The boiling point of methanol is 65.0^∘ C, and the standard...

The boiling point of methanol is $65.0^{\circ} \mathrm{C}$, and the standard enthalpy of formation of methanol vapor is $-201.2 \mathrm{kJ} / \mathrm{mol} .$ Calculate the vapor pressure of methanol (in $\mathrm{mmHg}$ ) at $25^{\circ} \mathrm{C}$. (Hint: See Appendix 2 for other thermodynamic data of methanol).

Key Concepts

Phase Equilibrium

Phase equilibrium refers to the state in which a substance exists in more than one phase (such as liquid and vapor) and the rates of change between the phases are balanced. In this state, the chemical potential of the substance is the same in each phase, meaning there is no net transfer of mass from one phase to the other.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid (or solid) phase at a given temperature. It is a direct measure of a substance’s volatility and is crucial in understanding how easily a liquid will evaporate.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation establishes the relationship between the vapor pressure of a substance and its temperature. It connects the rate of change of vapor pressure with temperature to the enthalpy change associated with the phase transition (typically the heat of vaporization), making it a valuable tool for predicting vapor pressures at different temperatures.

Boiling Point

The boiling point is the temperature at which the vapor pressure of a liquid equals the external pressure, resulting in the formation of bubbles within the liquid. It is an important physical property that provides a reference point for understanding phase transitions and vaporization behavior.

Enthalpy of Vaporization

The enthalpy of vaporization (or heat of vaporization) is the amount of energy required to convert one mole of a liquid into a vapor at constant pressure. It plays a key role in the temperature dependence of vapor pressure, as a higher enthalpy of vaporization typically indicates a lower vapor pressure at a given temperature.

Transcript

00:01 Question number 151 is not too difficult of a mathematical calculation.

00:08 However, it is a very conceptually complex question with multiple parts.

00:16 It provides you the boiling point of methanol.

00:19 It provides you the delta h of formation of vapor methanol.

00:25 And it asks, and that's it, and it asks you to calculate the vapor pressure of methanol at 25 degrees.

00:32 Celsius.

00:34 So there are several conceptual ideas that you need to pick up on first before you begin any calculation.

00:44 The first one is you need to use the clausius clapperon equation.

00:49 Anytime you are asked to calculate the vapor pressure of something at a particular temperature, that's the clousieus clapron equation.

00:59 So we know we need to use that.

01:01 But in the clousias -clap -ron equation, we don't have delta h as a formation.

01:07 We have delta h of vaporization.

01:09 So we need to figure out how to get delta h of vaporization from the information provided.

01:15 We also need to recognize that the vapor pressure at the boiling point of methanol is equal to one atmosphere, because by definition it wouldn't be boiling unless it's vapor pressure equaled atmospheric pressure, which we will assume is one atmosphere.

01:38 And then last of all, we need to recognize that we can calculate delta h of vaporization from delta h of formations for liquid and gaseous methanol.

01:51 To make it obvious, we will write the chemical reaction of liquid methanol, going to gaseous methanol.

01:59 The delta h for this process is the delta h of vaporization, the change in enthalpy to go from a liquid to a gas...

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