The EPA has proposed a new standard for microparticulates in air: for particles up to 2.5 µm in diameter, the maximum allowable amountin 50 µg/m^3. If your 9.3 ft x 9.25 ft x 11.3 ft dorm room just meets the new EPA standard, how many of these particles are in your room?

How many of these particles are in each 0.500 L breath you take?

(Assume the particles are spheres of 2.5 µm diameter and made primarily of soot, a form of carbon with a density of 2.5 g/cm^3.)

One of my friends got this problem for homework and I was trying to help her out. If someone could tell me if these are the right steps that would be awesome. Just for the first problem.

1. Find the volume of one particle.

2. Multiply the Volume by the density

3. The answer of that would give you the mass of one particle. Convert from grams to micrograms.

4. 50 micrograms divided by the mass of one particle.

6. That answer tells you the amount of particles per cubic meter

7. Multiply the amount of particles per cubic cm by the volume of the room in meters cubed.

does that sound right or is there in easier way?