PREPARATORY PROBLEM 36 (PRACTICAL) Phase Diagram and Enthalpy of Vaporization Introduction This expe — Physical Chemistry — Thermodynamics Chemistry Question

PREPARATORY PROBLEM 36 (PRACTICAL)
Phase Diagram and Enthalpy of Vaporization

Introduction
This experiment will allow you to construct a significant portion of the liquid – gas equilibrium curve in a phase diagram for water. The data will be used to determine an average value for the enthalpy of vaporization for the same compound making use of the Clausius – Clapeyron equation.

Theory
Every liquid can come to equilibrium with its vapor. The vapor pressure of a single–component liquid depends on the nature of the liquid and the temperature. At the temperature where the vapor pressure is equal to the total pressure applied to the liquid, the liquid boils. The normal boiling point is achieved when the pressure is 1 atm (= 1.013 bar = 101 325 Pa).
A phase diagram displays pressure versus temperature (or vice versa). For most compounds there are regions of the diagram where each phase (i.e., solid, liquid, gas) is shown and their boundaries are the two–phase equilibrium curves.
The Clapeyron equation is derived from basic thermodynamics. It states that the slope of any equilibrium curve is equal to the ratio of the change in molar enthalpy upon phase change over the corresponding molar volume change and over the temperature,

dp/dT = Δh / (T ΔV)

If we are interested in the liquid – gas or solid – gas equilibrium, we may assume that the gas follows the ideal gas state equation and that the molar volume of the gas is much larger than that for the condensed phase. With these assumptions, the Clausius^-Clapeyron equation is derived:

d(ln p) / d(T⁻¹) = -Δh / R

The derivative on the left–hand side of the equation is the slope of the lnp versus T⁻¹ diagram.

Method
By trapping water in a sealed container, heating the apparatus and monitoring the pressure and the temperature, we can record a section of the phase diagram.

Apparatus
A simple heater (100 – 200 W), a 0 – 200 °C thermometer, a 0 – 20 bar pressure gauge (Bourdon tube), insulating aluminium foil, a steel tube, H₂O.

Procedure
Assemble the apparatus: wrap tightly together water containing tube (copper tube 10 cm long, 6 mm dia., plugged on one end and fitted with pressure gauge) and thermometer with Al foil; insert assembly in core of heater coil; support properly. Apply power to heater. Monitor pressure and temperature and interrupt heating when either 16 bar or 180 °C are exceeded. Start recording pressure and temperature for every division on the pressure gauge, while the apparatus is cooling down until the temperature has reached below 80 °C. Enter your measurements in a table with 3 columns: point number, pressure (units), temperature (units).

Analysis – Presentation
Draw all recorded points on a p vs. θ graph (phase diagram). Spot out any irregularities, i.e., highly divergent measurements. Extend the above table to include columns for lnp, T, 1/T. Calculate lnp, T, 1/T. Draw diagram of lnp vs. 1/T. Draw a straight line through the points of the latter diagram. Determine the slope of the line and calculate the enthalpy of vaporization for water.