Question

The fact that water on Earth can readily be found in all three states (solid, liquid, and gas) is in part a consequence of the fact that the triple point of water \(\left(T=0.01^{\circ} \mathrm{C}, P=0.006 \mathrm{~atm}\right)\) falls within a range of temperatures and pressures found on Earth. Saturn's largest moon Titan has a considerable amount of methane in its atmosphere. The conditions on the surface of Titan are estimated to be \(P=1.6\) atm and \(T=-178^{\circ} \mathrm{C}\). As seen from the phase diagram of methane (Figure 11.30 ), these conditions are not far from the triple point of methane, raising the tantalizing possibility that solid, liquid, and gaseous methane can be found on Titan. (a) What state would you expect to find methane in on the surface of Titan? (b) On moving upward through the atmosphere the pressure will decrease. If we assume that the temperature does not change, what phase change would you expect to see as we move away from the surface?

Short answer

(a) On the surface of Titan, methane is expected to be in a liquid state, since this state corresponds to the conditions found at Titan's surface in the phase diagram of methane (\(T = 95.15\,K\) and \(P= 1.6\) atm). (b) As we move upward through the atmosphere, the pressure decreases while the temperature remains constant. In this situation, as seen from the phase diagram, methane is expected to undergo a phase change from a liquid to a gaseous state.

Step-by-step solution

Convert temperature to Kelvin scale

To begin, we should convert the temperature given in Celsius to Kelvin, which will make it easier to analyze in the context of the phase diagram. \[T_{K} = T_{C} + 273.15\] \[T_{K} = (-178) + 273.15\] \[T_{K} = 95.15\,K\]

Determine the state of methane on Titan's surface

Considering Titan's surface conditions, locate the point in the phase diagram with temperature \(T = 95.15\,K\) and pressure \(P= 1.6\) atm. Determine the phase of methane at this point, which will be the state in which methane is found on the surface of Titan. From the phase diagram, we know that at \(T = 95.15\,K\) and \(P= 1.6\) atm, we are above the triple point of methane but below the critical point. In this region, methane is in a liquid state. Thus, we can expect to find liquid methane on the surface of Titan.

Determine phase change while moving upward through the atmosphere

As we move upward in the atmosphere, the pressure will decrease while we assume the temperature remains constant at \(T = 95.15\,K\). Analyze the phase diagram to predict any phase changes that may occur when pressure decreases. If we start from the initial point representing Titan's surface condition, as the pressure decreases and temperature remains constant, we move vertically to the left in the phase diagram. Along this path, we will cross the phase boundary between the liquid and gas regions. This indicates that as pressure decreases while moving upwards in the atmosphere, we can expect methane to undergo a phase change from the liquid state to the gaseous state. The final answers are: (a) Methane is found in the liquid state on the surface of Titan. (b) As we move upward through the atmosphere and pressure decreases, methane will change from a liquid to a gaseous state.

Key concepts

Triple Point of Water

Understanding the triple point of water is essential for grasping how substances behave under different temperature and pressure conditions. The triple point is a unique set of conditions where a substance can simultaneously exist as a solid, liquid, and gas. For water, this occurs at a temperature of 0.01°C (273.16 K) and a pressure of 0.006 atmospheric pressures (atm).

At the triple point, the phases are in equilibrium; this means that you can see ice, liquid water, and water vapor all coexist without any one phase converting entirely into another. This principle is also pivotal when considering other substances under extraterrestrial conditions, like methane on Titan, Saturn's moon, where extreme conditions can create an environment for multiple phases to exist together.

• The triple point allows for the advanced study of phase transitions, which is critical in various scientific fields, from meteorology to materials science.
• Understanding the concept helps explain why Earth's water cycle is dependent on specific pressure and temperature ranges.

Phase Diagram of Methane

Phase diagrams are graphical representations that show the state of matter of a substance (solid, liquid, or gas) at different temperatures and pressures. The phase diagram of methane, as with any substance, includes lines that demarcate the conditions under which two phases can exist in equilibrium, such as solid & liquid (melting/freezing line), liquid & gas (evaporation/condensation line), and solid & gas (sublimation/deposition line).

Key points in the diagram include the triple point, where all three phases coexist, and the critical point, beyond which the liquid and gas phases are indistinguishable. In the context of Titan, methane's phase diagram helps determine that on its surface, where the pressure is 1.6 atm and temperature is -178°C (-94.15 K), methane exists predominantly in the liquid state.

Phase Changes in Methane on Titan

As the altitude increases and pressure decreases on Titan, the phase diagram predicts that methane would undergo a phase transition from liquid to gas. This phase change is crucial for understanding Titan's climate and potential for supporting life, as phase transitions play a significant role in weather patterns and other natural processes.

• The phase diagram is a valuable tool for predicting the existence and behavior of substances in different environments.
• Learning about methane's phase diagram is particularly interesting when considering the possibility of life or unique geological formations in extraterrestrial landscapes.

States of Matter

The states of matter—solid, liquid, and gas—are determined by the kinetic energy of particles and the strength of the attractive forces between them. In solids, particles are tightly bound in a structured network, resulting in a fixed shape. Liquids have more energy, allowing particles to flow around each other while still being moderately attracted, which means they take the shape of their container but maintain a consistent volume. Gases have high kinetic energy that overcomes attraction between particles, so they expand to fill their container and can be easily compressed.

In our exercise example, methane transitions through these states due to the pressures and temperatures experienced on Titan. These concepts are not only fundamental to chemistry and physics, but they also play a crucial role in environmental sciences, engineering, and many other scientific disciplines.

• Comprehension of these states helps us understand and predict the behavior of different materials in various settings.
• For instance, methane's physical states on Titan influence both extraterrestrial meteorology and the potential for astrobiological studies in our search for life beyond Earth.