The mass of the spring will depend on the density of the material, the thickness of the wire from which the spring is wound, the diameter of the turns of the coil, the number of turns per meter of spring length and the overall length of the spring.
Since the mass and the spring constant have some factors in common, they will in general not be independent of each other, but the spring constant may not vary in any simple way with the mass of a spring.
More exactly, the spring constant will probably change for springs of different mass, made out of the same material. If the change in mass is due only to a longer spring, the spring constant will decrease. Long springs tend to be softer than short ones. If the change in mass is due only to thicker wire, the spring constant will increase. Springs made of fat material are stiffer than those made of thin material. If the change in mass is due to some combination of changed wire and changed length, we may not be able to say. It might even be possible to construct two springs of different mass with the same spring constant.
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