WikiPremed Chem Question

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TheRealAngeleno

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Hey guys I came across this question and I was wondering if someone could please provide another answer explanation because I just can't conceptualize the provided the answer. Thanks a lot!

http://www.wikipremed.com/01physicscards.php?card=506

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They've given you molar heat capacity, but they ask for specific heat. Specific heat is similar to molar heat capacity, but is the heat capacity per gram, not per mole. Note the unit of specific heat is J/(g*C), whereas they give you J/(mol*C). So all you need to do is convert per mole to per gram. Divide each molar heat capacity by the atomic weight, pick the lowest result, and you have your answer (Pb). Also note that because all the molar heat capacities of similar, you're looking to divide by the biggest number. You can pick out Pb as the largest atomic weight without doing any math.
 
They've given you molar heat capacity, but they ask for specific heat. Specific heat is similar to molar heat capacity, but is the heat capacity per gram, not per mole. Note the unit of specific heat is J/(g*C), whereas they give you J/(mol*C). So all you need to do is convert per mole to per gram. Divide each molar heat capacity by the atomic weight, pick the lowest result, and you have your answer (Pb). Also note that because all the molar heat capacities of similar, you're looking to divide by the biggest number. You can pick out Pb as the largest atomic weight without doing any math.

Ah thanks a lot!
 
Although the chemistry of solid metals isn't so heavy on the MCAT, I come back to the rule of Dulong and Petit in the videos and questions at WikiPremed, that metals, regardless of atomic weight, have approximately the same molar heat capacity. I think it's a good rule to help you distinguish specific heat and molar heat capacity in the basic sense for problem solving, and in a more advanced sense, in that the relationship between temperature change and heat flow fundamentally has to do with the nature of the particles, their translational and rotational degrees of freedom, than their mass in themselves, which is why solid metals, where the metal atoms occupy lattice points in close packed crystalline solids, have approximately the same molar heat capacity. The metal atoms have roughly the same ways to move about, translation and vibration within the metallic electron sea shared between atoms, the same 'degrees of freedom' so the the heat flow is divided up among the modes of kinetic energy similarly. The most simple example of this you can see with ideal gases, where they all have the same molar heat capacity, 3/2 R, because the particles can move in the same ways, x,y, and z translational motion, but the specific heat may be different. This is a favorite MCAT distinction and crucial to understanding the kinetic theory of gasses. Cheers.
 
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