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Calculate the number of particles of gas in a room of known dimensions

Could someone please walk me through this problem please? Thank you.

Q: The new safety standard proposed by EPA for micro particles in air is for particles up to 2.5 µmeter in diameter, the maximum allowable amount is 50µgram/ meter3 air. If your 10.0ft x 8.25ft x 12.5ft dorm room just meets the new EPA standard, how many particles are in your room? ( Assume particles are spherical and are primarily soot which has a density of 2.5g/cm3). Volume of a sphere = 4/3 π r3

A: so i know i will multiply the ft's =1031.25ft^3

also, i fill in the equation for volume: 4/3 π r3. First I will half 2.5 to get the radius from the diameter. 8.181µmeter. I have the volume and density so i multiple. 1cm=1*104µmeter. I cube this. Am i going in the right direction please?

kingchemist Thu, 09/08/2011 - 07:32

I would convert the dimensions of the room to metres and find the volume of the room in m3. You can then find the mass of C in the room based on each m3 contain 50µg

Each particle of soot has a volume of 8,185µmeter3 so from the density you can find the mass of 1 soot particle. Then knowing the mass of soot in the room, you can find the number of particles (=mass of soot in room/mass of 1 particle)

Can't seem to find the change font size tool

nova Sat, 09/10/2011 - 12:39

okay so i found the volume which is 8.18micrometers. And then i divided 2.5g/cm^3 by 8.18micrometers. The answer i get is the density so do i divide the answer by 2.5g/cm^3 again to get the number of particles?

KMST Sat, 09/10/2011 - 15:25

The radius of your particles is 1.25 μm, so the volume of a particle is 8.181 μm3. If you had the volume in cubic centimeters, (cm3), you could just multiply by the density value you have (the mass of 1 cubic centimeter of soot) to get t he mass of one particle.

Since 1 cm = 10-2 m and 1 μm is 10-6 m, the conversion factor fo the measure of length is (10-4 cm/1 μm), and the conversion factor for measurements of volume is

(10-4 cm/1 μm)3 = (10-12 cm3/1 μm3)

And there are 106 μg in 1 g, so the mass of one particle is

(8.181μm3)(10-12cm3/1μm3)(2.5g/1cm3)(106μg/1g) = 2.045·10-5μg

Q: The new safety standard proposed by EPA for micro particles in air is for particles up to 2.5 µmeter in diameter, the maximum allowable amount is 50µgram/ meter3 air. If your 10.0ft x 8.25ft x 12.5ft dorm room just meets the new EPA standard, how many particles are in your room? ( Assume particles are spherical and are primarily soot which has a density of 2.5g/cm3). Volume of a sphere = 4/3 π r3

A: so i know i will multiply the ft's =1031.25ft^3

also, i fill in the equation for volume: 4/3 π r3. First I will half 2.5 to get the radius from the diameter. 8.181µmeter. I have the volume and density so i multiple. 1cm=1*104µmeter. I cube this. Am i going in the right direction please?

KMST Sat, 09/10/2011 - 15:37

You were going in the right direction. I tried to help and messed up, and now I do not find a way to edit my own post.

You will also need to convert cubic feet to cubic meters.

(0.3048m/1ft) is the conversion factor for measures of length

(0.3048m/1ft)3 = 2.8317·10-2m3/ft3) would be the conversion for volume units.