Understanding Disorder When Mixing Gases

The question asks about the degree of disorder when two gases are mixed. In thermodynamics, the degree of disorder or randomness of a system is measured by a property called entropy.

Entropy and Disorder

• Entropy is a measure of the number of possible arrangements of particles in a system.
• A higher number of arrangements means a higher degree of disorder or randomness, and thus higher entropy.

Mixing Two Different Gases

Consider two different gases, Gas A and Gas B, initially separated in two compartments. In this separated state, the molecules of Gas A are confined to one compartment, and the molecules of Gas B are confined to the other. There is a specific arrangement for the molecules.

When the two gases are mixed (e.g., by removing a partition), the molecules of Gas A and Gas B are free to occupy the entire combined volume. Now, a molecule of Gas A can be anywhere in the total volume, and similarly for a molecule of Gas B. There are many more possible positions and arrangements for the molecules when they are mixed compared to when they were separated.

Effect of Mixing on Disorder

Because the molecules have a larger space to move and intermingle when the gases are mixed, the number of possible microstates (arrangements) increases significantly. This increase in possible arrangements directly leads to an increase in the degree of disorder or entropy of the system.

Think of it like having red balls in one box and blue balls in another. When you mix them into a single larger box, there are many more ways the red and blue balls can be arranged together compared to when they were strictly separated. This is an increase in disorder.

Analyzing the Options

• less than that of individual gases: This is incorrect because mixing increases the space and possible arrangements for the molecules.
• higher than that of individual gases: This is correct because mixing allows molecules to explore a larger combined volume and intermingle, increasing randomness and disorder.
• unpredictable compared to individual gases: While the exact value depends on the specific gases and conditions, the trend for mixing different gases is a predictable increase in disorder.
• same as that of the individual gases: This is incorrect; the state of being mixed is inherently more disordered than the separated state.

Therefore, the degree of disorder when two gases are mixed is higher than that of individual gases.