Question

VI. Write out balanced chemical equations (complete with state symbols) for the following reactions and state whether DS is positive, negative, or approximately zero without looking up absolute molar entropies. Briefly explain your answer. (a) Gas phase methanol is completely combusted producing gas phase products. (b) Aqueous aluminum chloride reacts with aqueous strontium nitrate. (c) 1 mol of ethane at room temperature and pressure reacts with 7 mol of chlorine also at room temperature and pressure to produce gas phase carbon tetrachloride and gas phase hydrogen chloride gas.

Answer 1

The entropy of a system, S increases as the randomness of the system increases. Molecular motions are a measure of the randomness of a system.

The three states of matter are solid, liquid and gas. A solid has an organized structure with strong intermolecular forces and minimum molecular motions. Hence a solid must have the lowest entropy.

The liquid and gaseous states have weak intermolecular forces and increased molecular motions. Gas molecules move randomly and are held together by minimum intermolecular forces. Consequently, a gas is the most random or disorganized state of matter and will have the highest entropy.

a) Methanol (CH₃OH) in gas phase is combusted with O₂ to give CO₂ and H₂O.

2 CH₃OH (g) + 3 O₂ (g) -------> 2 CO₂ (g) + 4H₂O (g)

The number of moles of gaseous reactants is (2 + 3) = 5 while the number of moles of gaseous products is (2 + 4) = 6. The number of molecules is directly proportional to the number of moles; the higher the number of moles, the greater is the number of molecules. Since the product side has more gas molecules, the reaction proceeds with increase in randomness and hence the entropy change, ΔS is positive.

b) Aluminum chloride reacts with strontium nitrate to give aluminum nitrate and strontium chloride. Both are soluble in water.

2 AlCl₃ (aq) + 3 Sr(NO₃)₂ (aq) ------> 2 Al(NO₃)₃ (aq) + 3 SrCl₂ (aq)

The number of moles of reactants is (2 + 3) = 5 while the number of moles of products is (2 + 3) = 5. Since all the reactants and the products are in aqueous state and the number of moles remain unchanged, hence, the entropy change, ΔS remains unchanged.

c) The balanced chemical reaction is given as below.

C₂H₆ (g) + 7 Cl₂ (g) --------> 2 CCl₄ (g) + 6 HCl (g)

The number of moles of gaseous reactants is (2 + 7) = 9 while the number of moles of gaseous products is (2 + 6) = 8. Since the reaction proceeds with reduction in number of moles of gases, hence the randomness of the system decreases and consequently, the entropy change, ΔS is negative.