Ordinary constant is a real constant which is same in all time but arbitrary constant is not constant at all time intervals, especially we can see arbitrary constants in integrals.
For example the anti derivative of x+C is 1. Here we can replace C with any constant so C is arbitrary constant
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See this link.What_is_the_difference_between_ordinary_prism_and_constant_deviation_prism
A parameter is a variable which takes different values and, as it does, it affects the values of some other variable or variables.
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There is no difference between them they are same rate constant is another name of specific rate constant
the difference between a constant in a graph and a constant in a experiment is that when on a graph, the constant is the thing that changes, and in a experiment it is the part that stays the same.