Defining the Critical Temperature of Carbon Dioxide ($CO_2$)

The question centers on the critical temperature of carbon dioxide ($CO_2$). This is a fundamental concept in thermodynamics and chemistry, especially relevant when discussing states of matter and phase transitions.

What is Critical Temperature?

Every substance has a unique critical temperature ($T_c$). This temperature represents the highest possible temperature at which a gas can be converted into a liquid. If the temperature of a substance is increased beyond its critical temperature, it cannot be turned into a liquid, even if immense pressure is applied. Instead, the substance enters a unique state known as a supercritical fluid.

A supercritical fluid exhibits properties of both liquids and gases. It has a density similar to liquids (allowing it to dissolve substances) and a viscosity similar to gases (allowing it to penetrate porous materials easily).

Critical Temperature for Carbon Dioxide ($CO_2$)

The question specifically asks for the critical temperature of carbon dioxide ($CO_2$), noting its use as a supercritical fluid in industries. This specific value is a well-established physical property.

The critical temperature for carbon dioxide ($CO_2$) is approximately:

$ T_c \approx 31.1\text{^° C} $

At temperatures above $31.1\text{^° C}$, $CO_2$ cannot exist as a liquid. It will be a gas or, if sufficient pressure is applied, a supercritical fluid.

Analysis of Options

Let's examine the choices provided:

• $31.1\text{^° C}$: This value aligns precisely with the known critical temperature of $CO_2$. Above this point, $CO_2$ transitions into its supercritical state.
• $0\text{^° C}$: This temperature is significantly below the critical temperature. At $0\text{^° C}$, $CO_2$ can readily exist as a liquid under moderate pressure.
• $25\text{^° C}$: This is a common room temperature and is also below the critical temperature of $CO_2$. $CO_2$ can be liquefied at this temperature with sufficient pressure (around $57.3$ bar).
• $100\text{^° C}$: This temperature is well above the critical temperature of $CO_2$. At $100\text{^° C}$, $CO_2$ can only exist as a gas or a supercritical fluid; liquefaction is impossible regardless of pressure.

Conclusion

The defining characteristic of the critical temperature is that above it, a substance like carbon dioxide ($CO_2$) cannot be liquefied, even under high pressure. The established value for this threshold for $CO_2$ is $31.1\text{^° C}$.