A 2.0 L flask holds nitrogen gas (molar mass 28 g/mol) at a density of 1.25 kg/m^3, and the molecules' rms speed is 511 m/s. (a) Compute the pressure from kinetic theory. (b) Check it against the ideal gas estimate. Solution: (a) P = (1/3) rho c_rms^2 = (1/3)(1.25)(511)^2 = (0.4167)(1.25)(261,121) = 136,000 Pa ~ 1.36 x 10^5 Pa. (b) n = rho V/M = (1.25)(0.002)/0.028 = 0.0893 mol; with T from (1/2)m c^2 = (3/2)kT giving T ~ 300 K, P = nRT/V = (0.0893)(8.31)(300)/0.002 = 111,300 Pa - same order; the difference is rounding in the given numbers, confirming consistency.