The total number of intensive properties from the following is __________
Volume, Molar heat capacity, Molarity, E^θ cell, Gibbs free energy change, Molar mass, Mole

Solution

Chemistry ma’am · 3 steps

Ask one question of each property: if I double the amount of substance, does it double too?

1. The test. An intensive property does not depend on how much substance you have. An extensive property grows with the amount. A ratio of two extensive properties, like anything "per mole" or "per litre", is intensive.

   Property	Doubles with amount?	Type
   Volume	Yes	extensive
   Molar heat capacity	No, it is heat capacity per mole	intensive
   Molarity	No, it is moles per litre	intensive
   E°_(cell)	No, a bigger cell gives the same voltage	intensive
   Gibbs free energy change Δ G	Yes, Δ G = -nFE grows with n	extensive
   Molar mass	No, it is mass per mole	intensive
   Mole	Yes, it is the amount itself	extensive

2. Cell potential vs ΔG. Doubling a reaction doubles n and doubles Δ G, but E°_(cell) = -Δ G / nF stays the same. That is why one is extensive and the other intensive.
3. So. The intensive ones are molar heat capacity, molarity, E°_(cell) and molar mass, which makes 4.

The common slip: 5. Treating Δ G as intensive, like E°_(cell), gives 5. Δ G scales with the moles reacting, so it is extensive.

The idea to keep. Anything written "per mole" or "per volume" is intensive. Energies like Δ G, Δ H and Δ S are extensive, but the cell potential E is intensive.

Answer from the NTA final answer key. Solution by PrepWiser.