It’s not arbitrary, it’s the value of pH that we measure in pure water.
pH describes the concentration of hydrogen ions (H+) dissolved in a water solution. A solution with a pH of 1 will have about 0.1 gram of H+ per liter (note that number is written with 1 zero in it), a solution with a pH of 4 will have 0.0001 grams of H+ per liter (4 zeros), and pH of 11 corresponds to 0.00000000001 grams of H+ (11 zeros).
Water molecules (H2O) have two hydrogen atoms and one oxygen atom, and they sometimes spontaneously break up into H+ and OH-. In pure water, it so happens that at any given moment about 0.0000001 grams of hydrogen are in the form of loose H+ ions, so pure water has a pH of 7.
* A note for pedants: I’m sweeping a bunch of minor technical details involving activity, concentration, and atomic weight under the rug in the name of ELI5.
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