Hydrogen cyanide, hcn, is a poisonous gas. the lethal dose is approximately 300. mg hcn per kilogram of air when inhaled. the density of air at 26 ∘c is 0.00118 g/cm3. part a calculate the amount of hcn that gives the lethal dose in a small laboratory room measuring 12.0 ft×15.0 ft×9.60ft.

Given:

Lethal dose of HCN = 300 mg/kg of air

Density of air at 26 C = 0.00118 g/cm3

Dimension of the room = 12 * 15 *9.6 ft

To determine:

The dose of HCN in the given conditions

Explanation:

Volume of air  = volume of the room = 12*15*9.6 ft = 1728 ft³

Now, 1 ft³ = 28317 cm³

therefore the calculated volume of air = 1728*28317 = 48.93*10⁶ cm³

Density of air = 0.00118 g/cm3

Mass of air = volume * density = 0.00118 g.cm⁻³*48.93*10⁶ cm³

                  =5.77*10⁴ g = 57.7 kg

Since the lethal dose of HCN = 300 mg per kg of air

Then for 57.7 kg of air the lethal dose of HCN = 300 * 57.7 = 17310 mg

Ans: The amount of HCN under the given conditions is 17310 mg or 17.3 g