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Yes, it depends on the units that the given heat capacity is in. For example, if you're given the molar heat capacity, you should be using moles. On the other hand, if you're given the specific heat capacity, you should be using grams. Looking at the units is your best bet in determining whether you should be working with grams or moles.
It depends on the units of the heat capacity equation. I believe that only the equation for specific heat uses grams though, so that is a good starting place for trying to work out or memorize the others.
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