A sample of air contains 32.7 µg/m3
of beryllium dust. How many atoms of beryllium are
present in a room with dimensions of 8 feet by
13.6 feet by 15.6 feet?
Answer in units of atoms
To calculate the number of atoms of beryllium present in the room, we need to follow these steps:
Step 1: Calculate the volume of the room:
Given the room dimensions of 8 feet by 13.6 feet by 15.6 feet, the volume can be calculated by multiplying the three dimensions together:
Volume = 8 ft * 13.6 ft * 15.6 ft
Step 2: Convert the volume from cubic feet to cubic meters:
Since the concentration of beryllium dust is given in µg/m^3 (micrograms per cubic meter), we need to convert the volume to cubic meters:
Volume(m^3) = Volume(ft^3) * 0.0283168
Step 3: Calculate the mass of beryllium dust in the room:
Given the concentration of beryllium dust in µg/m^3, we can calculate the mass of beryllium dust using the following formula:
Mass = Concentration * Volume(m^3)
Step 4: Convert the mass from micrograms to grams:
Since the atomic mass unit (amu) is based on grams, we need to convert the mass of beryllium 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 calculate the number of moles using the following formula:
Moles = Mass(g) / Atomic Mass(g/mol)
Step 6: Calculate the number of atoms in the moles of beryllium:
Since one mole of any substance contains Avogadro's number of atoms (6.022 x 10^23 atoms/mol), we can calculate the number of atoms:
Number of Atoms = Moles * Avogadro's Number
Now we can plug in the given values and calculate the number of atoms of beryllium in the room.
Let's do the calculations:
Step 1: Volume of the room = 8 ft * 13.6 ft * 15.6 ft = 1705.088 ft^3
Step 2: Volume of the room in cubic meters = 1705.088 ft^3 * 0.0283168 = 48.3157 m^3
Step 3: Mass of beryllium dust in the room = 32.7 µg/m^3 * 48.3157 m^3 = 1580.1794 µg
Step 4: Mass of beryllium dust in the room in grams = 1580.1794 µg * 10^(-6) = 0.0015801794 g
Step 5: Number of moles of beryllium = 0.0015801794 g / 9.012 g/mol ≈ 0.000175392 moles
Step 6: Number of atoms of beryllium = 0.000175392 moles * 6.022 x 10^23 atoms/mol ≈ 1.0555 x 10^20 atoms
Therefore, there are approximately 1.0555 x 10^20 atoms of beryllium present in the given room.
To find the number of atoms of beryllium present in the room, we need to convert the volume of the room into cubic meters and then calculate the number of moles of beryllium in the given mass.
First, let's convert the room dimensions from feet to meters. We know that 1 foot is equal to 0.3048 meters.
Length of the room: 8 feet * 0.3048 meters/foot = 2.4384 meters
Width of the room: 13.6 feet * 0.3048 meters/foot = 4.14528 meters
Height of the room: 15.6 feet * 0.3048 meters/foot = 4.75584 meters
Now, let's calculate the volume of the room:
Volume of the room = Length * Width * Height
= 2.4384 meters * 4.14528 meters * 4.75584 meters
= 49.5037820768 cubic meters (approximately 49.5 cubic meters)
Next, we need to determine the number of moles of beryllium by using the given mass of 32.7 µg/m3. But before that, we need to convert µg to grams.
1 µg is equal to 1 × 10^-9 grams.
Mass of beryllium in the room = 32.7 µg/m3 * 49.5 cubic meters
= 1.61715 grams
Now, let's calculate the number of moles of beryllium:
Atomic mass of beryllium = 9.012 g/mol (approximately)
Number of moles of beryllium = Mass of beryllium / Atomic mass of beryllium
= 1.61715 grams / 9.012 g/mol
= 0.1795 moles (approximately)
Finally, we can calculate the number of atoms of beryllium by multiplying the number of moles by Avogadro's number:
Number of atoms of beryllium = Number of moles * Avogadro's number
= 0.1795 moles * 6.022 × 10^23 atoms/mol
= 1.080749 × 10^23 atoms (approximately)
Therefore, there are approximately 1.08 × 10^23 atoms of beryllium present in the given room.
Compute the room volume in ft^3 and convert it to cubic meters.
8*13.6*15.6 = 1797 ft^3 = 50.9 m^3
With 32.7*10^-6 g per m^3, there are 1.66*10^-3 gram of Be dust in the room.
Convert that to moles using the atomic weight of Be (9.0 g/mol), and then use Avogadro's number for the number of atoms.