Chemistry

Chemistry

Problem

Mercury diffusion pumps may be used in the laboratory to produce a high vacuum. Cold traps are generally placed between the pump and the system to be evacuated. These cause condensation of mercury vapours and prevent mercury from diffusing back into the system. The minimum pressure of mercury that can exist in the system is the vapour pressure of mercury at the temperature of cold trap. Calculate the number of mercury atom per unit volume in a cold trap at −120∘C-120^\circ\text{C} . The vapour pressure of mercury at this temperature is 10−1610^{-16} torr.
Intuitive explanation

This problem asks you to find the number density of mercury atoms in equilibrium with its vapor at extremely low pressure and temperature. The key insight is that even at such a low vapor pressure, mercury atoms still behave as an ideal gas—the ideal gas law PV=NkTPV = NkT relates pressure directly to the number of particles per unit volume. Convert the pressure to SI units and the temperature to Kelvin, then rearrange to find N/V=P/(kT)N/V = P/(kT), where kk is Boltzmann's constant.

Intuitive explanation

This problem asks you to find the number density of mercury atoms in equilibrium with its vapor at extremely low pressure and temperature. The key insight is that even at such a low vapor pressure, mercury atoms still behave as an ideal gas—the ideal gas law PV=NkTPV = NkT relates pressure directly to the number of particles per unit volume. Convert the pressure to SI units and the temperature to Kelvin, then rearrange to find N/V=P/(kT)N/V = P/(kT), where kk is Boltzmann's constant.

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