Question

Part 1.) Using the Law of Dulong and Petit and the given heat capacities determine the molar masses for the following metals: Metal Specific heat J/ g⋅ oC Gold 0.1285 Silver 0.236 Magnesium 1.0419 Calculated Molar Mass of Silver in g/mol. (Put your answer in 4 significant figures) Part 2.) Using the Law of Dulong and Petit and the given heat capacities determine the molar masses for the following metals: Metal Specific heat J/ g⋅ oC Gold 0.129 Silver 0.2357 Magnesium 1.0413 Calculated Molar Mass of Gold in g/mol. (Put your answer in 4 significant figures) Part 3.) Using the Law of Dulong and Petit and the given heat capacities determine the molar masses for the following metals: Metal Specific heat J/ g⋅ oC Gold 0.1288 Silver 0.2361 Magnesium 1.0398 Calculated Molar Mass of Magnesium in g/mol. (Put your answer in 4 significant figures) Part 4.) Using the Law of Dulong and Petit and the given heat capacities determine the molar masses for the following non-metals: Non-metal Specific heat J/g⋅ oC Diamond (carbon) 0.6178 Oxygen 1.7043 Argon 1.1446 Calculated molar mass of Carbon in g/mol, (Put your answer in 4 significant figures)

Answer 1

Dulong petit law

Approximate atomic weight ( molar mass of monoatomic substance) = $\frac{6.4}{specific \:heat(cal/g^{o}c)}$

Part 1.

Given, specific heat of silver = 0.236 J/g^oc. = (0.236/4.184) = 0.0564 cal/g^oc

Then, atomic weight or molar mass of silver

= (6.4/0.0564)

= 113.4 g/mol.

Part 2.

Specific heat of gold = 0.129 J/g^oc = (0.129/4.184) = 0.0308 cal/g^oc.

Molar mass = (6.4/0.0308) = 207.8 g/mol.

Part 3.

Specific heat of Magnesium = 1.0398 J/g^oc = (1.0398/4.184) = 0.248 cal/g^oc

Molar mass of Magnesium = (6.4/0.248) = 25.81 g/mol.

Part 4.

Specific heat of carbon ( diamond) = 0.6178 J/g^oc = (0.6178/4.184) = 0.147 cal/g^oc.

Then.

Molar mass of carbon = (6.4/0.147) = 43.53 g/mol.

For Argon

Specific heat = (1.1446/4.184) = 0.274 cal/g^oc.

Molar mass of Argon = (6.4/0.274) = 23.35 g/mol.

For oxygen

Specific heat = (1.7043/4.184) = 0.407 Cal/g^oc.

Atomic mass of oxygen = ( 6.4/0.407) = 15.72 g/mol.

Then, molar mass of Oxygen = 15.72×2 = 31.44 g/mol.

Hence Dulong petit law is not valid for carbon and Argon.