Question

How would we estimate the average distance between molecules at STP?

(e) Chemists often use the shorthand notation "STP' for standard temperature and pres- sure, or T = 273 K and P = 1.0 bar. What is the number density of an ideal gas at STP, nstp? Estimate the average distance between molecules at STP, in nanometers, and compare this to the size of a typical diatomic molecule (e.g., N2 or 02) of ~ 400 pm (1 pm = 10-12m).

Answer 1

@ Given, number density of an ideal gas. (ASTP) at STP. T= 273K, pel baro N> Avogadro's no. number density (MSTP) = = Total volume Now, for an ideal gas, v- NRT Inz 1 mol 1x0.08314243 R=0.082 litatumol/ = 0.082x 1.0132) lit. bur/milla = 22.68 lit = 0.0831 lit bar/mol/k = 22.68x10?m3 T2 273 k P= I bare number density (STP) = N / 6.023x 1023 22.68 x103 = 2.656x1019 Thus cach molecule occupies, 22.68x10 Yu = 6023x1023 -26 = 3.76x tom avarage distance between molecules at STP = √ 3.76x10-26) = 3-35x109 m non Inmz 10-9 m. = 3.35 nm Giren. For typical diatowic molecules (es. N2002) this value is ~400 pm = 0.4mm [1 pm 2 10-12m] : the determined value is large