Calculate the number of atoms and volume of 1 gallon of helium gas at stp.

Hello!

STP means standard temperature and pressure. Denote the temperature as `T` (in Kelvin) and the pressure as `P.` They may be different for different standards.

The formula we need is  `PV = nRT,` where `V` is the volume of a gas, `n` is the number of moles and `R` is the ideal gas constant, about `8.3 J/(mol*K).` The volume is also given, it is `1 gallon approx 3.8*10^(-3) m^3.`

From all this data we can find the quantity of helium in moles:  `n = (PV)/(RT).` The number of atoms in each mole is a constant called Avogadro's constant, `N_A approx6*10^(23) (mol)^(-1),` so the number of atoms is `n*N_A = (PV)/(RT)*N_A.`

Let `T = 273 K` and `P = 10^5 Pa,` then the number of atoms is about

`(10^5*3.8*10^(-3)*6*10^(23)) / (8.3*273) approx 0.01*10^(25) = 10^23.`

This is the answer.