# 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/ meter^{3} 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/cm^{3}). Volume of a sphere = 4/3 π r^{3}

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

also, i fill in the equation for volume: 4/3 π r^{3. First I will half 2.5 to get the radius from the diameter. 8.181}µmeter. I have the volume and density so i multiple. 1cm=1*10^{4}µmeter. I cube this. Am i going in the right direction please?

### The radius of your particles

The radius of your particles is 1.25 μm, so the volume of a particle is 8.181 μm^{3}. If you had the volume in cubic centimeters, (cm^{3}), 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} cm^{3}/1 μm^{3})

And there are 10^{6} μg in 1 g, so the mass of one particle is

(8.181μm^{3})(10^{-12}cm^{3}/1μm^{3})(2.5g/1cm^{3})(10^{6}μg/1g) = 2.045·10^{-5}μg

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/ meter^{3} 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/cm^{3}). Volume of a sphere = 4/3 π r^{3}

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

also, i fill in the equation for volume: 4/3 π r^{3. First I will half 2.5 to get the radius from the diameter. 8.181}µmeter. I have the volume and density so i multiple. 1cm=1*10^{4}µmeter. I cube this. Am i going in the right direction please?

### You were going in the right

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^{-2}m^{3}/ft^{3}) would be the conversion for volume units.

## I would convert the

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)

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