related energetic transitions.

Phase Equilibrium

Phase equilibrium occurs when the rate of transition between phases (such as liquid and vapor) is balanced, resulting in constant physical properties like pressure and temperature. This concept is crucial for studying and predicting the conditions under which a substance will change phases, and it underpins the use of equations like the Clausius-Clapeyron equation in thermodynamics.

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