Calculate the number of $\textrm{molecules/m}^3$ in an ideal gas at STP.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. P V equals the number of molecules times the Boltzmann constant times temperature. And we can solve for N over V, number of molecules per cubic meter by dividing both sides by V K and T. So, on the left side the V's cancel, we'll have P over K T. And on the right side we'll have N over V and then we'll switch the sides around. So, the number of molecules per cubic meter is pressure over Boltzmann constant times temperature. And we're told to assume standard temperature and pressure. So, we have 1.013 times 10 to the 5 pascals atmospheric pressure divided by 1.38 times 10 to the minus 23 joules per kelvin Boltzmann constant times 273 kelvin standard temperature. And that gives about 2.69 times 10 to the 25 molecules per cubic meter.