Question

The gas which can be liquefied under high pressure and \(40^{\circ} \mathrm{C}\) is (a) nitrogen (b) hydrogen (c) oxygen (d) ammonia

Short answer

The gas that can be liquefied under high pressure and a temperature of \(40^{\circ} \mathrm{C}\) is ammonia.

Step-by-step solution

Understanding Liquefaction

Gas liquefaction occurs when a gas is cooled or compressed to a temperature below its critical temperature. The critical temperature of a gas is the temperature above and below which gas and liquid states coexist. The provided conditions are high pressure and a temperature of \(40^{\circ} \mathrm{C}\).

Determine the Critical Temperature of the Gases

Critical temperatures for selected gases are as follows - Nitrogen: -147℃, Oxygen: -118.4℃, Hydrogen: -240℃, Ammonia: 132.4℃. Looking at these values, it can be noticed that the given temperature, \(40^{\circ} \mathrm{C}\), is above the critical temperature of nitrogen, oxygen, and hydrogen, but below the critical temperature of ammonia.

Concluding Which Gas Can be Liquefied

Under the given conditions, ammonia is the only gas that can be liquefied because its critical temperature is higher than the provided temperature of \(40^{\circ} \mathrm{C}\). For a gas to be liquefied, the temperature must be lower than the gas's critical temperature which holds true for ammonia in these conditions.

Key concepts

Critical Temperature

Understanding the concept of critical temperature is essential when studying the properties of gases and their transition to liquids. Critical temperature is the maximum temperature at which a substance can exist as a liquid at any pressure. This means that no matter how much you increase the pressure on a gas above its critical temperature, it cannot be liquified.

Let's explore the conditions under which gases can be converted to liquids. For example, water has a critical temperature of about 374°C, above which it is impossible to liquefy, regardless of the pressure applied. In our exercise, we looked at various gases such as nitrogen, oxygen, hydrogen, and ammonia. Each of these gases has its own unique critical temperature, below which they can potentially be converted to a liquid state when subjected to high pressure.

It's fascinating to note that the critical temperature provides insight into intermolecular forces within a substance. Substances with high critical temperatures have strong intermolecular forces, making them easier to liquefy. Conversely, gases with low critical temperatures, like hydrogen, have weak intermolecular forces and exhibit significant resistance to liquefaction. Understanding this principle helps us realize why under a specific condition as mentioned in the exercise, ammonia—with a comparatively higher critical temperature—can be liquefied at 40°C.

Phase States of Matter

The different states of matter—solid, liquid, gas, and plasma—are determined by the energy level of the particles within a substance. The phase of a substance can change through processes such as melting, evaporation, condensation, or sublimation, depending on temperature and pressure conditions.

For gases, the transition to a liquid state, known as condensation, occurs when the gas is cooled or compressed to below its critical temperature, as illustrated in our exercise with ammonia. Gases have particles that are widely spaced, and they move freely at high speeds. When you cool or compress a gas, the particles slow down and come closer together, paving the way for condensation to take place.

Under the right conditions, a substance can move directly between the solid and gas phases, or become supercritical fluid, where it doesn't behave distinctly like a liquid or a gas. This myriad of possibilities defies the simplification of the states of matter, but for educational purposes, understanding the basic phases and their transformations is a key step in grasping the physical behavior of substances.

Pressure and Gases

The relationship between pressure and gases is described by the gas laws, which are a set of rules that predict how a gas will react to changes in pressure, temperature, and volume.

When you apply pressure to a gas, you effectively force the particles closer together. At the same time, if the temperature is below the critical point, this pressure can induce a phase transition from gas to liquid. This is why many gases are stored as liquids in high-pressure containers. The efficiency of liquefaction depends on the gas's critical temperature and the ambient temperature. If the ambient temperature is higher than the gas's critical temperature, like with hydrogen at 40°C, increasing the pressure alone will not be sufficient to liquefy the gas.

Understanding the delicate balance of pressure and temperature is crucial for applications ranging from industrial gas storage and transport to the cooling systems within our homes. As seen in the exercise, by manipulating these conditions, we can successfully liquefy certain gases for various uses, once again demonstrating the profound impact of physical principles on practical technology.