Given very low number of particles in a system (e.g. in the 100s), is there a way to accurately measure the number of particles in the system? Assume temperature, pressure and volume is constant and we are using state of the art pressure and temperature sensors. Is it possible to do it from observing the speed distribution of particles?
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This greatly depends on the volume of the box. While the ideal gas law given by John probably holds, for any macroscopic box (say, $V = 1\textrm{ m}^3$), $n = 100$ is close to a perfect vacuum (in fact, better than any vacuums we can achieve nowadays). Wikipedia mentions a minimum of $10^{-12} \textrm{ Torr}$ for the cold cathode method of pressure measurement. This is equivalent to $1.3\cdot10^{-12} \textrm{ hPa}$. However, using the ideal gas law for $V = 1\textrm{ m}^3$, $T = 300\textrm{ K}$ and $n = 100$ yields $p = 4\cdot 10^{-21}\textrm{ hPa}$, that is, 9 orders of magnitude less. I would therefore be very surprised if it were possible to measure the number of particles in this system correctly. However, the result will change if the volume or temperature changes. For example, for $V = 1 \textrm{ mm}^3$, we get $p = 4\cdot 10^{-12}\textrm{ hPa}$, which is at least in the same range as the number given by Wikipedia. |
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Yes, the number of moles of (ideal) gas is given by: $$ n = \frac{PV}{RT} $$ Then multiply by $6.023 \times 10^{23}$ to get the number of atoms. |
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