Question

The melting point of a fictional substance \(X\) is \(225^{\circ} \mathrm{C}\) at \(10.0 \mathrm{~atm}\). If the density of the solid phase of \(\mathrm{X}\) is \(2.67 \mathrm{~g} / \mathrm{cm}^{3}\) and the density of the liquid phase is \(2.78 \mathrm{~g} / \mathrm{cm}^{3}\) at \(10.0 \mathrm{~atm}\), predict whether the normal melting point of \(X\) will be less than, equal to, or greater than \(225^{\circ} \mathrm{C}\). Explain.

Short answer

The normal melting point of substance X is predicted to be greater than \(225^{\circ}\mathrm{C}\), as the solid phase is less dense (2.67 g/cm³) than the liquid phase (2.78 g/cm³) at 10 atm pressure. When pressure is decreased to 1 atm, the substance will favor transitioning to the denser liquid phase, leading to a higher melting point.

Step-by-step solution

Compare the densities at 10 atm pressure

We are given the density of the solid phase as 2.67 g/cm³ and the density of the liquid phase as 2.78 g/cm³ at 10 atm pressure. Let's compare these two densities: 2.67 g/cm³ (solid) < 2.78 g/cm³ (liquid) This means that the solid phase is less dense than the liquid phase at this pressure.

Determine the effect of the density difference on the melting point

Since the solid is less dense than the liquid at 10 atm pressure, it means that the substance will favor transitioning from the solid to the liquid phase. Generally, if the solid phase of a substance is less dense than its liquid phase, an increase in pressure will lead to a decrease in melting point, as the substance will favor the more dense phase (liquid in this case). Conversely, if the solid phase is denser than the liquid phase, an increase in pressure will lead to an increase in the melting point, as the substance will favor the denser solid phase. As the density of solid is less than the density of liquid, we can infer that at a lower pressure (i.e. going from 10 atm to 1 atm), the melting point will be higher.

State the prediction

Based on the density comparison and the explanation given in Step 2, we can predict that the normal melting point of substance X (at 1 atm pressure) will be greater than 225°C.

Key concepts

Phase Transition

Understanding phase transitions is crucial when analyzing changes in states of matter. A phase transition occurs when a substance changes from one state of matter to another—such as from solid to liquid, which is precisely what a melting point signifies. A substance's melting point is the temperature at which it converts from a solid phase to a liquid phase. At this temperature, the molecular forces holding the solid together are overcome by the thermal energy providing enough motion to the molecules to break free into a less ordered liquid state.

When we look at a substance like the fictional substance X, understanding the melting point helps us predict how the substance will behave under different conditions. If a substance's solid phase has a lower density than its liquid phase, as is the case with substance X, the solid will float on its liquid. This peculiarity plays a significant role when we start changing the surrounding pressure and examine the melting point's variation.

Density Comparison

Comparing the densities of different phases of a substance is very helpful in understanding a substance's behavior under various conditions. Density, defined as mass per unit volume, can provide insights into the structural properties of a substance. Materials with higher densities have particles that are more closely packed together than those with lower densities.

For the fictional substance X, when we compare the density of the solid phase (2.67 g/cm³) with the liquid phase (2.78 g/cm³) at the given pressure of 10 atm, we observe that the solid is less dense than the liquid. This is an unusual property, as most substances are denser in their solid state. This characteristic is pertinent to predicting the melting point under standard atmospheric pressure. In the context of substance X, because the solid phase is less dense, it implies that upon increasing the surrounding pressure, the melting point is likely to decrease, as the denser liquid phase becomes more favored energetically.

Pressure Effect on Melting Point

Pressure plays a pivotal role in determining the melting points of substances. The melting point of a substance can change with variations in external pressure due to the physical concept known as 'Le Chatelier’s principle'. This principle suggests that a system at equilibrium, when subjected to a change in conditions (such as pressure), will adjust to counteract the impact of that change.

For a substance like X, which becomes denser when it melts, increasing pressure could lead to a decrease in melting point. This is because applying pressure favors the phase with the higher density in order to minimize volume, in this case, the liquid phase. Hence, under higher pressure, a solid with a lower density compared to its liquid form will melt at a lower temperature. Conversely, if we decrease the pressure from 10 atm to normal atmospheric pressure (1 atm), we would expect the melting point to increase. This aligns with our prediction for substance X, where its normal melting point under standard atmospheric conditions would be higher than 225°C due to the reduced pressure allowing the less dense solid phase to be stable at higher temperatures.