You get invited to a party at a 1,200 sf apartment, where there are a total of 23 people. The apartment has ceilings that are 8 ft above the floor. Three people begin smoking 2 cigarettes per hour each. The air handler system has a make-up air ventilation rate of 600 cfm. Assume an overhead fan ensures the air is well-mixed. Eye irritation from formaldehyde can start at concentrations of 0.01 ppm, with irritation of the lungs at 5 ppm. Will the concentrations become high enough to cause eye irritation

concentration of air = 0.0000366 ppm is not sufficient to cause any eye irritation

Explanation:

Average amount of aldehyde generated by a cigarette = 1 mg = 10⁻⁶g

Room volume = Height * Base area

Room volume = 8ft * 1200 sq. ft = 9600 cubic feet

number of people in the room = 23

If 1 person smokes 2 cigarette in 1 hour,

23 people will smoke 23*2 cigarettes = 46 cigarettes in 1 hr

Mass of aldehyde generated by 1 cigarette = 10⁻⁶g

Mass of aldehyde generated by 46 cigarettes = 46 * 10⁻⁶g

Based on the law of mass conservation,

Mass of aldehyde coming in = mass of aldehyde going out = Rate of accumulation of aldehyde

Rate of accumulation of aldehyde in the steady state = 0

m*C*V = 0

m = 46 * 10⁻⁶g

C = concentration in the steady state

V = Volumetic flow of the fresh air

V = 600 ft³/min = 600 * 60

V = 36000 ft³/hr

Density = Mass/volume

Density = 46 * 10⁻⁶g / 36*10³

Density = 1.28 * 10⁻⁹ g/ft³

If the density of air is taken as 36 g/ft³

concentration = (1.28 * 10⁻⁹ g/ft³) / 36 g/ft³

concentration = 3.66 * 10⁻¹¹g/g

1*10⁻⁶g/g of air = 1ppm (part per million)

concentration of air = (3.66 * 10⁻¹¹) (/1*10⁻⁶)

concentration of air = 3.66 * 10⁻⁵ppm = 0.0000366 ppm

concentration of air = 0.0000366 ppm is not sufficient to cause any eye irritation