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Chapter 12: Problem 50

Sketch a plausible phase diagram for hydrazine \(\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)\) from the following data: triple point \(\left(2.0^{\circ} \mathrm{C}\right)\) and \(3.4 \mathrm{mm} \mathrm{Hg}\) ), the normal melting point \(\left(2^{\circ} \mathrm{C}\right),\) the normal boiling point \(\left(113.5^{\circ} \mathrm{C}\right),\) and the critical point \(\left(380^{\circ} \mathrm{C} \text { and } 145 \mathrm{atm}\right) .\) The density of the liquid is less than that of the solid. Label significant data points on this diagram. Are there any features of the diagram that remain uncertain? Explain.

Short Answer

Expert verified
A phase diagram for hydrazine has been sketched based on the given data. The plotted diagram has a negative slope for solid-liquid phase transition due to the density difference. Uncertainties exist because of the lack of information about phase boundary data and unknown phase changes at pressures above 145 atm and temperatures above 380°C.

Step by step solution

01

Identifying the Axes of the Phase Diagram

Consider the y-axis as pressure and the x-axis as temperature. The temperature is plotted from -2°C to 400°C and the pressure from 0 mmHg to 150 atm, so that all the given points can be covered.
02

Labelling the Data Points on the Diagram

Plot and label the following points: (1) the triple point at \((2.0°C, 3.4mmHg)\), (2) the melting point at \(2°C\), (3) the boiling point at \(113.5°C\), and (4) the critical point at \((380°C, 145atm)\). It is worth mentioning that the normal melting and boiling points correspond to a pressure of 1 atm.
03

Sketching the Phase Boundaries

After plotting the points, connect them with smooth curves to define the boundaries between different phases—solid, liquid, and gas. It is known that the density of the liquid is less than that of the solid, which means the solid-liquid phase boundary should have a negative slope.
04

Identifying Uncertainties

An uncertain aspect of the phase diagram would be the exact pathway of the phase boundaries, as we are not provided with any phase boundary data and must make assumptions based on general physical knowledge. Also, we can't say anything about the phase changes at pressures above 145 atm and temperatures above 380°C as we do not have data beyond the critical point.

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