To calculate the mass we use the following formulas:
PV=nRT (1)
and
n = m / M (2)
where:
P - pressure (atm)
V - volume (L)
n - moles
R - gas constant = 0.082 (L × atm) / (mol × K)
T - temperature (°K) (25°C + 273 = 298°K)
m - mass (g)
M - molecular mass (g/mole)
Now we rewrite equation (1):
n = PV / RT
And replace n with m / M from equation (2):
m / M = PV / RT
m = (P × V × M) / (R ×T)
1 L of He will have a mass of:
m = (1 × 1 × 4) / (0.082 × 298) = 0.1637 g
1 L of Cl₂ will have a mass of:
m = (1 × 1 × 71) / (0.082 × 298) = 2.9055 g
1.0 L of air will contain 0.79 L of N₂ and 0.21 L of O₂
0.79 L of N₂ will have a mass of:
m = (1 × 0.79 × 28) / (0.082 × 298) = 0.9052 g
0.21 L of O₂ will have a mass of:
m = (1 × 0.21 × 32) / (0.082 × 298) = 0.2750 g
mass of air = mass of N₂ + mass of O₂
mass of air = 0.9052 + 0.2750 = 1.1802 g
A balloon filed with helium will rise because as you see 1 L of helium is lighter than 1 L of air.
Chlorine gas is dangerous because chlorine is very toxic for human life and more of that is heavier than the air so will diffuse very hard from the area where the leak appeared.
