Recently, there has been much concern about pollution in the home from radon, a
radioactive gas whose elemental molar mass is 222 g/mol. The Environmental
Protection Agency say that a level or radon of 3.6 X 10-11 giL of air is unhealthy. At
this level, how many moles of radon would there be in a living room whose volume is
2455 L? How many atoms is this?
Its suppose to be 3.6e-11g/L
what i ended up doing was got 3.6e-11g/L(2455L)= 8.838x10^-8g/2455L
then, 8.838x10^-8g converted them into moles then into atms. right or wrong?
Yes, that's right.
To determine the number of moles of radon in the living room, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (unknown)
V = volume of the gas (2455 L)
n = number of moles of the gas (unknown)
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (assuming room temperature, around 25°C)
First, let's convert the given radon level from giL to moles per liter (mol/L). We can use the molar mass of radon (222 g/mol) to convert between these units.
3.6 x 10^-11 giL * (1 mol / 222 g) * (1 L / 1 mol) = 1.62 x 10^-13 mol/L
Now, plug the values into the ideal gas law equation and solve for n (number of moles):
P * 2455 L = (1.62 x 10^-13 mol/L) * (0.0821 L·atm/(mol·K)) * (298 K)
P * 2455 L = 0.0401 atm
Solving for P:
P = 0.0401 atm / 2455 L
P ≈ 1.63 x 10^-5 atm/L
Now that we have the pressure (P) and volume (V), we can calculate the number of moles (n) using the ideal gas law equation:
n = PV / RT
n = (1.63 x 10^-5 atm/L) * 2455 L / (0.0821 L·atm/(mol·K)) * (298 K)
n ≈ 0.406 moles
To find the number of atoms in this amount of radon, we can use Avogadro's number (6.022 x 10^23 atoms/mol):
Number of atoms = n * Avogadro's number
Number of atoms = 0.406 moles * 6.022 x 10^23 atoms/mol
Number of atoms ≈ 2.45 x 10^23 atoms
Therefore, at a radon level of 3.6 x 10^-11 giL, there would be approximately 0.406 moles of radon in a living room with a volume of 2455 L, which corresponds to approximately 2.45 x 10^23 atoms of radon.