Problem 50 - General Chemistry: Principles and Modern Applications

Question

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.

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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.

Key Concepts

Triple Point Explained

The triple point is a unique set of conditions where all three phases of matter—solid, liquid, and gas—can coexist in equilibrium. For any substance, this specific point on the phase diagram represents a precise balance of temperature and pressure. In the case of hydrazine (\(\mathrm{N}_{2}\mathrm{H}_{4}\)), this point is given as \(2.0^{\circ} \mathrm{C}\) and \(3.4 \mathrm{mm} \mathrm{Hg}\). This means at these conditions, hydrazine can exist simultaneously as ice, liquid, and vapor.

• This is an essential feature on the phase diagram since it marks the intersection of the boundaries separating the three phases.
• It is also important to plot this point accurately as it affects the overall shape of the diagram, particularly how the solid-liquid and liquid-vapor boundaries extend from it.

In nature, this kind of balance is rare and slight changes in pressure or temperature can shift the substance entirely into one particular phase. Thus, the concept of a triple point not only adds a point of interest in the phase diagram but also helps in understanding phase transitions.

Understanding the Critical Point

The critical point on a phase diagram represents the highest temperature and pressure at which a liquid can exist. Beyond this point, we encounter what is called a supercritical fluid, where the separate liquid and gas phases become indistinguishable. For hydrazine, the critical point is specified at \(380^{\circ} \mathrm{C}\) and \(145 \mathrm{atm}\).

• Above the critical temperature, no increase in pressure will result in liquefaction of a gas.
• This point represents not an endpoint but rather a threshold of different phase behavior.

In the sketch of the hydrazine phase diagram, this critical point serves as the endpoint of the liquid-vapor boundary known as the critical line. Linking phases up to this line provides valuable insights into the necessary energy required for transitions and the behavior of hydrazine under extreme conditions. Nevertheless, beyond this point, phase descriptions using typical terms like liquid or gas become inadequate.

Phase Boundaries and Their Significance

Phase boundaries are the lines on a phase diagram indicating the conditions under which two phases exist in equilibrium. Each boundary represents a different kind of equilibrium:

• Solid-liquid boundary, where melting and freezing occur.
• Liquid-vapor boundary, where boiling and condensation happen.
• Solid-vapor boundary, correlating to sublimation and deposition processes.

In hydrazine’s phase diagram:

• The solid-liquid boundary has a negative slope, illustrating that hydrazine contracts upon freezing. This rare occurrence emphasizes that the solid is denser than the liquid, deviating from more common positive slopes as seen in water’s phase diagram.
• As we move toward the critical point, the liquid-vapor boundary marks the pressures and temperatures where hydrazine can transition between liquid and gas under equilibrium conditions.

Understanding these boundaries is crucial because they guide predictions about how substances will react under varied temperatures and pressures, considering both lab-based science and industrial applications. The uncertainty in drawing these boundaries without specific experimental data highlights the necessity for assumptions based on general physical principles.