Why the PH scale has no unit?
pH has no unit because it's a it's a logarithmic scale, not a
measurement like grams or degrees.
The pH number directly relates mathematically to the actual
concentrations in solution. Concentration itself does have units,
but pH really only looks at the power (or exponent) of the
concentrations. And, for that reason the unit doesn't carry.
pH = - log [H30+] (mathematical definition)
= negative logarithm of the hydronium ion concentration.
What this means is that if a solution has a concentration of
10-7 M [H30+] or (0.0000001 moles per litre of the hydronium ion),
the negative log of this number = 7. Therefore the pH = 7.
But it's not 7 moles per litre or 7 moles or any other
transferable unit. It's just 7.
Hope that helps a little.