A sample of air contains 21.9ìg/m3 of beryllium dust. How many atoms of beryllium are present in a room with dimensions of 8 feet by 12.3 feet by 18.3 feet? Answer in units of atoms.
I would change feet to meters for all three dimensions, then L x W x H of the room (in meters) will give you the volume in cubic meters. volume x concn Be dust (the 21.9 something g/m^3) will give you grams Be dust. Divide by atomic mass to arrive at moles, then remember there are 6.022 x 10^23 atoms in a mole.
To find the number of atoms of beryllium present in the room, we first need to determine the volume of the room in meters cubed.
Given room dimensions:
Length = 8 feet
Width = 12.3 feet
Height = 18.3 feet
We convert these dimensions to meters by multiplying each value by 0.3048 (1 foot = 0.3048 meters).
Length = 8 feet * 0.3048 meters/foot = 2.4384 meters
Width = 12.3 feet * 0.3048 meters/foot = 3.7494 meters
Height = 18.3 feet * 0.3048 meters/foot = 5.5784 meters
Now, we can calculate the volume of the room in meters cubed by multiplying the length, width, and height:
Volume = Length * Width * Height = 2.4384 meters * 3.7494 meters * 5.5784 meters = 42.95159 meters cubed
Next, we need to convert the concentration of beryllium dust from µg/m3 (micrograms per cubic meter) to grams per cubic meter.
1 µg = 1 × 10^-9 grams (1 microgram = 1 times 10 to the power of negative 9 grams)
So, the concentration of beryllium dust in grams per cubic meter is:
Concentration = 21.9 µg/m3 * 1 × 10^-9 grams/µg = 21.9 × 10^-9 grams/m3
Now, we can calculate the mass of beryllium in the room by multiplying the concentration by the volume:
Mass = Concentration * Volume = (21.9 × 10^-9 grams/m3) * 42.95159 meters cubed
Now, let's convert the mass of beryllium to the number of atoms. To do this, we need to know the molar mass of beryllium, which is 9.01218 grams/mole.
Number of moles of beryllium = Mass of beryllium / Molar mass of beryllium
Number of moles of beryllium = (21.9 × 10^-9 grams / m3 * 42.95159 meters cubed) / 9.01218 grams/mole
Finally, we can calculate the number of atoms using Avogadro's number, which is 6.022 × 10^23 atoms/mole.
Number of atoms of beryllium = Number of moles of beryllium * Avogadro's number
Number of atoms of beryllium = (21.9 × 10^-9 grams / m3 * 42.95159 meters cubed) / 9.01218 grams/mole * 6.022 × 10^23 atoms/mole
Calculating this expression will give us the answer in units of atoms.