# Show that the volume of 1.23 x 10^22 atoms of helium at standard laboratory conditions is equal to 0.49L.

justaguide | Certified Educator

Like the standard temperature and pressure set by the IUPAC, the standard laboratory condition (SLC) refers to the standard temperature and pressure values in a laboratory. The temperature and pressure is does not have a uniform value for all countries. In the US, the temperature at SLC is 25 degree Celsius and the pressure is one atmosphere; at this temperature and pressure the volume of one mole of a gas is equal to 24.5 liters.

One mole of a gas has 6.023*10^23 particles.

1.23*10^22 atoms of helium are equivalent to 1.23*10^22/6.023*10^23 mole = 0.0204 moles.

At SLC one mole of a gas occupies 24.5 l, 0.0204 mole of a gas occupies 0.0204*24.5 = 0.5 l.

shekmodi | Student

At SLC,
Temperature is 25 Celcius (298 K) and Pressure is 1atm

Gas Constant (R) = 0.082 L atm K−1 mol−1

Also, number of moles (n) = Total atoms/Avagadro number

= 1.23 * 10^22 / 6.022*10^23

n  = 0.02042 mol

Now using the formula,

PV=NRT

1*V = 0.02042*0.082*298

V= 0.49898 L