If the recently released activist advocates unrest tonight at the rally, no amount of placating will be able to prevent a riot.
If the recently released activist advocates unrest tonight at the rally, no number of placating will be able to prevent a riot.
If the recently released activist advocates unrest tonight at the rally, no amount of placating will be able to prevent a riot.
If the recently released activist advocates unrest tonight at the rally, no number of placating will be able to prevent a riot.
When talking about something uncountable, something for which we would ask "how much?" instead of "how many?" then we need to use "amount," not "number."