Question

The density of a substance is greater in its solid state than in its liquid state. If the triple point in the phase diagram of the substance is below 1.0 atm, which will necessarily be at a lower temperature, the triple point or the normal melting point?

Short answer

The triple point will be at a lower temperature than the normal melting point.

Step-by-step solution

Understand the Properties of the Substance

The given substance is denser in its solid state than in its liquid state. In most substances, the solid phase is denser since the molecules are packed more closely together, indicating that the substance likely has a sloping line for its solid-liquid equilibrium on a phase diagram that slopes from top left to bottom right.

Analyze Triple Point Characteristics

The triple point is where all three states of matter (solid, liquid, and gas) coexist in equilibrium. The given triple point of the substance is below 1.0 atm. For substances with a downward sloping solid-liquid equilibrium line, the triple point will occur at lower temperatures and pressures than the normal melting point.

Compare Triple Point and Normal Melting Point

Since the substance has a higher density in the solid state and the triple point occurs below 1.0 atm, the triple point temperature must be lower than the normal melting point, which typically occurs at 1.0 atm.

Key concepts

Density of Substances

When exploring the properties of matter, one key aspect is understanding the density of substances. Density is defined as the mass per unit volume of a material and is represented by the formula \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume.

The density of a substance can vary based on its state (solid, liquid, or gas). Typically, the molecules in a solid are more closely packed together than in a liquid, resulting in a higher density for the solid phase. This concept is vital when analyzing phase diagrams, as it can explain why the solid-liquid equilibrium line has a particular slope.

For substances whose solid state is denser than their liquid state, the solid-liquid equilibrium line in a phase diagram slopes downward from left to right. This indicates that as pressure increases, the substance can transition from solid to liquid—a behavior observed in materials like water ice. When working with phase diagrams, remembering how density varies with phase changes is essential for accurate interpretation.

Triple Point

The triple point of a substance is a pivotal concept in thermodynamics and phase diagrams. It is the unique set of temperature and pressure conditions at which three phases of matter—solid, liquid, and gas—coexist in equilibrium. The triple point represents a singular point on the phase diagram, indicating the specific scenario where all three phases achieve balance.

Understanding the triple point is crucial because it provides insight into the inherent properties of a substance. At the triple point, the temperature and pressure are exactly right for the simultaneous presence of solid, liquid, and vaporous forms. For a substance where the triple point occurs below 1.0 atm pressure, it suggests that the conditions for the coexistence of all three phases happen at relatively low pressures, which can influence various scientific and engineering calculations.

In a phase diagram, the triple point is depicted as the intersection of the phase boundaries—where the solid, liquid, and gas regions meet. Its position can inform scientists about the necessary conditions for preserving a substance in a particular state, which is especially important in fields such as material science and meteorology.

Melting Point

The melting point is another fundamental concept closely examined in phase diagrams. It refers to the temperature at which a solid will begin to transition into a liquid. At the melting point, the solid and liquid phases of a substance are in equilibrium, meaning that the solid turns to liquid as fast as the liquid turns back into solid.

Moreover, the normal melting point corresponds to the melting point at one atmospheric pressure (1 atm). For many substances, normal melting points are a characteristic property and can be used to help identify or characterize a material. An understanding of melting points is also critical for a wide range of practical applications—from the design of materials that must withstand high temperatures to the culinary arts, where the melting point of fats and sugars is an important consideration.

When comparing the triple point and the normal melting point, the key difference lies in the fact that the normal melting point is fixed at a pressure of 1 atm, while the triple point is dependent on the substance's unique properties. This comparison is particularly useful in a phase diagram that depicts the conditions under which the different states of a substance are stable or in equilibrium.