Question

A substance has a triple point at a temperature of \(17^{\circ} \mathrm{C}\) and a pressure of 3.2 atmospheres. In what states can the substance exist on the surface of Earth at sea level (open to the atmosphere)?

Short answer

On the surface of Earth at sea level, the substance can exist as a liquid and a gas, and potentially as a solid if the temperature is sufficiently low (below 17 degrees Celsius). It will not exist in all three states simultaneously as it does at the triple point.

Step-by-step solution

Understand the concept of a triple point

The triple point of a substance is the specific temperature and pressure at which the three phases (solid, liquid, and gas) of that substance coexist in thermodynamic equilibrium. For the substance in question, this triple point occurs at a temperature of 17 degrees Celsius and a pressure of 3.2 atmospheres.

Compare Earth's atmospheric pressure at sea level to the triple point pressure

At sea level, the standard atmospheric pressure is approximately 1 atmosphere. To determine the states in which the substance can exist at sea level, we compare this pressure to the pressure at the substance's triple point, which is 3.2 atmospheres. Since sea level pressure is lower than the pressure required for the triple point, the substance will not be at its triple point at sea level.

Determine possible phases of the substance at sea level

Given that Earth's atmospheric pressure is less than the pressure at the substance's triple point, and assuming that the temperature is around or above 17 degrees Celsius, the substance could exist as both a liquid and a gas (if the ambient temperature is lower, it could also exist as a solid). However, it will not exist in all three states simultaneously, which is what occurs at the triple point.

Key concepts

Phase Transition

When a substance changes from one state of matter to another, such as from solid to liquid or liquid to gas, this process is known as a phase transition. These transitions occur when energy is added or removed from a system, commonly in the form of heat. For example, ice (solid water) melts into liquid water when it absorbs heat and water vaporizes into steam (gas) when heated further.

Each substance has specific temperatures and pressures at which these transitions occur under normal conditions. However, at the triple point, a unique set of conditions, a substance can simultaneously exist in all three states: solid, liquid, and gas. The exercise involving the triple point illustrates the specific conditions necessary for such coexistence. If the atmospheric pressure is lower than the pressure required for the triple point, as it is at sea level on Earth, the substance will not experience the triple point and will instead exist in only one or two phases, depending on the temperature.

Thermodynamic Equilibrium

Thermodynamic equilibrium refers to a state where a system's macroscopic properties such as temperature, pressure, and volume do not change over time. In the specific context of the triple point, equilibrium signifies a balance where the substance's solid, liquid, and gaseous phases coexist without any phase overtaking the others.

At the triple point, the rates of melting, freezing, vaporization, condensation, sublimation, and deposition are equal, so there's no net change in the amount of each phase. This is a fine balance that can only be achieved under the specific conditions of the triple point. The fact that our atmosphere at sea level has a pressure of around 1 atmosphere, which is less than the 3.2 atmospheres required for the triple point given in the exercise, means that the substance will not be in thermodynamic equilibrium with all three phases present.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of air in the Earth's atmosphere onto a surface. At sea level, this pressure averages about 1 atmosphere, which is approximately 101.325 kPa or 760 mmHg. This value can fluctuate based on altitude, weather conditions, and temperature.

The triple point of the mentioned substance occurs at a pressure of 3.2 atmospheres, significantly higher than the average atmospheric pressure at sea level. Thus, the lower atmospheric pressure affects the phase in which the substance can exist when exposed to the Earth's atmosphere. For the given substance to reach its triple point, a closed environment where the pressure could be increased to 3.2 atmospheres would be required. On the surface of the Earth, where the pressure is too low for the triple point to be achieved, the substance will typically transition between the solid, liquid, and gas phases depending on the ambient temperature and without the simultaneous presence of all three states.