A Maxwell–Boltzmann speed distribution for nitrogen gas is described verbally as…
CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
A Maxwell–Boltzmann speed distribution for nitrogen gas is described verbally as follows: at 300 K the curve peaks at 422 m s⁻¹ and is relatively narrow; at 600 K the peak shifts to 597 m s⁻¹ and the curve broadens noticeably, displaying a longer tail toward higher speeds.
(a) Explain qualitatively how the distribution of molecular speeds changes as the temperature doubles from 300 K to 600 K.
(b) Relate the changes in the speed distribution to changes in the number of accessible microstates for the gas. Based on this analysis, determine whether the molar entropy of nitrogen gas is greater at 600 K or at 300 K, and justify your answer.
(c) Discuss how the observed change in the speed distribution with temperature supports the general relationship between entropy and temperature for an ideal gas.