 Solution

Convert the molar mass to $0.0288\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ before substitution:The often-used environmental value near $-6.5\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$ is less steep because rising moist air can condense water vapor, releasing latent heat and offsetting some expansion cooling. A saturated parcel therefore follows a smaller-magnitude moist adiabatic lapse rate, which varies with temperature, pressure and water content. Real environmental profiles also reflect radiation, mixing and weather systems; $6.5\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$ is a representative profile value, not a universal parcel law.