Question

The melting point of a fictional substance \(X\) is \(225^{\circ} \mathrm{C}\) at \(10.0\) 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 at 1 atm will be greater than 225℃. This is because substance X contracts upon melting, as the density of the liquid phase is higher than the density of the solid phase. According to the Clausius-Clapeyron equation, a decrease in pressure from 10 atm to 1 atm should lead to an increase in the melting point.

Step-by-step solution

Understand the relationship between melting point, pressure, and density

According to the Clausius-Clapeyron equation, an increase in pressure will lead to an increase in the melting point if the substance expands upon melting (liquid phase density lower than solid phase). In contrast, if the substance contracts upon melting (liquid phase density higher than solid phase), an increase in pressure will lead to a decrease in the melting point.

Compare the given densities of substance X

We are given the density of the solid phase of substance X as \(2.67 \frac{g}{cm^3}\), and the density of the liquid phase as \(2.78 \frac{g}{cm^3}\). Comparing these values, we can see that the density of the liquid phase is higher than the density of the solid phase.

Predict the effect of changing pressure on the melting point of substance X

Since the density of the liquid phase is higher than the density of the solid phase for substance X, it implies that substance X contracts upon melting. As a result, a decrease in pressure from 10 atm to 1 atm (normal pressure) should lead to an increase in the melting point of substance X.

Conclude the prediction

Based on our analysis, we can predict that the normal melting point of substance X at 1 atm will be greater than 225℃. The reason for this is that substance X contracts upon melting, and a decrease in pressure will lead to an increase in the melting point.

Key concepts

Melting Point

The melting point is the specific temperature at which a solid changes into a liquid. It's a crucial property for any material because it defines the boundary where a solid can transition into its liquid form.
For our fictional substance, X, its melting point at a certain pressure tells us how it will behave under those conditions.
When analyzing melting points, it is essential to consider the relationship between melting point and surrounding pressure, due to the influence this can have on the phase transition. In general, substances that expand when melting (solid density higher than liquid) will have a higher melting point with increased pressure. Conversely, if the substance contracts (solid density lower than liquid density upon melting), as with substance X, the direction is the opposite.

Density

Density plays a vital role in understanding phase changes, as it is the measure of mass per unit volume of a substance.
For substance X, the density is different in both solid and liquid states, providing insight into how the substance behaves at its melting point. With the solid phase having a density of 2.67 g/cm³ and the liquid phase having a higher density of 2.78 g/cm³, we can deduce that X contracts upon melting.
This contraction indicates that under higher pressures, the substance prefers to remain in a phase with higher density, impacting its melting characteristics. Understanding density differences helps in predicting how the material reacts during transitions between different states.

Pressure Effect on Phase Transition

Pressure profoundly affects how a material transitions between different phases. The Clausius-Clapeyron equation provides a framework to understand this. It predicts how changes in pressure will influence the temperature at which a phase transition occurs, like melting.
For substance X, which contracts upon melting (higher liquid density), reducing the pressure means its melting point will increase. This is because lower pressure reduces the force keeping the molecules close, making it easier for the substance to stay in the more stable, higher density liquid state.
Thus, as pressure decreases from 10 atm to 1 atm, we predict the normal melting point of X will rise above 225°C, emphasizing how closely pressure and density interrelate in determining phase changes.