30.4 kJ of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is 28.4 J K⁻¹ mol⁻¹ at 1 atm. The melting point of sodium chloride is _______________ K (Nearest Integer)

Solution

Chemistry ma’am · 4 steps

At the melting point solid and liquid are in equilibrium, so put ΔG = 0 and solve for T.

1. Equilibrium condition. At the melting point, solid and liquid NaCl coexist in equilibrium at 1 atm. That means Δ G = 0 for melting.

   Δ G = Δ H - TΔ S = 0 ⇒ T = (Δ H)/(Δ S)

2. Match the units. Δ H is in kJ but Δ S is in J, so convert first: Δ H = 30.4 kJ mol⁻¹ = 30400 J mol⁻¹.
3. Put in numbers. T = (30400 J mol⁻¹)/(28.4 J K⁻¹ mol⁻¹) = 1070.4 K.
4. So. The melting point of sodium chloride is about 1070 K.

The common slip: 1. Dividing 30.4 kJ by 28.4 J without converting kJ to J gives about 1 K, not 1070.

The idea to keep. At any phase-change temperature the two phases are in equilibrium, so Δ G = 0 and T = Δ H / Δ S. Always bring Δ H and Δ S to the same energy unit first.

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