A sample of air contains 38.5 ìg/m3 of beryl-
lium dust. How many atoms of beryllium are
present in a room with dimensions of 8 feet by
12.9 feet by 17.1 feet?
Answer in units of atoms
What unit is ig/m3?
i think its suppose to be the u symbol thing.
OK We'll assume 38.5 ug/m^3.
I would convert 8 feet,12.9 feet, and 17.1 feet to meters.
Then volume of room is length x width x height in m^3.
Total Be is 38.5 ug/m^3 x volume room = ug Be. That x 1E-6 converts ug Be to grams Be. Convert to mols (mol = grams/molar mass) and that x 6.02E23 = atoms Be.
To calculate the number of atoms of beryllium in the given sample of air, we need to follow these steps:
Step 1: Convert the dimensions of the room from feet to meters.
Step 2: Calculate the volume of the room in cubic meters.
Step 3: Convert the concentration from micrograms per cubic meter to grams per cubic meter.
Step 4: Calculate the mass of beryllium in the room.
Step 5: Calculate the number of moles of beryllium using its molar mass.
Step 6: Use Avogadro's number to convert moles of beryllium into atoms.
Let's calculate each step in detail:
Step 1: Convert the dimensions of the room from feet to meters.
1 foot = 0.3048 meters
So, the room dimensions are:
Length = 8 ft * 0.3048 m/ft = 2.4384 meters
Width = 12.9 ft * 0.3048 m/ft = 3.93252 meters
Height = 17.1 ft * 0.3048 m/ft = 5.21208 meters
Step 2: Calculate the volume of the room in cubic meters.
Volume = Length * Width * Height
Volume = 2.4384 m * 3.93252 m * 5.21208 m = 62.8626511 cubic meters
Step 3: Convert the concentration from micrograms per cubic meter to grams per cubic meter.
1 µg/m^3 = 1 * 10^-9 g/m^3
Beryllium concentration = 38.5 µg/m^3 = 38.5 * 10^-9 g/m^3
Step 4: Calculate the mass of beryllium in the room.
Mass = Concentration * Volume
Mass = 38.5 * 10^-9 g/m^3 * 62.8626511 m^3 = 2.4197909515 * 10^-6 grams
Step 5: Calculate the number of moles of beryllium using its molar mass.
The molar mass of beryllium is 9.0121831 grams/mole.
Number of moles = Mass / Molar mass
Number of moles = 2.4197909515 * 10^-6 grams / 9.0121831 grams/mole = 2.68371682 * 10^-7 moles
Step 6: Use Avogadro's number to convert moles of beryllium into atoms.
Avogadro's number = 6.022 * 10^23 atoms/mole
Number of atoms = Number of moles * Avogadro's number
Number of atoms = 2.68371682 * 10^-7 moles * 6.022 * 10^23 atoms/mole = 1.6169684 * 10^17 atoms
Therefore, there are approximately 1.6169684 * 10^17 atoms of beryllium in the given room.