Question

It is easier to liquefy oxygen than hydrogen because (1) Oxygen has higher critical temperature and lower inversion temperature than hydrogen (2) Oxygen has lower critical temperature and higher inversion temperature than hydrogen (3) Oxygen has higher critical temperature and higher inversion temperature than hydrogen (4) The critical temperature and inversion temperature of oxygen is very low

Short answer

Option (3): Oxygen has higher critical temperature and higher inversion temperature than hydrogen.

Step-by-step solution

- Understanding Critical Temperature

Critical temperature is the highest temperature at which a gas can be liquefied by pressure alone. Above this temperature, no amount of pressure can turn the gas into a liquid.

- Understanding Inversion Temperature

Inversion temperature is the temperature at which the Joule-Thomson effect changes its sign. Above this temperature, gas heats up when allowed to expand without doing work, and below this temperature gas cools down during such expansion.

- Comparing Oxygen and Hydrogen

Oxygen has a higher critical temperature and a higher inversion temperature compared to hydrogen. This makes it easier to liquefy oxygen than hydrogen.

- Selecting the Correct Option

Based on the explanation, option (3) which states 'Oxygen has higher critical temperature and higher inversion temperature than hydrogen' is the correct answer.

Key concepts

Critical Temperature

Critical temperature is a key concept to understand when discussing the liquefaction of gases. The critical temperature of a gas is defined as the maximum temperature at which it can be liquefied by applying pressure alone. This is important because above the critical temperature, no amount of pressure will convert the gas into a liquid.
For example, oxygen has a critical temperature of 154.6 K, whereas hydrogen has a much lower critical temperature of 33.2 K.
This means that at room temperature, oxygen is much closer to its critical temperature than hydrogen, making it easier to liquefy.
In practical terms, gases with higher critical temperatures can be liquefied under more accessible conditions, which is an important factor in industrial and scientific applications.

Inversion Temperature

The inversion temperature is another important property to understand in the context of gas liquefaction. It is the temperature at which the Joule-Thomson effect changes sign.
Below the inversion temperature, a gas will cool down when it expands without performing work; above this temperature, the gas will heat up upon expanding.
For instance, oxygen has an inversion temperature of around 763 K, while hydrogen has a lower inversion temperature of approximately 202 K.
This means that oxygen will more effectively cool down when it expands below its inversion temperature, aiding in its liquefaction.
Therefore, the higher inversion temperature of oxygen compared to hydrogen also contributes to its easier liquefaction.

Joule-Thomson Effect

The Joule-Thomson effect is a temperature change that occurs in a gas when it expands without performing work, such as when it passes through a porous plug or valve. This effect is crucial in the process of gas liquefaction.
When a gas is below its inversion temperature, it will cool down as it expands, which is beneficial for the liquefaction process.
For example, if oxygen is allowed to expand below its inversion temperature, it cools down, making it easier to reach the temperature at which it can be liquefied.
Conversely, if the gas is above its inversion temperature, it heats up upon expansion, which can complicate the liquefaction process.
Hence, understanding and utilizing the Joule-Thomson effect is essential in the liquefaction of gases like oxygen and hydrogen.