Question

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

Short answer

Explain your reasoning.

Step-by-step solution

Define mass diffusivity

Mass diffusivity is a measure of how fast a substance (such as a solute) diffuses or spreads through another substance (such as a solvent), typically in units of square meters per second (m^2/s). It is dependent on factors like temperature, pressure, and the properties of the substances involved.

Explain the factors affecting mass diffusivity

The primary factors affecting mass diffusivity are: 1. Temperature: Higher temperatures lead to greater molecular movement, resulting in increased diffusion rates. 2. Pressure: Higher pressures generally reduce the diffusion rate because the molecules of the substances are forced closer together, making it more difficult for them to move. 3. Atomic size: Smaller atoms can move more easily between larger atoms, resulting in a higher diffusion rate. 4. Lattice structure: Different materials have different lattice structures, which can influence diffusion.

Consider the atomic size and lattice structures of copper and aluminum

In our case, copper and aluminum have different atomic sizes and lattice structures. Copper has an atomic size of 0.128 nm, while aluminum has an atomic size of 0.143 nm. Additionally, copper has a face-centered cubic (FCC) lattice structure, and aluminum has a similar but not identical FCC lattice structure.

Analyze how the differences in atomic size and lattice structures influence mass diffusivity

The differences in atomic size and lattice structures between copper and aluminum will affect their mass diffusivity. Since copper has a smaller atomic size, it is expected to have a higher diffusion rate when it is diffused in aluminum, which has a larger atomic size. However, when aluminum is diffused in copper, it should have a lower diffusion rate due to the larger atomic size. Furthermore, since the lattice structures of copper and aluminum are different, there will be differences in the pathways available for diffusion, which would also result in differences in mass diffusivity between the two cases.

Conclusion

In conclusion, due to the differences in atomic sizes and lattice structures of copper and aluminum, the mass diffusivity of copper in aluminum will not be equal to the mass diffusivity of aluminum in copper, even under the same temperature and pressure conditions. The differences in atomic size and lattice structures result in different diffusion rates and available pathways for diffusion; hence, the mass diffusivities in these two-component systems will differ.