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Based on different formula that can be used to compute the corrosion rate of metals, all of them involves weight loss, time, surface area, and density. I thought that the weight loss, surface are, and time should definitely be considered. But, I got confused about the relevance of the metal's density. How does that affects metal's corrosion?

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The reason you need density is to determine the mass lost by the system, assuming that the equations you are talking about look something like:

$$ m_{loss} = k\rho S_{area} t $$

Where $k$ is a constant defining how fast the corrosion is occurring in your system (in this case k would be in units of [length]/[time]), $\rho$ is the density of the material, $S_{area}$ is the surface area, and $t$ is time: the equation outputs the total mass of material lost.

In more comprehensive corrosion equations $k$ would be substituted with equations describing the system causing the corrosion and may be dependent on (not a complete list): pH, temperature, surface activity, liquid flow, concentration of certain chemicals, passive layer growth, ect.

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