Question

At a given temperature and pressure, do you think the mass diffusivity of air in water vapor will be equal to the mass diffusivity of water vapor in air? Explain.

Short answer

Answer: No, the mass diffusivity of air in water vapor is not expected to be equal to the mass diffusivity of water vapor in air, even when both systems are under the same temperature and pressure. This is because the overall properties and molecular interactions in the two systems differ due to the different ratios of the components.

Step-by-step solution

Understand Mass Diffusivity

Mass diffusivity, also known as diffusion coefficient, is a measure of how easily one substance mixes with another due to the random motion of its particles. It is often represented by the letter D, and its units are m²/s. Factors affecting mass diffusivity include temperature, pressure, and the properties of the gases involved.

Analyze the given system

In this case, we are comparing the mass diffusivity of two different gas systems: air in water vapor (System A) and water vapor in air (System B). Both systems are maintained at the same temperature and pressure.

Understand the factors involved in diffusivity

The diffusivity of a gas system is generally a function of the physical properties of the gas molecules, such as molecular size, shape, and weight, as well as the interaction between the gas molecules. Other factors, such as temperature and pressure, also influence diffusivity.

Compare the systems in question

In both System A and System B, the gases involved are the same - air and water vapor. However, the ratio of air to water vapor differs between the two systems. In System A, the majority of the gas present is water vapor, so the diffusivity of air in water vapor will be mostly influenced by the properties of water vapor. In System B, the majority of the gas is air, so the diffusivity of water vapor in air will be mostly influenced by the properties of air.

Conclude whether mass diffusivity is equal in both systems

Because the ratios of air and water vapor are different in the two systems, the overall properties of the systems are not identical, even though both have the same temperature and pressure. The effects of molecular size, shape, and weight, as well as the interaction between molecules, will not be identical in the two systems. As a result, it's unlikely that the mass diffusivities of the two systems will be equal. In conclusion, the mass diffusivity of air in water vapor is not expected to be equal to the mass diffusivity of water vapor in air, even when both systems are under the same temperature and pressure. This is because the overall properties and molecular interactions in the two systems differ due to the different ratios of the components.