Question

This is a Thermodynamics course

A commonly used unit for gas pressure is torr, where 1 atmosphere = 760 torr, and 1 atmosphere is 1.01 x 10⁵ Pascals, where a Pascal is Newtons/m². For a pure ideal gas at a very low pressure of 1 torr and a temperature T = 310 K, how many molecules would be present in 1 cubic centimeter? Show your work.

(Hint: Recall that PV = Nk_BT, where N is the number of molecules, and k_B is Boltzmann's constant. From this, you can find the quantity N/V, which is the desired answer, once converted to units of molecules/cm³.)

Answer 1

Answer – We are given, P = 1 torr, T = 310 K , volume = 1 cm³

We know formula

PV = N*kB*T

So, N/V = P / kB*T

We need to convert the pressure torr to N/m²

1 torr = 133.22 N/m²

N/V = 133.32 N.m^-2 / 1.380*10^-23 J.K^-1 * 310 K

       = 3.12*10²² molecules/m³

        = 3.12*10²² molecules /m³ * m³ /1.0*10⁶ cm³

        = 3.12*10¹⁶ molecules/cm³

So, the molecules would be present in 1 cubic centimeter is 3.12*10¹⁶ molecules/cm³