Q.Calculate the average molecular kinetic energy

[!TLDR] Average KE per mole = (3/2)RT; scale to kmol, kg, and per molecule using molar mass and Avogadro's number. [!ANSWER] Per kmol: 4.986×10⁶ J. Per kg: 1.558×10⁵ J (s …

The average kinetic energy per mole of gas is E = (3/2)RT. At T = 127 ºC = 400 K, with R = 8.31 J mol⁻¹K⁻¹: E(per mole) = 1.5 × 8.31 × 400 = 4986 J/mol.

1. PER KMOL: since 1 kmol = 1000 mol, E(per kmol) = 4986 × 1000 = 4.986×10^6 J, matching the textbook's printed answer exactly.
2. PER KG: the molar mass of O2 is 32 g/mol = 0.032 kg/mol, so the number of moles in 1 kg is 1/0.032 = 31.25 mol. E(per kg) = 31.25 × 4986 = 155,812.5 J/kg ≈ 1.558×10^5 J/kg. Note: the textbook's own printed answer states this as '1.558×10² J', which appears to have lost several orders of magnitude in typesetting (consistent with other exponent/superscript corruption seen throughout this scanned chapter) -- the value computed directly and independently here, 1.558×10^5 J/kg, is the value consistent with both the per-kmol and per …

Compute average KE per mole as (3/2)RT, then scale to per-kmol (×1000), per-kg (÷ molar mass in kg), and …

For 'per kg', dividing by the molar mass in GRAMS instead of kilograms (or vice versa) -- this is exactly the kind of order-of-magnitude slip that appears …