# Problem: Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 310 mg HCN per kilogram of air when inhaled.Calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring 13 ft 16 ft 8.0 ft.The density of air at 26°C^circ m C is 0.00118 g/cm3 m g/cm^3.

###### FREE Expert Solution

We’re asked to calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring 13 ft x 16 ft x 8.0 ft and given the lethal dose of HCN and density of air

Recall that density is the ratio of the mass and volume of an object:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume is given by:

$\overline{){\mathbf{V}}{\mathbf{=}}{\mathbf{l}}{\mathbf{×}}{\mathbf{w}}{\mathbf{×}}{\mathbf{h}}}$

where:

l = length, w = width, h = height

To solve for the amount of HCN (in mg), we need to do these steps:

Step 1: Calculate the volume of the small laboratory room

Step 2: Get the mass of air (inside the room) from its density and volume (from step 1)

Step 3:  Solve for the lethal amount of HCN in the air inside the room based on its lethal dose

###### Problem Details

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 310 mg HCN per kilogram of air when inhaled.

Calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring 13 ft 16 ft 8.0 ft.
The density of air at 26°C is 0.00118 g/cm3.