# Regarding units of water potential and chemical potential

If water potential is nothing but the chemical potential of a given solution, then why do their units differ?

If the unit for the latter is taken as 'Energy per molecule' (which makes sense to me mathematically), then why is the former measured is 'Pressure'(Pascal)?

According to German Wikipedia water potential is defined as

$$\psi := \frac{\mu - \mu_0}{\bar{V}},\tag{1}$$

where $$\mu_0$$ is the standard chemical potential (usually pure water at atmospheric pressure at a specified reference height), and $$\bar{V} \approx \pu{18 cm3 mol-1}$$ is the molar volume of pure liquid water.

This means that water potential $$\psi$$ is defined as energy $$E$$ per volume $$V$$, which is equivalent to pressure $$p$$ if you perform dimensional analysis:

$$[\psi] = \frac{[E]}{[V]} = \frac{\mathsf{L}^2·\mathsf{M}·\mathsf{T}^{−2}}{\mathsf{L}^3} = \mathsf{M}·\mathsf{L}^{−1}·\mathsf{T}^{−2} = [p]\tag{2}$$

Megapascal $$\pu{MPa}$$ is usually used as the unit of measurement; tensiometers are usually graded in hectopascals $$\pu{hPa}.$$

Chemical potential is a portion of water potential, but not all of it. Factors like gravity and bulk fluid properties also affect the water potential. Water potential is typically used for macroscopic quantities of water, so it is more natural to consider the amount of water by volume rather than the number of molecules. If you convert the number of molecules in the units of chemical potential to a corresponding volume, you will see that this is equivalent to energy per volume, which is pressure.