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 must be at a lower temperature, the triple point or the normal melting point?

Short answer

The triple point must be at a lower temperature than the normal melting point because the substance has a greater density in solid state, and the triple point occurs below 1.0 atm.

Step-by-step solution

Understand the Definition of Triple Point

The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.

Compare Densities of Different States

If the density of a substance is greater in its solid state than in its liquid state, it means that as the pressure is increased at temperatures below the triple point, the solid form will be the more stable phase.

Analyze Effect of Pressure on Melting Point

When the pressure is below 1.0 atm, the melting point of the solid will be lower because the solid phase is more dense. If the solid were less dense than the liquid, the melting point would increase with a decrease in pressure.

Determine the Temperature Relationship

Since the triple point is a specific condition where all three phases exist, it will have a unique temperature and pressure. For most substances with higher solid density, if the triple point is below atmospheric pressure, the triple point temperature must be lower than the normal melting point at 1 atm.

Key concepts

Triple Point

The triple point of a substance is a unique combination of temperature and pressure where solid, liquid, and gas phases coexist in a state of thermodynamic equilibrium. Imagine a scenario where water can freeze, melt, and boil all at once. That's what happens at the triple point! It's like a magic moment in the phase diagram where all three phases shake hands and agree to be present together.

For a better understanding, visualize the phase diagram: it’s a graph plotting pressure against temperature. The triple point is marked by a singular dot where the boundaries of solid, liquid, and gas meet. It’s a fundamental concept in thermodynamics because it represents the condition under which a substance can exist in all three states equally. In the context of our exercise, if a substance's triple point is below 1.0 atm (atmospheric pressure), we know that this point would also be at a lower temperature than the one where the substance normally transitions from solid to liquid, or its melting point, at atmospheric pressure.

Density of Substances

Density is basically how much 'stuff' you can pack into a given volume. When we say a substance is more dense in its solid state than its liquid state, we mean its particles are more tightly packed together when it's frozen. Ice sinking in alcohol, unlike floating in water, is a classic example.

Understanding density variations across phases is vital not just in chemistry but in many real-world applications such as ice skating—yes, the ice melts a bit under the skates due to pressure, allowing for smoother gliding! In our exercise context, the solid phase being denser implies that it's favored over the liquid phase at pressures below the triple point.

Melting Point

Many of us are familiar with the term 'melting point,' which is the temperature at which a solid becomes a liquid. It's like when ice cream on a hot day turns from solid goodness to a sweet puddle. The melting point is pretty straightforward when you don't mess with the pressure too much—it's consistent.

However, with substances that have a denser solid state, the melting point can change with pressure. This ties back to our exercise because a substance with a denser solid state than its liquid state will have a lower melting point under lower pressures. This change is explained by the principles that govern how solid molecules interact under varying pressures.

Thermodynamic Equilibrium

Thermodynamic equilibrium is a big phrase for a simple idea: it's when a substance isn't in the mood for change anymore. This means energy such as temperature and pressure is all balanced out, and there's no net transfer happening. It's like when you settle into a comfortable spot on the couch, and you just don’t want to move!

In the context of our exercise, at the triple point, all three phases of the substance achieve this chill state, existing together without trying to turn completely into one phase or another. This concept is crucial for understanding the behavior of substances under different conditions, be it in nature or industrial processes.