Question

Can carbon monoxide \(\left(T_{c}=132.9 \mathrm{K} ; P_{c}=34.5 \mathrm{atm}\right)\) be liquefied at or above room temperature? Explain briefly.

Short answer

Carbon monoxide cannot be liquefied at or above room temperature.

Step-by-step solution

Identify the Critical Temperature

The critical temperature \(T_c\) of carbon monoxide is the temperature above which it cannot be liquefied, no matter how much pressure is applied. For carbon monoxide, this value is given as \(T_c = 132.9 \, \text{K}\).

Convert Room Temperature to Kelvin

Room temperature is typically around 25°C. To convert this to Kelvin, use the formula \(T_K = T_{°C} + 273.15\). Thus, \(T_K = 25 + 273.15 = 298.15 \, \text{K}\).

Compare Temperatures

Now, compare the critical temperature \(T_c = 132.9 \, \text{K}\) with the converted room temperature \(T_K = 298.15 \, \text{K}\). Since 298.15 K is greater than 132.9 K, this means room temperature is above the critical temperature.

Conclusion on Liquefaction at Room Temperature

Since the room temperature is above the critical temperature of carbon monoxide, it cannot be liquefied at or above room temperature regardless of the pressure applied. Therefore, carbon monoxide cannot be liquefied at or above room temperature.

Key concepts

Understanding Carbon Monoxide

Carbon monoxide (CO) is a colorless and odorless gas that is slightly less dense than air. It's a simple molecule composed of one carbon atom and one oxygen atom, connected by a triple bond. It's produced in various combustion processes, particularly when there is not enough oxygen to produce carbon dioxide (CO₂). Despite its simplicity, carbon monoxide is highly toxic to humans and animals when inhaled, as it interrupts the ability of blood to transport oxygen.
The critical temperature

• The critical temperature of a substance is the temperature above which it cannot be converted into a liquid state, irrespective of the pressure applied.
• For carbon monoxide, this critical temperature is 132.9 Kelvin.
• This means that above this temperature, no amount of pressure can liquefy the substance.

Liquefaction and Its Limitations

Liquefaction is the process of converting a gas into a liquid. This process can typically be achieved by either increasing the pressure or lowering the temperature of the gas. At the molecular level, this means the gas particles are brought closer together, overcoming their kinetic energy that keeps them apart.

For each gas, there's a critical temperature that defines its limit for being liquefied. As you probably recall, the critical temperature is the maximum temperature below which a gas can transition into a liquid with the application of pressure.

Limitations

• If a gas is above its critical temperature, like carbon monoxide at room temperature, it cannot be transformed into a liquid by pressure alone.
• This explains why CO cannot be liquefied in these conditions: room temperature exceeds its critical temperature of 132.9 Kelvin.

Kelvin Conversion Simplified

Temperature conversion can be confusing, but the Kelvin scale simplifies scientific calculations related to gases because it starts from absolute zero. Kelvin is a thermodynamic temperature scale used worldwide in science and engine design. It's useful because it aligns directly with the laws of thermodynamics, making it a natural choice for scientific work.
How to Convert Celsius to Kelvin

• Converting Celsius to Kelvin is straightforward: add 273.15 to the Celsius value.
• For example, room temperature is 25°C, which converts to 298.15 Kelvin.

Kelvin’s Benefits

• Using Kelvin avoids negative numbers when dealing with thermodynamic equations, simplifying many scientific calculations.
• It's particularly useful in situations involving gas laws and critical phenomena, such as the liquefaction of gases.