Which of the following choices would have a positive entropy change?

A. 4NO2 (g) + 2H2O (l) + O2 (g) - >4HNO3 (aq)

B. Fe2O3 (s) + 3C (s) - >2Fe (s) + 3CO (g)

C. 6CO2 (g) + 6H2O (g) - >C6H12O6 (s) + 6O2 (g)

D. CaO (s) + CO2 (g) - >CaCO3 (s)

The option B) Fe₂O₃ (s) + 3C (s) → 2Fe (s) + 3CO₂ (g), because the reactants are only solid units and the products contain gas molecules.

Explanation:

A positive entropy change means that the entropy of the products is greater than the entropy of the reactants.

Entropy in a measure of the radomness or disorder of the system.

Let's see every reaction:

A) 4NO₂ (g) + 2 H₂O (l) + O₂ (g) → 4 HNO₃ (aq)

Since 5 molecules of a gas (high disorder) combines with 2 molecules of liquid to produce 4 units of aqueous HNO₃ you may expect that the product is more ordered than the reactants, which means that the change in entropy is negative (the entropy decreases).

B) Fe₂O₃ (s) + 3C (s) → 2Fe (s) + 3CO₂ (g)

The left side (reactants) show only solid substances which is a highly ordered arrangement while the right side (products) show the formation a solid (ordered arrangement) and a gas (highly disoredered arrangement), so you can predict the increase of the system entropy, i. e. a positive entropy change.

The equation C) shows the combination of 12 gas molecules to produce 1 solid and 6 gas molecules, so you can expect that the entropy will decrease, i. e. a negative entropy change.

For equation D) the products include solid and gas reactants while the product is just one unit of solid substance, letting you to predict a negative entropy change.