Problem 101 - General Chemistry

Question

Describe the behavior of carbon dioxide gas when compressed at the following temperatures: a. \(20^{\circ} \mathrm{C}\) b. \(-70^{\circ} \mathrm{C}\) c. \(40^{\circ} \mathrm{C}\) The triple point of carbon dioxide is \(-57^{\circ} \mathrm{C}\) and \(5.1 \mathrm{~atm}\), and the critical point is \(31^{\circ} \mathrm{C}\) and \(73 \mathrm{~atm}\).

Step-by-Step Solution

Answer

At 20°C, CO2 can become a liquid under enough pressure. At -70°C, CO2 is solid. At 40°C, CO2 is a supercritical fluid.

Step 1: Identify the Temperature Regime

For each temperature, determine whether it is above, below, or within the critical point and triple point regime.- At \(20^{\circ}\, \mathrm{C}\), the temperature is above the triple point and below the critical point.- At \(-70^{\circ}\, \mathrm{C}\), the temperature is below the triple point.- At \(40^{\circ}\, \mathrm{C}\), the temperature is above the critical point.

Step 2: Behavior of CO2 at 20°C

The temperature \(20^{\circ}\, \mathrm{C}\) is between the triple and critical points, meaning compression can transition the gas into a liquid state if the pressure is increased past 5.1 atm, where the gas becomes a liquid.

Step 3: Behavior of CO2 at -70°C

The temperature \(-70^{\circ}\, \mathrm{C}\) is below the triple point. At this temperature, CO2 will be in the solid state (dry ice) and any compression will primarily increase its density as a solid rather than convert it to a liquid.

Step 4: Behavior of CO2 at 40°C

At \(40^{\circ}\, \mathrm{C}\), the temperature is above the critical point of \(31^{\circ}\, \mathrm{C}\). This means CO2 becomes a supercritical fluid when compressed beyond 73 atm, without distinct phase separation.

Key Concepts

Triple Point

The triple point of a substance is an extraordinary condition where three phases—solid, liquid, and gas—exist in equilibrium. For carbon dioxide, this point is at -57°C and 5.1 atm. This means at these specific conditions, CO2 can coexist as a gas, liquid, and solid, all at the same time. Isn't that fascinating?
The reason the triple point is significant is that it defines the lowest pressure at which a liquid can exist. Below the triple point pressure, CO2 will not transition into a liquid state; instead, going from a solid to a gas or vice versa. For CO2, this is famously known as sublimation, where dry ice (solid CO2) transitions directly into a gas without passing through the liquid phase.
Understanding the triple point is important in processes that require precise control over phase changes, such as in the food industry for freeze-drying.

Critical Point

The critical point marks the end of the liquid-gas boundary. Beyond this point, a substance cannot exist as a liquid and gas distinctly. For carbon dioxide, the critical point is at 31°C and 73 atm. This means beyond 31°C, trying to distinguish between liquid CO2 and its gas form becomes impossible.
The critical point is crucial for understanding how gases and liquids can transition into new states. At this point, CO2 exhibits unique properties where it can no longer condense into a liquid by increasing the pressure alone. Instead, it forms a supercritical fluid, which shows characteristics of both gases and liquids. This unique state is beneficial in various industries, notably for CO2 extraction processes such as decaffeination of coffee.

Supercritical Fluid

Supercritical fluids are fascinating and useful states of matter where the gas and liquid phases no longer separate. Carbon dioxide becomes a supercritical fluid when it is at or above its critical temperature of 31°C and critical pressure of 73 atm. In this state, CO2 has the density of a liquid but moves through materials like a gas.
One of the most interesting features of supercritical CO2 is its ability to dissolve substances like a liquid, yet diffuse through materials like a gas. This trait makes it highly valuable for applications like extracting flavors or oils from substances without leaving harmful residues. It's a cleaner alternative to traditional solvents, which is why industries prefer it for processes like extracting flavors in the food industry or cleaning delicate equipment.

Phase Transition

Phase transitions refer to the transformation of matter from one state to another, such as from solid to liquid, liquid to gas, or directly from solid to gas (in sublimation). For carbon dioxide, the understanding of its phase transitions is vital when dealing with its storage and practical applications.
At temperatures and pressures below the triple point, CO2 transitions directly between solid and gas. At conditions above the triple point and below the critical point, it behaves typically, transitioning between gas and liquid. However, beyond the critical point, there's no distinct transition from liquid to gas—it goes directly into a supercritical state. This knowledge is key in industries like refrigeration, where maintaining CO2 in the desired phase is crucial for process efficiency.
The study of phase transitions ensures that scientists and engineers can predict how a substance behaves under different thermal and pressure conditions, allowing for more efficient design and use of materials.