A sample of air contains 14.5 µg/m3
of beryllium dust. How many atoms of beryllium are
present in a room with dimensions of 11 feet
by 13.9 feet by 17.5 feet?
Answer in units of atoms.
To determine the number of beryllium atoms present in the given room, we will follow these steps:
Step 1: Calculate the volume of the room.
The volume of a room can be calculated by multiplying its length, width, and height. In this case, the room dimensions are given as 11 feet, 13.9 feet, and 17.5 feet. Therefore, the volume of the room would be:
Volume = (Length) × (Width) × (Height)
= 11 ft × 13.9 ft × 17.5 ft.
Step 2: Convert the volume to the appropriate unit for the calculation.
For convenience, let's convert the volume from cubic feet to cubic meters since the concentration of beryllium dust is given in µg/m3. Since 1 meter is approximately equal to 3.28 feet, we can convert the volume from cubic feet to cubic meters by dividing by (3.28)^3.
Step 3: Calculate the mass of beryllium present in the room.
Using the given concentration of beryllium dust as 14.5 µg/m3, we can multiply it by the converted volume of the room to obtain the mass of beryllium in µg.
Step 4: Convert the mass of beryllium to the number of atoms.
To convert the mass of beryllium from µg to grams, divide by 1,000,000 (since 1 μg is equal to 1 × 10^-6 grams). Then, using Avogadro's number (6.022 × 10^23 atoms/mole), convert the mass from grams to moles, and finally, convert moles to the number of atoms.
Following these steps, we can calculate the number of atoms of beryllium present in the room.