Define a mole of a substance - Leaving Cert Chemistry - Question b - 2005

Avogadro's law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules (or particles). This means that the number of particles in a given volume of gas is directly proportional to the volume itself, provided all other conditions remain constant.

To calculate the number of helium atoms in the balloon:

1. Determine the volume of helium in the balloon:

   • The mixture is 10% (v/v), which means that for every 100 litres of the mixture, there are 10 litres of helium.

   • For a 10-litre balloon:

     egin{align*} ext{Volume of helium} &= 10 ext{ litres} imes rac{10 ext{ cm}^3}{100 ext{ litres}}
     &= 1 ext{ litre}
     imes ext{(1 litre = 1000 cm}^3 ext{)}
     &= 1000 ext{ cm}^3 ext{ } ext{At room temperature and pressure (RTP), 1 mole occupies about 24.0 litres.}
     2. Calculate the number of moles of helium:

     • Using the ideal gas law, the volume of helium is ext{approximately } 1 ext{ litre}, which gives:
       ext{Number of moles of helium} = rac{1 ext{ litre}}{24 ext{ litres/mole}}
       = 0.04167 ext{ moles} \
     3. Calculate the number of atoms:
     • Using Avogadro's number:
       Number of atoms = Number of moles × Avogadro's number \
       = 0.04167 ext{ moles} imes 6.022 imes 10^{23} ext{ atoms/mole} \
       
       ext{Thus, the final calculation is:}
       Number of helium atoms ≈ 2.5 imes 10^{22} ext{ atoms.}