A sample of air contains 12.8 µg/m3

of beryllium
dust. How many atoms of beryllium are
present in a room with dimensions of 8 feet by
13 feet by 15.1 feet?
Answer in units of atoms

Change feet to meters.

Find volume in m^3. length x width x height = ? m^3

12.8 ug/m^3 x ? m^3 from above = total ug Be.
Convert ug Be to g Be and convert that to mols Be. mols Be = grams Be/atomic mass Be.

Then there are 6.022E23 atoms in 1 mol Be.
Post your work if you get stuck.

To calculate the number of atoms of beryllium in the given room, we need to follow these steps:

Step 1: Determine the volume of the room.
The volume of the room is obtained by multiplying its dimensions.

Volume = Length × Width × Height
Volume = 8 ft × 13 ft × 15.1 ft

Step 2: Convert the volume from cubic feet to cubic meters.
Since the concentration of beryllium dust is given in micrograms per cubic meter, we need to convert the room volume to cubic meters for proper calculation.

1 cubic foot (ft^3) = 0.0283168466 cubic meters (m^3)
Volume (m^3) = Volume (ft^3) × 0.0283168466

Step 3: Multiply the volume by the concentration of beryllium dust to obtain the mass of beryllium in the room.
Since we are given the concentration of beryllium dust as 12.8 µg/m^3, we can directly multiply it by the volume to get the mass.

Mass (µg) = Volume (m^3) × Concentration (µg/m^3)

Step 4: Convert the mass of beryllium to grams.
To ensure consistent units, we should convert the mass from micrograms to grams.

Mass (g) = Mass (µg) × 10^(-6)

Step 5: Calculate the number of moles of beryllium.
Using the atomic mass of beryllium (9.012 g/mol), we can convert the mass to moles.

Moles = Mass (g) / Atomic Mass (g/mol)

Step 6: Convert moles to atoms.
Finally, to determine the number of atoms, we need to multiply moles by Avogadro's number (6.022 x 10^23 atoms/mol).

Number of atoms = Moles × Avogadro's number

Let's calculate the number of atoms of beryllium in the given room:

Step 1: Volume = 8 ft × 13 ft × 15.1 ft
Volume = 1568 ft^3

Step 2: Volume (m^3) = 1568 ft^3 × 0.0283168466
Volume (m^3) ≈ 44.3808 m^3

Step 3: Mass (µg) ≈ 44.3808 m^3 × 12.8 µg/m^3
Mass (µg) ≈ 567.5456 µg

Step 4: Mass (g) = 567.5456 µg × 10^(-6)
Mass (g) ≈ 0.0005675456 g

Step 5: Moles = 0.0005675456 g / 9.012 g/mol
Moles ≈ 6.2982993 x 10^(-5) mol

Step 6: Number of atoms = 6.2982993 x 10^(-5) mol × 6.022 x 10^23 atoms/mol
Number of atoms ≈ 3.7912319 x 10^18 atoms

Therefore, there are approximately 3.7912319 x 10^18 atoms of beryllium in the given room.